Electromagnetism laboratory workshop in physics. Electromagnetism. Laboratory works. What is impedance?

Ministry of Education and Science of the Russian Federation Federal State Budgetary Educational Institution of Higher Professional Education "Voronezh State Forestry Academy" PHYSICS LABORATORY PRACTICUM MAGNETISM VORONEZH 2014 2 UDC 537 F-50 Published by decision of the educational and methodological council of the FSBEI HPE "VGLTA" Biryukova I.P. Physics [Text]: lab. workshop Magnetism: I.P. Biryukova, V.N. Borodin, N.S. Kamalova, N.Yu. Evsikova, N.N. Matveev, V.V. Saushkin; Ministry of Education and Science of the Russian Federation, Federal State Budgetary Educational Institution of Higher Professional Education "VGLTA". – Voronezh, 2014. – 40 p. Executive editor Saushkin V.V. Reviewer: Ph.D. physics and mathematics Sciences, Associate Professor Department of Physics VSAU V.A. Beloglazov Provides the necessary theoretical information, a description and procedure for performing laboratory work on the study of terrestrial magnetism, the Lorentz force and the Ampere force, and the determination of the specific charge of an electron. The device and principle of operation of an electronic oscilloscope are considered. The textbook is intended for full-time and part-time students in areas and specialties whose curricula include a laboratory workshop in physics. 3 CONTENTS Laboratory work No. 5.1 (25) Determination of the horizontal component of the induction of the Earth’s magnetic field …………………………………………………………………… 4 Laboratory work No. 5.2 (26) Definition of magnetic induction …………………………………………. 12 Laboratory work No. 5.3 (27) Determination of the specific charge of an electron using a cathode ray tube …………………………………………………………………………………. 17 Laboratory work No. 5.4 (28) Determination of the specific charge of an electron using an indicator lamp ………………………………………………………………………………….... 25 Laboratory work No. 5.5 (29) Study of the magnetic properties of a ferromagnet………………………. 32 APPENDIX 1. Some physical constants.................................................... ................ 38 2. Decimal prefixes to the names of units...........………………………. 38 3. Symbols on the scale of electrical measuring instruments...... 38 Bibliography................................... ............................................... 39 Laboratory work No. 5.1 (25) DETERMINATION OF THE HORIZONTAL COMPONENT OF INDUCTION OF THE EARTH'S MAGNETIC FIELD Purpose of the work: study of the laws of the magnetic field in a vacuum; measurement of the horizontal component of the Earth's magnetic field induction. THEORETICAL MINIMUM Magnetic field A magnetic field is created by moving electric charges (electric current), magnetized bodies (permanent magnets) or a time-varying electric field. The presence of a magnetic field is manifested by its force effect on a moving electric charge (conductor with current), as well as by the orienting effect of the field on a magnetic needle or a closed conductor (frame) with current. Magnetic induction Magnetic induction B is a vector whose modulus is determined by the ratio of the maximum moment of force Mmax acting on a frame with current in a magnetic field to the magnetic moment pm of this frame with current M B = max. (1) pm The direction of vector B coincides with the direction of the normal to the current-carrying frame established in a magnetic field. The magnetic moment pm of the frame with current is equal in magnitude to the product of the current strength I and the area S limited by the frame pm = IS. The direction of the vector p m coincides with the direction of the normal to the frame. The direction of the normal to the frame with current is determined by the right-hand screw rule: if a screw with a right-hand thread is rotated in the direction of the current in the frame, then the translational movement of the screw will coincide with the direction of the normal to the plane of the frame (Fig. 1). The direction of magnetic induction B also shows the northern end of the magnetic needle established in the magnetic field. The SI unit of magnetic induction is tesla (T). 2 Bio-Savart-Laplace law Each element dl of a conductor with current I creates at some point A a magnetic field with induction dB, the magnitude of which is proportional to the vector product of vectors dl and radius vector r drawn from the element dl to a given point A (Fig. 2 ) μ μI dB = 0 3 , (2) 4π r where dl is an infinitesimal element of the conductor, the direction of which coincides with the direction of the current in the conductor; r – modulus of vector r; μ0 – magnetic constant; μ is the magnetic permeability of the medium in which the element and point A are located (for vacuum μ = 1, for air μ ≅ 1). dB is perpendicular to the vector of the plane in which the vectors dl and r are located (Fig. 2). The direction of the vector dB is determined by the right-hand screw rule: if a screw with a right-hand thread is rotated from dl to r towards a smaller angle, then the translational movement of the screw will coincide with the direction dB. Vector equation (2) in scalar form determines the magnetic induction module μ μ I dl sinα dB = 0, (3) 4π r 2 where α is the angle between vectors dl and r. Principle of superposition of magnetic fields If a magnetic field is created by several current-carrying conductors (moving charges, magnets, etc.), then the induction of the resulting magnetic field is equal to the sum of the inductions of magnetic fields created by each conductor separately: B res = ∑ B i . i Summation is carried out according to the rules of vector addition. Magnetic induction on the axis of a circular conductor with current Using the Biot-Savart-Laplace law and the principle of superposition, it is possible to calculate the induction of the magnetic field created by an arbitrary conductor with current. To do this, the conductor is divided into elements dl and the induction dB of the field created by each element at the considered point in space is calculated using formula (2). The induction B of the magnetic field created by all 3 conductors will be equal to the sum of the induction fields created by each element (since the elements are infinitesimal, the summation is reduced to calculating the integral over the length of the conductor l) B = ∫ dB. (4) l As an example, let us determine the magnetic induction in the center of a circular conductor with current I (Fig. 3,a). Let R be the radius of the conductor. At the center of the turn, the vectors dB of all elements dl of the conductor are directed in the same way - perpendicular to the plane of the turn in accordance with the right-hand screw rule. The vector B of the resulting field of the entire circular conductor is also directed at this point. Since all elements dl are perpendicular to the radius vector r, then sinα = 1, and the distance from each element dl to the center of the circle is the same and equal to the radius R of the turn. In this case, equation (3) takes the form μ μ I dl. dB = 0 4 π R2 Integrating this expression over the length of the conductor l in the range from 0 to 2πR, we obtain the magnetic field induction in the center of a circular conductor with current I. (5) B = μ0 μ 2R Similarly, we can obtain an expression for the magnetic induction on the axis of a circular conductor at a distance h from the center of the coil with current (Fig. 3,b) B = μ0 μ I R 2 2(R 2 + h 2)3 / 2. EXPERIMENTAL PROCEDURE (6) 4 The Earth is a natural magnet, the poles of which are located close to the geographic poles. The Earth's magnetic field is similar to the field of a straight magnet. The magnetic induction vector near the earth's surface can be decomposed into horizontal BG and vertical BB components: BEarth = VG + VV. The method for measuring the modulus of the horizontal component VG of the Earth's magnetic field in this work is based on the principle of superposition of magnetic fields. If a magnetic needle (for example, a compass needle) can rotate freely around a vertical axis, then under the influence of the horizontal component of the Earth’s magnetic field it will be installed in the plane of the magnetic meridian, along the direction B G. If another magnetic field is created near the needle, the induction B of which is located in horizontal plane, then the arrow will rotate through a certain angle α and set in the direction of the resulting induction of both fields. Knowing B and measuring the angle α, we can determine BG. A general view of the installation, called a tangent galvanometer, is shown in Fig. 4, the electrical circuit is shown in Fig. 5. In the center of the circular conductors (turns) 1 there is a compass 2, which can be moved along the axis of the turns. The current source ε is located in housing 3, on the front panel of which there are: key K (network); the handle of the potentiometer R, which allows you to adjust the current strength in the circular conductor; mA milliammeter, which measures the current in a conductor; switch P, with which you can change the direction of the current in the circular conductor of the tangent galvanometer. Before starting measurements, the magnetic compass needle is installed in the plane of the circular turns in the center (Fig. 6). In this case, in the absence of current in the turns, the magnetic needle will show the direction of the horizontal component B Г of the induction of the Earth's magnetic field. If you turn on the current in a circular conductor, then the induction vector B of the field it creates will be perpendicular to B G. The magnetic needle of the tangent galvanometer will rotate through a certain angle α and set in the direction of the induction of the resulting field (Fig. 6 and Fig. 7). The tangent of the angle α of deflection of the magnetic needle is determined by the formula 5 tgα = From equations (5) and (7) we obtain BГ = B. BG (7) μo μ I . 2 R tgα In a laboratory installation to increase magnetic induction, a circular conductor consists of N turns, which in terms of magnetic action is equivalent to increasing the current strength by N times. Therefore, the calculation formula for determining the horizontal component of the VG induction of the Earth's magnetic field has the form μ μIN BG = o. (8) 2 R tgα Instruments and accessories: laboratory stand. PROCEDURE FOR PERFORMANCE OF THE WORK The volume of work and conditions for conducting the experiment are established by the teacher or by an individual assignment. Measuring the horizontal component of the VG induction of the Earth's magnetic field 1. By rotating the installation body, ensure that the magnetic needle is located in the plane of the turns. In this case, the plane of the tangent galvanometer turns will coincide with the plane of the Earth’s magnetic meridian. 2. Place the potentiometer R knob to the extreme left position. Set key K (network) to the On position. Place switch P in one of the extreme positions (in the middle position of switch P the circuit of turns is open). 3. Use the potentiometer R to set the first set value of the current I (for example, 0.05 A) and determine the angle α1 of the pointer’s deviation from the original position. 6 4. Change the direction of the current by switching switch P to another extreme position. Determine the angle α 2 of the new arrow deflection. Changing the direction of the current allows you to get rid of the error caused by the inaccurate coincidence of the plane of the turns with the plane of the magnetic meridian. Enter the measurement results in the table. 1. Table 1 Measurement number I, A α1, deg. α 2, deg. α, deg B G, T 1 2 3 4 5 Calculate the average value of α using the formula α + α2 α = 1. 2 5. Carry out the measurements specified in paragraphs 3 and 4 at four more different current values ​​in the range from 0.1 to 0.5 A. 6. For each current value, use formula (8) to calculate the horizontal component B G of induction Earth's magnetic field. Substitute the average value α into the formula. Radius of the circular conductor R = 0.14 m; the number of turns N is indicated on the installation. The magnetic permeability μ of air can be approximately considered equal to unity. 7. Calculate the average value of the horizontal component B Г of the Earth's magnetic field induction. Compare it with the table value B Gtable = 2 ⋅ 10 −5 T. 8. For one of the current values, calculate the error Δ B Г = ε ⋅ B Г and write down the resulting confidence interval B Г = (B Г ± ΔB Г) T. Relative error in measuring the value B Г ε = ε I 2 + ε R 2 + εα 2. Calculate relative partial errors using the formulas 2Δ α ΔI ΔR ; εR = ; εα = εI = , I R sin 2 α where Δ α is the absolute error of angle α, expressed in radians (to convert angle α to radians, its value in degrees must be multiplied by π and divided by 180). 9. Write a conclusion in which - compare the measured value of BG with the table value; – write the resulting confidence interval for the value B Г; 7 - indicate which measurement made the main contribution to the error in the value B G. Study of the dependence of magnetic induction on the current strength in the conductor 10. To complete this task, complete steps 1 to 5. Enter the measurement results in the table. 2. Table 2 Measurement number I, A α1, deg. α 2, deg. α , deg Vexp, T Vteor, T 1 2 3 4 5 11. Using the table value of the quantity B Gtable = 2 ⋅ 10 −5 T, for each current value using formula (7) calculate the experimental value of induction Vexp of the magnetic field created by the turns . Substitute the average value α into the formula. Enter the results in the table. 2. 12. For each current value, using the formula μ μI N (9) Btheor = o 2R, calculate the theoretical value of the magnetic field induction created by the turns. Radius of the circular conductor R = 0.14 m; the number of turns N is indicated on the installation. The magnetic permeability μ of air can be approximately considered equal to unity. Enter the results in the table. 2. 13. Draw a coordinate system: the x-axis is the current strength I in turns, the ordinate axis is the magnetic induction B, where plot the dependence of Vexp on the current strength I in turns. Do not connect the obtained experimental points with a line. 14. On the same graph, depict the dependence of Btheor on I by drawing a straight line through the points of Btheor. 15. Evaluate the degree of agreement between the obtained experimental and theoretical dependences B(I). Give possible reasons for their discrepancy. 16. Write a conclusion in which you indicate whether the experiment confirms the linear dependence B(I); – do the experimental values ​​of the magnetic field induction created by the coils coincide with the theoretical ones; indicate possible reasons for the discrepancy. 17. The tangent galvanometer compass can move perpendicular to the plane of the coils. By measuring the angles α of deflection of the magnetic needle for various distances h from the center of the turns at a constant current strength I in the turns and knowing the value of B Г, you can check the validity of the theoretical formula (6). 8 CHECK QUESTIONS 1. Explain the concepts of magnetic field, magnetic induction. 2. What is the Biot-Savart-Laplace law? 3. What is the direction and on what values ​​does the magnetic induction in the center of a circular conductor with current depend? 4. What is the principle of superposition of magnetic fields? How is it used in this work? 5. How is the magnetic needle installed: a) in the absence of current in the turns of the tangent galvanometer; b) when current flows through the turns? 6. Why does the position of the magnetic needle change when the direction of the current in the turns changes? 7. How will the magnetic needle of a tangent galvanometer be installed if the installation is shielded from the Earth’s magnetic field? 8. For what purpose is not one, but several dozen turns used in a tangent galvanometer? 9. Why, when conducting experiments, should the plane of the turns of the tangent galvanometer coincide with the plane of the Earth’s magnetic meridian? 10. Why should the magnetic needle be much smaller in size than the radius of the turns? 11. Why does conducting experiments with two opposite directions of current in the turns increase the accuracy of the measurement of B G? What experimental error is excluded in this case? Bibliography 1. Trofimova, T.I. Physics course. 2000. §§ 109, 110. 12 Laboratory work No. 5.2 (26) DETERMINATION OF MAGNETIC INDUCTION Purpose of the work: study and verification of Ampere's law; study of the dependence of the magnetic field induction of an electromagnet on the current strength in its winding. THEORETICAL MINIMUM Magnetic field (see p. 4) Magnetic induction (see p. 4) Ampere's law Each element dl of a conductor with current I, located in a magnetic field with induction B, is acted upon by a force dF = I dl × B. (1) The direction of the vector dF is determined by the vector product rule: the vectors dl, B and dF form a right-hand triple of vectors (Fig. 1). The vector dF is perpendicular to the plane in which the vectors dl and B lie. The direction of the Ampere force dF can be determined by the left hand rule: if the magnetic induction vector enters the palm, and the extended four fingers are located in the direction of the current in the conductor, then the thumb bent 90° will show the direction of the Ampere force acting on this element of the conductor. The Ampere force modulus is calculated by the formula dF = I B sin α ⋅ dl, where α is the angle between vectors B and dl. (2) 13 EXPERIMENTAL METHOD The Ampere force in work is determined using scales (Fig. 2). A conductor through which current I flows is suspended from the balance beam. To increase the measured force, the conductor is made in the form of a rectangular frame 1, which contains N turns. The lower side of the frame is located between the poles of electromagnet 2, which creates a magnetic field. The electromagnet is connected to a direct current source with a voltage of 12 V. The current I EM in the electromagnet circuit is regulated using a rheostat R 1 and measured with an ammeter A1. The voltage from the source is connected to the electromagnet through terminals 4 located on the scale body. The current I in the frame is created by a 12 V DC source, measured by ammeter A2 and regulated by rheostat R2. Voltage is supplied to the frame through terminals 5 on the scale body. Through the frame conductors located between the poles of the electromagnet, current flows in one direction. Therefore, the Ampere force F = I lBN acts on the lower side of the frame, (3) where l is the length of the lower side of the frame; B is the magnetic field induction between the poles of the electromagnet. If the direction of the current in the frame is chosen so that the Ampere force is directed vertically downward, then it can be balanced by the force of gravity of the weights placed on the pan of 3 scales. If the mass of weights is m, then their gravity mg and, according to formula (4), magnetic induction mg. (4) B= IlN Instruments and accessories: installation for measuring Ampere force and magnetic field induction; set of weights. 14 PROCEDURE FOR PERFORMANCE OF WORK The volume of work and conditions for conducting the experiment are established by the teacher or by an individual assignment. 1. Make sure that the electrical circuit of the installation is assembled correctly. At rheostats R 1 and R 2, the maximum resistance must be entered. 2. Before starting measurements, the scale must be balanced. Access to the scale pan is only through the side door. The scales are released (removed from the lock) by turning handle 6 to the OPEN position (Fig. 1). The scales should be handled carefully; after completing measurements, turn handle 6 to the CLOSED position. 3. The teacher connects the installation to the network. 4. Fill out the table. 1 characteristics of electrical measuring instruments. Table 1 Name of the device Device system Measurement limit Ammeter for measuring the current in the frame Ammeter for measuring the current in the electromagnet Price Class Instrument accuracy division error ΔI pr ΔI EM pr Checking Ampere's law 5. Place the weight of the required mass on the cup of a caged scale (for example, m = 0.5 g). Using rheostat R 1, set the current in the electromagnet circuit to the required value (for example, I EM = 0.2 A). 6. Release the scales and, using rheostat R 2, select such a current I in the frame so that the scales are balanced. Record the results obtained in Table 2. Table 2 No. of measurement I EM, A t, g I, A F, N 1 2 3 4 5 7. At the same value of I EM, carry out four more measurements specified in paragraph 5, each time increasing the mass of weights by approximately 0.2 15 8. For each experiment, calculate the Ampere force equal to the gravity force of the weights F = mg. 9. Construct a graph of the dependence of F on the current strength I in the conductor, plotting the values ​​along the I abscissa axis. This dependence was obtained at a certain constant value of the electromagnet current I EM, therefore, the value of magnetic induction is also constant. Therefore, the obtained result allows us to draw a conclusion about the feasibility of Ampere’s law in terms of the proportionality of Ampere’s force to the current strength in the conductor: F ~ I. Determination of the dependence of magnetic induction on the electromagnet current 10. Place a load of a given mass on the scale pan (for example, m = 1 g). For five different values ​​of the electromagnet current I EM (for example, from 0.2 to 0.5 A), select currents I in the frame circuit that balance the scales. Record the results in the table. 3. Table 3 No. of measurements m, g I EM, A I, A B, T 1 2 3 4 5 11. Using formula (5), calculate the values ​​of magnetic induction B in each experiment. The values ​​of l and N are indicated on the installation. Plot the dependence of B on the electromagnet current, plotting the values ​​of I EM along the abscissa axis. 12. For one of the experiments, determine the error Δ B. Calculate relative partial errors using the formulas Δl ΔI εl = ; ε I = ; ε m = 10 −3. l I Record the resulting confidence interval in the report. In the conclusions, discuss: – what the test of Ampere’s law showed, whether it is fulfilled; on what basis is the conclusion made; – how does the magnetic induction of an electromagnet depend on the current in its winding; – will this dependence remain with a further increase in I EM (take into account that the magnetic field is due to the magnetization of the iron core). 16 CHECK QUESTIONS 1. What is Ampere’s law? What is the direction of Ampere's force? How does it depend on the location of the conductor in the magnetic field? 2. How is a uniform magnetic field created in work? What is the direction of the magnetic induction vector? 3. Why should direct current flow in the frame in this work? What will the use of alternating current lead to? 4. Why is a frame consisting of several dozen turns used in the work? 5. Why is it necessary to select a certain direction of current in the frame for normal operation of the installation? What will a change in the direction of current lead to? How can you change the direction of current in a frame? 6. What will a change in the direction of current in the electromagnet winding lead to? 7. Under what conditions in work is equilibrium of the scales achieved? 8. What corollary of Ampere’s law is tested in this work? Bibliography 1. Trofimova T.I. Physics course. 2000. §§ 109, 111, 112. 17 Laboratory work No. 5.3 (27) DETERMINATION OF THE SPECIFIC CHARGE OF AN ELECTRON USING A CHODE RAY TUBE Purpose of the work: to study the patterns of movement of charged particles in electric and magnetic fields; determination of the speed and specific charge of the electron. THEORETICAL MINIMUM Lorentz force A charge q moving with a speed v in an electromagnetic field is acted upon by the Lorentz force F l = qE + q v B , (1) where E is the electric field strength; B - magnetic field induction. The Lorentz force can be represented as the sum of the electric and magnetic components: F l = Fe + F m. The electric component of the Lorentz force F e = qE (2) does not depend on the speed of the charge. The direction of the electrical component is determined by the sign of the charge: for q > 0, the vectors E and Fe are directed in the same way; at q< 0 – противоположно. Магнитная составляющая силы Лоренца Fм = q v B (3) зависит от скорости движения заряда. Модуль магнитной составляющей определяется по формуле (4) F м = qvB sin α , где α - угол между векторами v и B . Направление магнитной составляющей определяется правилом векторного произведения и знаком заряда: для положительного заряда (q >0) the right triple of vectors is formed by the vectors v, B and Fm (Fig. 1), for a negative charge (q< 0) – векторы v , B и − F м. Направление магнитной составляющей силы Лоренца можно определить и с помощью правила левой руки. Правило левой руки: расположите ладонь левой руки так, чтобы в нее входил вектор B , а четыре пальца направьте вдоль вектора v , тогда отогнутый на 90° большой палец покажет направление силы Fм, действующей на положительный заряд. В случае отрицательного заряда направление вектора Fм противоположно. В любом случае вектор Fм перпендикулярен плоскости, в которой лежат векторы v и B . Движение заряженных частиц в магнитном поле Если частица движется вдоль линии магнитной индукции (α = 0 или α = π), то sin α = 0 . Тогда согласно выражению (4) F м = 0 . В этом случае магнитное поле не влияет на движение заряженной частицы (рис. 2). Если заряженная частица движется перпендикулярно линиям магнитной индукции (α = π 2) , то sin α = 1 . Тогда согласно (4) Fм = qvB . Так как вектор этой силы всегда перпендикулярен вектору скорости v частицы, то сила Fм создает только нормальное (центростремительное) ускорение v2 an = , при этом скорость заряженной частицы изменяется только по наr правлению, не изменяясь по модулю. Частица в этом случае равномерно движется по дуге окружности, плоскость которой перпендикулярна линиям индукции (рис. 3). Если вектор скорости v заряженной частицы составляет с вектором B угол α , то магнитная составляющая силы Лоренца будет определяться согласно (3), а модуль согласно выражению (4). В этом случае частица участвует одновременно в двух движениях: поступательном с постоянной скоростью v || и равномерном вращении по окружности со скоростью v ⊥ . В результате траектория заряженной частицы имеет форму винтовой линии (рис. 4). 19 Удельный заряд частицы Удельный заряд частицы – это отношение заряда q частицы к ее массе q m. Величина – важная характеристика заряженной частицы. Для электрона m q e Кл = = 1,78 ⋅ 1011 . m me кг МЕТОДИКА ЭКСПЕРИМЕНТА В работе изучается движение электронов в однородных электрическом и магнитном полях. Источником электронов является электронная пушка 1 электроннолучевой трубки осциллографа (рис. 5). Электрическое поле создается между парой вертикально отклоняющих пластин 2 электроннолучевой трубки при подаче на них напряжения U. (Горизонтально отклоняющие пластины 3 в работе не используются.) Напряженность E электрического поля направлена вертикально. Магнитное поле создается двумя катушками 4, симметрично расположенными вне электроннолучевой трубки, при пропускании по ним электрического тока. Вектор магнитной индукции B направлен горизонтально и перпендикулярно оси трубки. В отсутствии электрического и магнитного полей электроны движутся вдоль оси трубки с начальной скоростью v o , при этом светящееся пятно на- 20 ходится в центре экрана. При подаче напряжения U на пластины 2 между ними создается электрическое поле, напряженность которого E перпендикулярно вектору начальной скорости электронов. В результате пятно смещается. Величину y этого смещения можно измерить, воспользовавшись шкалой на экране осциллографа. Однако в электрическом поле на электрон действует согласно (2) электрическая составляющая силы Лоренца FЭ = eE , (5) где е – заряд электрона. Заряд электрона отрицательный (е < 0), поэтому сила FЭ направлена противоположно полю. Эта сила сообщает электрону ускорение a y в направлении оси Y, не влияя на величину скорости электрона вдоль оси X: v x = v 0 . Из основного закона динамики поступательного движения eE FЭ = ma y и (5) a y = , где m – масса электрона. В результате, пролетая m l область электрического поля за время t = 1 , где l1 – длина пластин, электрон vo смещается по оси Y на расстояние a y t 2 eE l12 y1 = = . 2 2mvo2 После вылета из поля электрон летит прямолинейно под некоторым v y a y t eE l1 = = . углом α к оси Х, причем согласно рисунку tgα = v x v o mvo2 21 Окончательно смещение пятна от центра экрана (рис. 2) в электрическом поле равно y = y1 + y 2 , где eE l 1 ⎛ l 1 ⎞ ⎜⎜ + l 2 ⎟⎟ . (6) y = y1 + l 2tgα = mvo2 ⎝ 2 ⎠ Если по катушкам 4 (рис. 5) пропустить электрический ток, то на пути электронов возникнет магнитное поле. Изменяя силу тока I в катушках, можно подобрать такую величину и направление магнитной индукции B , что магнитная составляющая силы Лоренца FМ скомпенсирует электрическую составляющую FЭ. В этом случае пятно снова окажется в центре экрана. Это будет при условии равенства нулю силы Лоренца eE + e v o B = 0 или E + v o B = 0 . Как видно из рис. 7, это условие выполняется, если вектор магнитной индукции B перпендикулярен векторам E и v o , что реализовано в установке. Из этого условия можно определить скорость электронов E (7) vo = . B Поскольку практически измеряется напряжение U, приложенное к пластинам, и расстояние d между ними, то пренебрегая краевыми эффектами можно считать, что E = [ U d ] , тогда U . (8) Bd Измеряя смещение у электронного пучка, вызванное электрическим полем Е, а затем подбирая такое магнитное поле В, чтобы смещение стало равным нулю, можно из уравнений (6) и (8) определить удельный заряд электрона yU e . (9) = m ⎛ l1 ⎞ 2 B dl 1 ⎜ + l 2 ⎟ ⎝2 ⎠ Схема установки показана на рис. 8. Электроннолучевая трубка расположена в корпусе осциллографа 1, на передней панели которого находится экран трубки 2 и две пары клемм. Клеммы ПЛАСТИНЫ соединены с вертикально отклоняющими пластинами трубки. Клеммы КАТУШКИ соединены с катушками 4 электромагнита, создающего магнитное поле. (Расположение катушек видно через прозрачную боковую стенку осциллографа.) Выпрямитель 5 и блок 6 служат для создания, регулировки и измерения постоянного напряжения на управляющих пластинах трубки и постоянного тока через катушки электромагнита. Переключатель K1 позволяет изменить полярность vo = 22 напряжения на пластинах, а переключатель K 2 – направление тока через катушки электромагнита. Параметры установки: d = 7,0 мм; l1 = 25,0 мм; l 2 = 250 мм. Приборы и принадлежности: осциллограф с электроннолучевой трубкой; выпрямитель; блок коммутации с электроизмерительными приборами. ПОРЯДОК ВЫПОЛНЕНИЯ РАБОТЫ 1. Заполните табл. 1 характеристик электроизмерительных приборов. Таблица 1 Наименование прибора Вольтметр Миллиамперметр Система прибора Предел измерения Цена Класс Приборная деления точности погрешность ΔU пр ΔI пр 2. Тумблером 3 (рис. 8) включите осциллограф. Ручками ЯРКОСТЬ и ФОКУС, расположенными на верхней панели осциллографа, добейтесь четкости пятна на экране. Ручкой ↔ установите пятно в центр экрана. 3. Тумблером К включите выпрямитель. Ручками П 1 и П 2 установите нулевые показания вольтметра и миллиамперметра. 4. Условия проведения эксперимента (значения напряжения U на пластинах) задаются преподавателем или вариант индивидуального занятия. 23 5. Ручкой П 1 установите нужное напряжение на пластинах и измерьте смещение у луча от центра экрана. Результат измерения в зависимости от направления смещения («вверх» или «вниз») запишите в табл.2. Таблица 2 U, В y y вверх, вниз, мм мм у, мм I1, А I2, А I , А В, Тл vo , м/с e/m, Кл/кг 6. С помощью ручки П 2 и переключателя K 2 подберите такой ток I1 в катушках, чтобы пятно вернулось в центр экрана. Значение силы тока запишите в табл. 2. 7. Измерения, указанные в пункте 5 и 6, проведите при двух других значениях напряжения U . 8. Тумблером K 1 измените полярность напряжения на пластинах и повторите измерения, указанные в пунктах 5, 6 и 7. 9. По приложенному к установке градуировочному графику электромагнита и по среднему значению силы тока I в каждом испытании определите значения магнитной индукции В и занесите их в табл. 2. 10. По формуле (8) рассчитайте скорость электронов в каждом опыте и среднее значение v o по всем испытаниям. 11. Используя формулу eU a = m vo 2 2 , рассчитайте анодное напряжение в электронной пушке. 12. По формуле (9) рассчитайте значение удельного заряда электрона в e по всем испытаниям. каждом опыте и среднее значение m 13. По результатам одного из опытов рассчитайте абсолютную погрешность удельного заряда электрона Δ me = ε e me . Здесь ε = ε y2 + εU2 + ε B2 + ε d2 + ε l21 + ε l22 . Относительные частные погрешности рассчитайте по формулам Δy ΔU 2ΔB Δd Δ l (l +l) Δl εy = ; εU = ; εB = ; εd = ; ε l1 = 1l 1 2 ; ε l 2 = l 2 . ⎞ ⎛ 1 +l y U B d l1 ⎜ 1 +l 2 ⎟ 2 ⎝2 ⎠ 2 В качестве Δу используйте приборную погрешность шкалы на экране осциллографа, в качестве ΔU – приборную погрешность вольтметра. Погрешность ΔВ определяется по градуировочному графику по величине ΔI пр. Запишите в отчет полученный доверительный интервал величины e m . 24 15. В выводах – укажите, что наблюдалось в работе; e ; согласие считается хоро– сравнить полученное и табличное значения m шим, если табличное значение попадает в найденный доверительный интервал; – указать, измерение какой величины внесло основной вклад в погрешe . ность величины m КОНТРОЛЬНЫЕ ВОПРОСЫ 1. Сила Лоренца. Направление ее составляющих. 2. Зависит ли от знака заряда сила, действующая на него со стороны: а) электрического поля; б) магнитного поля? 3. Зависит ли от скорости и направления движения заряда сила, действующая на него: а) в электрическом поле; б) в магнитном поле? 4. Как движется электрон: а) в поле между пластинами; б) слева от пластин; в) справа от пластин? 5. Отличается ли скорость электрона до и после пластин? 6. Как изменится смещение пятна на экране, если а) скорость электронов увеличить вдвое; б) анодное напряжение увеличить вдвое? 7. Изменяется ли при движении заряда в однородном магнитном поле: а) направление скорости; б) величина скорости? 8. Каким должно быть взаимное расположение однородных электрического и магнитного полей, чтобы электрон мог двигаться в них с постоянной скоростью? При каком условии возможно такое движение? 9. Какую роль в электронной пушке играют катод, модулятор, аноды? 10. Какую роль в электроннолучевой трубке играют: а) электронная пушка; б) отклоняющие пластины; в) экран? 11. Как в установке создаются однородные поля: а) электрическое; б) магнитное? 12. Как изменяется смешение пятна на экране при изменении направления тока в катушках? Библиографический список 1. Трофимова Т.И. Курс физики. 2000. §§ 114, 115. 25 Лабораторная работа № 4 (28) ОПРЕДЕЛЕНИЕ УДЕЛЬНОГО ЗАРЯДА ЭЛЕКТРОНА С ПОМОЩЬЮ ИНДИКАТОРНОЙ ЛАМПЫ Цель работы: изучение закономерностей движения заряженных частиц в электрическом и магнитном полях; определение удельного заряда электрона. ТЕОРЕТИЧЕСКИЙ МИНИМУМ Магнитная индукция (смотрите с. 4) Сила Лоренца (смотрите с. 17) Движение заряженных частиц в магнитном поле (смотрите с. 18) Удельный заряд электрона (смотрите с. 19) МЕТОДИКА ЭКСПЕРИМЕНТА В работе удельный заряд me электрона определяется путем наблюдения движения электронов в скрещенных электрическом и магнитном полях. Электрическое поле создается в пространстве между анодом и катодом вакуумной электронной лампы. Катод К расположен по оси цилиндрического анода А (рис.1), между ними приложено анодное напряжение U a . На рис. 2 показано сечение лампы плоскостью XOY . Как видим, напряженность электричеr ского поля E имеет радиальное направление. Лампа расположена в центре соленоида (катушки), создающего однородное магнитное поле, вектор индукции r B которого параллелен оси лампы. На электроны, выходящие из катода благодаря термоэлектронной эмиссии, со стороны электрического поля действует электрическая составляющая r r силы Лоренца FЭ = eE , которая ускоряет электроны к аноду. Со стороны магr r r нитного поля действует магнитная составляющая силы Лоренца FM = e , r которая направлена перпендикулярно скорости v электрона (рис. 2), поэтому его траектория искривляется. 26 На рис. 3 показаны траектории электронов в лампе при различных значениях индукции В магнитного поля. В отсутствии магнитного поля (В = 0) траектория электрона прямолинейна и направлена вдоль радиуса. При слабом поле траектория несколько искривляется. При некотором значении индукции B = B 0 траектория искривляется настолько, что касается анода. При достаточно сильном поле (B > B 0) the electron does not reach the anode at all and returns to the cathode. In the case of B = B 0, we can assume that the electron moves in a circle with radius r = ra / 2, where ra is the radius of the anode. The force FM = evB creates normal (centripetal) acceleration, therefore, according to the basic law of translational motion dynamics, mv 2 (1) = evB. r The speed of electron motion can be found from the condition that the kinetic energy of the electron is equal to the work of the electric field forces on the path of the electron from the cathode to the anode mv 2 = eU a , from which 2 v = 2eU a . m (2) 27 Substituting this value for the speed v into equation (1) and taking into account that r = ra / 2, we obtain the expression for the specific charge of the electron 8U e = 2 a2. m B o ra Formula (3) allows you to calculate the value (3) em if, for a given value of the anode voltage U a, you find a value of magnetic induction Bo at which the electron trajectory touches the anode surface. An indicator lamp is used to observe the electron trajectory (Fig. 4). Cathode K is located along the axis of the cylindrical anode A. The cathode is heated by a filament. Between the cathode and anode there is a screen E, which has the shape of a conical surface. The screen is covered with a layer of phosphor, which glows when electrons hit it. Parallel to the axis of the lamp near the cathode there is a thin wire - an antennae U, connected to the anode. Electrons passing near the antennae are captured by it, so a shadow is formed on the screen (Fig. 5). The shadow boundary corresponds to the trajectory of electrons in the lamp. The lamp is placed in the center of a solenoid that creates a magnetic field, the induction vector r of which B is directed along the axis of the lamp. Solenoid 1 and lamp 2 are mounted on the stand (Fig. 6). The terminals located on the panel are connected to the solenoid winding, to the cathode filament, to the cathode and anode of the lamp. The solenoid is powered from rectifier 3. The source of the anode voltage and cathode filament voltage is rectifier 4. The current strength in the solenoid is measured using an ammeter A, the anode voltage U a is measured with a voltmeter V. Switch P allows you to change the direction of the current in the solenoid winding. 28 Magnetic induction in the center of the solenoid, and therefore inside the indicator lamp, is determined by the relation μo I N , (4) B= 2 2 4R + l where μ0 = 1.26·10 – 6 H/m - magnetic constant; I - current strength in the solenoid; N is the number of turns, R is the radius, l is the length of the solenoid. Substituting this value of B into expression (3), we obtain a formula for determining the specific charge of the electron e 8U a (4R 2 + l 2) , = m μo2 I o2 N 2ra2 (5) where I o is the current value in the solenoid at which the electron trajectory touches the outer edge of the screen. Considering that Ua and I0 are practically measured, and the values ​​N, R, l, ra are the parameters of the installation, from formula (5) we obtain the calculation formula for determining the specific charge of the electron U e (6) = A ⋅ 2a, m Io where A is installation constant A= (8 4R 2 + l 2 μo2 N 2ra2). (7) 29 Instruments and accessories: laboratory bench with indicator lamp, solenoid, ammeter and voltmeter; two rectifiers. ORDER OF PERFORMANCE 1. Fill out the table. 1 characteristics of ammeter and voltmeter. Table 1 Name Instrument system Voltmeter Measurement limit Division price Accuracy class ΔI pr Ammeter 2. 3. 4. Instrument error ΔU pr Check the correct connection of the wires according to Fig. 6. Move the rectifier adjustment knobs to the extreme left position. Write down in the report the parameters indicated on the installation: the number of turns N, the length l and the radius R of the solenoid. Anode radius ra = 1.2 cm. Write in the table. 2 results of measurements of the U a value specified by the teacher or an individual assignment option. Table 2 Measurement No. Ua , V I o1 , A I o2 , A Io , A e m , C/kg 1 2 3 5. 6. Connect the rectifiers to the ~220 V network. A few minutes later, after warming up the lamp cathode, install using rectifier adjustment knob 4 required voltage value U a. At the same time, the lamp screen begins to glow. Gradually increase the current I in the solenoid using the rectifier adjustment knob 3 and observe the curvature of the electron trajectory. Select and record in the table. 2 is the current value I o1 at which the electron trajectory touches the outer edge of the screen. 30 7. 8. 9. Reduce the current in the solenoid to zero. Move switch P to another position, thereby reversing the direction of current in the solenoid. Select and record in the table. 2 is the current value I o 2 at which the electron trajectory again touches the outer edge of the screen. Carry out the measurements specified in paragraphs 5-7 at two more values ​​of the anode voltage U a. For each value of the anode voltage, calculate and record in the table. 2 average current values ​​I o = (I o1 + I o 2) / 2. 10. Using formula (7), calculate the installation constant A and write the result in the report. 11. Using the value of A and the average value of I o, calculate using formula (6) e for each value of U a. Write the results of the calculations in the table. 2. e. 12. Calculate and write down the average value t 13. Based on the results of one of the experiments, calculate the absolute error e e e Δ in determining the specific charge of an electron using the formula Δ = ⋅ε, m m m specific charge where ε = ε U2 a + ε 2I o + ε 2ra + ε l2 + ε 2R , ΔU a 2ΔI o 2Δra 2lΔl 8RΔR , ε ra = , ε Io = , εl = , . ε = R Io Ua ra 4R 2 + l 2 4R 2 + l 2 Here ΔU a is the instrument error of the voltmeter. As the current error ΔI o, select the largest of two errors: random in εU a = error ΔI 0sl = I o1 − I o 2 2 and instrument error of the ammeter ΔI pr (see table of device characteristics). Errors Δra, Δl, ΔR are defined as errors of quantities specified numerically. 14. The final result of determining the specific charge of an electron is written in the form of a confidence interval: = ±Δ. m m m 31 15. In your conclusions about the work, write down: - what was studied in the work; - how does the radius of curvature of the electron trajectory depend (qualitatively) on the magnitude of the magnetic field; - how and why the direction of current in the solenoid affects the trajectory of electrons; - what result was obtained; - does the table value of the specific electron charge fall within the resulting confidence interval; - what measurement error made the main contribution to the error in measuring the specific charge of the electron. CHECK QUESTIONS What determines and how they are directed: a) the electrical component of the Lorentz force; b) magnetic component of the Lorentz force? 2. How are they directed and how do they change in magnitude in the indicator lamp: a) electric field; b) magnetic field? 3. How does the speed of electrons in the lamp change with distance from the cathode? Does the magnetic field affect the speed? 4. What is the trajectory of electrons in a lamp with magnetic induction: a) B = 0; b) B = Bo; c) B< Bo ; г) B >Bo? 5. What is the acceleration of electrons near the anode and how is it directed at magnetic induction B = Bo? 6. What role does the following play in the indicator lamp: a) screen; b) tendril wire? 7. Why does the brightness of the lamp screen increase when the anode voltage Ua increases? 8. How is the following created in a lamp: a) an electric field; b) magnetic field? 9. What role does the solenoid play in this work? Why should the solenoid have a fairly large number of turns (several hundred)? 10. Does the work: a) electrical; b) magnetic component of the Lorentz force? 1. Bibliography 1. Trofimova T.I. Physics course, 2000, § 114, 115. 32 Laboratory work No. 5.5 (29) STUDY OF THE MAGNETIC PROPERTIES OF A FERROMAGNET Purpose of the work: study of the magnetic properties of matter; determination of the magnetic hysteresis loop of a ferromagnet. THEORETICAL MINIMUM Magnetic properties of a substance All substances, when introduced into a magnetic field, exhibit magnetic properties to one degree or another and, according to these properties, are divided into diamagnetic, paramagnetic and ferromagnetic. The magnetic properties of a substance are determined by the magnetic moments of its atoms. Any substance placed in an external magnetic field creates its own magnetic field, which is superimposed on the external field. A quantitative characteristic of such a state of matter is magnetization J, equal to the sum of the magnetic moments of atoms per unit volume of the substance. Magnetization is proportional to the strength H of the external magnetic field J = χH, (1) where χ is a dimensionless quantity called magnetic susceptibility. The magnetic properties of a substance, in addition to the value χ, are also characterized by magnetic permeability μ = χ +1. (2) Magnetic permeability μ is included in the relationship that connects the intensity H and the induction B of the magnetic field in the substance B = μo μ H, (3) where μo = 1.26 ⋅10 −6 H/m is the magnetic constant. The magnetic moment of diamagnetic atoms in the absence of an external magnetic field is zero. In an external magnetic field, the induced magnetic moments of atoms, according to Lenz's rule, are directed against the external field. The magnetization J is also directed, therefore for diamagnetic materials χ< 0 и μ < 1 . После удаления диамагнетика из поля его намагниченность вследствие теплового движения атомов исчезает. Магнитные моменты атомов парамагнетиков в отсутствии внешнего магнитного поля не равны нулю, но без внешнего поля они ориентированы хаотично. Внешнее магнитное поле приводит к частичной ориентации магнитных моментов по направлению внешнего поля в той степени, насколько это позволяет тепловое движение атомов. Для парамагнетиков 0 < χ << 1 ; величина μ чуть превосходит единицу. При выключении внешнего магнитного поля намагниченность парамагнетиков исчезает под действием теплового движения. Магнитные моменты атомов ферромагнетиков в пределах малых областей (доменов) самопроизвольно (спонтанно) ориентированы одинаково. В 33 отсутствии внешнего магнитного поля в размагниченном ферромагнетике магнитные моменты доменов ориентированы хаотично. При включении внешнего магнитного поля результирующие магнитные моменты доменов ориентируются по полю, значительно усиливая его. Магнитная восприимчивость χ ферромагнетиков может достигать нескольких тысяч. Магнитный гистерезис Величина намагниченности J ферромагнетика зависит от напряженности Н внешнего поля и от предыстории образца. На рис. 1 приведена зависимость J(H), которая характеризует процесс намагничивания ферромагнетика. В точке 0 ферромагнетик полностью размагничен. По мере увеличения напряженности Н намагниченность J образца увеличивается нелинейно. Участок 0-1 называется основной кривой намагничивания. Уже при сравнительно небольших значениях Н намагниченность стремится к насыщению Jнас, что соответствует ориентации всех магнитных моментов доменов по направлению индукции внешнего поля. Если после достижения Jнас уменьшать напряженность внешнего магнитного поля, то намагниченность будет изменяться по кривой 1-2, расположенной выше основной кривой намагниченности. Когда внешнее поле станет равным нулю, в ферромагнетике сохранится остаточная намагниченность Jост. При противоположном направлении напряженности внешнего поля намагниченность, следуя по кривой 2-3, вначале обратится в ноль, а затем, также изменив направление на противоположное, будет стремиться к насыщению. Значение напряженности Нк, при котором J обращается в ноль, называется коэрцитивной силой. Если продолжить процесс перемагничивания вещества, то получится замкнутая кривая 1-2-3-4-1, которая называется петлей магнитного гистерезиса. По форме петли гистерезиса ферромагнетики разделяются на жесткие и мягкие. Жестким ферромагнетикам соответствует широкая петля и большая коэрцитивная сила (Н К ≥ 10 3 А/м). Такие вещества используются для изготовления постоянных магнитов. Мягким ферромагнетикам присуща узкая петля и небольшое значение коэрцитивной силы (Н К = 1K10 2 А/м). Они используются для изготовления сердечников трансформаторов, электромагнитов, реле. Ферромагнетики в отличие от диамагнетиков и парамагнетиков обладают существенной особенностью: для каждого из таких материалов имеется присущая только им температура, при которой исчезают ферромагнитные свойства. Эта температура называется точкой Кюри. При нагревании материала выше точки Кюри ферромагнетик превращается в парамагнетик. Это 34 объясняется тем, что при высоких температурах доменные образования в ферромагнетике исчезают. МЕТОДИКА ЭКСПЕРИМЕНТА Намагниченность ферромагнитного образца в данной работе измеряется с помощью магнитометрической установки, схема которой показана на рис. 2. Между одинаковыми соленоидами (катушками) 1 на их оси расположен компас 2. По соленоидам протекают одинаковые токи силой I , но в про- тивоположных направлениях. Поэтому вблизи магнитной стрелки компаса соленоиды создают равные, но противоположные по направлению магнитные поля, которые взаимно компенсируются и не вызывают отклонения стрелки. В этом случае стрелка устанавливается в направлении горизонтальной составляющей B Г индукции магнитного поля Земли. Ось соленоидов предварительно ориентируется перпендикулярно вектору B Г. При помещении в один из соленоидов ферромагнитного образца 3 образец намагничивается и создает вблизи стрелки компаса некоторое магнитное поле с индукцией B ⊥ B Г. Стрелка повернется на угол ϕ и установится вдоль результирующего поля B рез = B + B Г. Как следует из рис. 2, (1) B = B Г ⋅ tgϕ . Величина индукции В магнитного поля, создаваемого образцом вблизи стрелки, пропорциональна намагниченности J образца B = kJ , (2) где коэффициент k зависит от формы и размеров образца и его расположения относительно компаса, то есть является постоянной установки. Таким образом, расчетная формула для определения намагниченности B tgϕ . (3) J= Г k 35 Напряженность H магнитного поля соленоида может быть рассчитана по формуле H = nI , (4) где I - сила тока в соленоиде; n - число витков, приходящихся на единицу длины соленоида. Значения k и n указаны на установке. Общий вид установки показан на рис.3. Соленоиды 1, компас 2 и амперметр 3 размещены на подставке 4. С помощью переключателя 5 изменяется направление тока в соленоидах. Соленоиды питаются от выпрямителя 6. Переключателем 9 соленоиды подключаются к постоянному или к переменному напряжению. Приборы и принадлежности: магнитометрическая установка; выпрямитель; ферромагнитный образец. ПОРЯДОК ВЫПОЛНЕНИЯ РАБОТЫ Объем работы, и условия проведения опыта устанавливаются преподавателем или вариантом индивидуального задания. 1. Заполните табл. 1 характеристик миллиамперметра. Таблица 1 Наименование прибора Миллиамперметр Система прибора Предел измерения Цена Класс Приборная деления точности погрешность ΔI пр 2. Расположите подставку с соленоидами так, чтобы ось соленоидов была перпендикулярна горизонтальной составляющей B Г магнитного поля Земли. Компас закреплен так, что при этом его стрелка установится на нуле- 36 вое деление. Подайте на соленоиды постоянное напряжение, для этого переключатель 9 (рис.3) поставьте в положение (=). При этом соленоиды подключаются к клеммам 7. Не вставляя ферромагнитный образец в соленоид, включите выпрямитель и убедитесь, что магнитные поля соленоидов вблизи стрелки компаса компенсируются: стрелка не должна заметно отклоняться при увеличении силы тока в соленоидах с помощью ручки 10 выпрямителя. 3. Выключите выпрямитель, вставьте образец в один из соленоидов. Далее необходимо размагнитить образец. Для этого подключите соленоиды к клеммам 8 переменного напряжения, то есть, поставьте переключатель 9 в положение (~) . Включите выпрямитель и ручкой 10 доведите силу переменного тока в соленоидах до 2 А (измеряется амперметром выпрямителя) и постепенно уменьшайте его до нуля. Магнитная стрела должна находиться попрежнему на нулевом делении. 4. При нулевом значении силы тока в соленоидах (ручка 10 находится в крайнем левом положении) поставьте переключатель 9 в положение (=), подключив тем самым соленоиды к источнику постоянного напряжения. Установка и образец готовы к проведению изучения магнитных свойств образца. 5. Ступенчато увеличивая силу тока I от 0 до 500 мА, измерьте угол ϕ отклонения стрелки компаса, соответствующий каждому значению силы тока I . В интервале значений от 0 до 100 мА измерения надо делать через каждые 20 мА, а при больших значениях – через каждые 100 мА. Силу тока можно изменять только в сторону возрастания, уменьшение силы тока при его регулировке недопустимо. Измеренные значения I и ϕ запишите в две первые колонки (Ток +) табл. 2. Таблица 2 Ток + I , мА ϕ , град. Ток – I , мА ϕ , град. Ток + I , мА ϕ , град. (Еще 17 строк) В результате выполнения этого пункта строится основная кривая намагничивания (участок 0–1 на рис. 1). 6. Уменьшая ток в соленоидах до нуля так же, как указано в пункте 4, измерьте необходимые величины на участке 1–2 петли гистерезиса (рис.1). При этом ток можно регулировать только в сторону уменьшения. Результаты измерений I и ϕ запишите по-прежнему в две первые колонки табл. 2. 7. При нулевом значении силы тока в соленоидах переключите тумблер 5 (рис.3) в другое крайнее положение, изменив при этом направление тока в соленоидах на противоположное. Измерьте необходимые величины на участке 2–3 кривой гистерезиса (рис. 1). При этом силу тока следует регулировать только в направлении увеличения такими же ступенями, как в пункте 4. Результаты измерений I и ϕ запишите в две средние колонки «Ток–». Обратите внимание, что на этом участке кривой намагничивания происходит изме- 37 нение знака величины J и, следовательно, знака угла ϕ . Это надо отметить в таблице, указывая знак ϕ . 8. Постепенно уменьшая ток до нуля, измерьте величины I и ϕ на участке 3–4 кривой намагничивания. Результаты запишите в колонки «Ток–». 9. Тумблером 5 (рис. 3) измените, направление тока и, увеличивая силу тока, измерьте необходимые величины на последнем участке 4–1 кривой гистерезиса. Результаты измерений I и ϕ запишите в две правые колонки (Ток +) с указанием знака угла ϕ . 10. Постройте кривую магнитного гистерезиса, откладывая по осям координат (в зависимости от задания) или I и ϕ , или J и H , или B и H . 11. На основании полученной кривой гистерезиса рассчитайте по формулам (3) и (4) остаточную намагниченность J ост образца и коэрцитивную силу Н к. Величины k и n указаны на установке. 12. Для одной из точек на основной кривой намагничивания рассчитайте по формулам (3), (4), (1) и (2) значения магнитной восприимчивости χ и магнитной проницаемости μ ферромагнетика. КОНТРОЛЬНЫЕ ВОПРОСЫ 1. Чем обусловлены магнитные свойства: а) парамагнетиков; б) ферромагнетиков; в) диамагнетиков? 2. Дайте определение намагниченности. 3. Что характеризуют: а) магнитная восприимчивость; б) магнитная проницаемость? 4. Что такое основная кривая намагничивания? 5. Что такое: а) остаточная намагниченность; б) коэрцитивная сила; в) намагниченность насыщения? 6. В чем различие между жесткими и мягкими ферромагнетиками? Где они применяются? 7. Какая температура для ферромагнетиков называется точкой Кюри? 8. Как располагается магнитная стрелка, если ток в соленоидах отсутствует? Почему включение тока в соленоидах не влияет на положение стрелки? 9. Как надо ориентировать установку перед началом измерений? 10. Как устанавливается магнитная стрелка при намагничивании образца? 11. Почему перед получением петли гистерезиса образец должен быть размагничен? Как осуществляется размагничивание? ЛИТЕРАТУРА 1. Трофимова Т.И. Курс физики. 2000. § 132, 133, 135, 136. 2. Матвеев Н.Н., Постников В.В., Саушкин В.В. Физика. 2002.- С. 79-82. 38 ПРИЛОЖЕНИЕ 1. НЕКОТОРЫЕ ФИЗИЧЕСКИЕ ПОСТОЯННЫЕ Универсальная газовая постоянная Магнитная постоянная Электрическая постоянная Заряд электрона Масса электрона Удельный заряд электрона Горизонтальная составляющая индукции магнитного поля Земли (на широте Воронежа) R = 8,31 Дж/(моль⋅К) μ o = 1,26⋅10 – 6 Гн/м ε o = 8,85⋅10 – 12 Ф/м е = 1,6⋅10 – 19 Кл m = 0,91⋅10 – 30 кг e/m = 1,76⋅10 11 Кл/кг B Г = 2,0⋅10 – 5 Тл 2. ДЕСЯТИЧНЫЕ ПРИСТАВКИ К НАЗВАНИЯМ ЕДИНИЦ Г – гига (10 9) М – мега (10 6) к – кило (10 3) д – деци (10 – 1) с – санти (10 – 2) м – милли (10 – 3) Например: 1 кОм = 10 3 Ом; мк – микро (10 – 6) н – нано (10 – 9) п – пико (10 – 12) 1мА = 10 – 3 А; 1 мкФ = 10 – 6 Ф. 3. УСЛОВНЫЕ ОБОЗНАЧЕНИЯ НА ШКАЛЕ ЭЛЕКТРОИЗМЕРИТЕЛЬНЫХ ПРИБОРОВ Обозначение единицы измерения Ампер Вольт Миллиампер, милливольт Микроампер, микровольт А V mA, mV μ А, μ V Обозначение принципа действия (системы) прибора Магнитоэлектрический прибор с подвижной рамкой Электромагнитный прибор с подвижным ферромагнитным сердечником Положение шкалы прибора Горизонтальное Вертикальное Обозначение рода тока Прибор для измерения постоянного тока (напряжения) Прибор для измерения переменного тока (напряжения) Другие обозначения Класс точности Изоляция между электрической цепью прибора и корпусом испытана напряжением (кВ) ⊥ –– ~ 0,5 1,0 и др. 39 Пределом измерения прибора называется то значение измеряемой величины, при котором стрелка прибора отклоняется до конца шкалы. На многопредельных приборах пределы измерений указаны около клемм или около переключателей диапазонов. Цена деления шкалы равна значению измеряемой величины, которое вызывает отклонение стрелки прибора на одно деление шкалы. Если предел измерения xm и шкала имеет N делений, то цена деления c = x m / N . Δ x np Класс точности прибора γ = ⋅ 100% , где Δ x np - максимальная xm погрешность прибора; x m - предел измерения. Значение γ приведено на шкале прибора. Зная класс точности γ , можно определить приборную погрешность x Δ x np = γ m ., 100 БИБЛИОГРАФИЧЕСКИЙ СПИСОК Основная литература 1 Трофимова, Т.И. Курс физики [Текст]: Учебное пособие.– 6-е изд. – М.: Высш. шк., 2000.– 542 с. Дополнительная литература 1 Курс физики [Текст] / под ред. В.Н. Лозовского.– 2-е изд., испр.– СПб.: Лань, 2001.–Т.1.– 576 с. 2 Курс физики [Текст] / под ред. В.Н. Лозовского.– 2-е изд., испр.– СПб.: Лань.– 2001.Т.2.– 592 с. 3 Дмитриева, В.Ф. Основы физики [Текст]: учеб. пособие / В.Ф. Дмитриева, В.Л. Прокофьев – М.: Высш. шк., 2001.– 527 с. 4 Грибов, Л.А. Основы физики [Текст] / Л.А. Грибов, Н.И. Прокофьва.– М.: Гароарика, 1998.– 456 с. 40 Учебное издание Бирюкова Ирина Петровна Бородин Василий Николаевич Камалова Нина Сергеевна Евсикова Наталья Юрьевна Матвеев Николай Николаевич Саушкин Виктор Васильевич Физика Лабораторный практикум Магнетизм ЭЛЕКТРОННАЯ ВЕРСИЯ

Ministry of Education and Science of the Russian Federation

Baltic State Technical University "Voenmech"

ELECTROMAGNETISM

Laboratory workshop in physics

Part 2

Edited by L.I. Vasilyeva And V.A. Zhivulina

Saint Petersburg

Compiled by: D.L. Fedorov, Doctor of Physics and Mathematics sciences, prof.; L.I. Vasilyeva, prof.; ON THE. Ivanova, assistant professor; E.P. Denisov, assistant professor; V.A. Zhivulin, assistant professor; A.N. Starukhin, prof.

UDC 537.8(076)

E

Electromagnetism: laboratory workshop in physics / comp.: D.L. Fedorov [and others]; Balt. state tech. univ. – St. Petersburg, 2009. – 90 p.

The workshop contains a description of laboratory works Nos. 14–22 on the topics “Electricity and Magnetism” in addition to the description of works Nos. 1–13 presented in the workshop of the same name, published in 2006.

Designed for students of all specialties.

45

UDC 537.8(076)

REVIEWER: Dr. Tech. Sciences, prof., head. department Information and Energy Technologies BSTU S.P. Prisyazhnyuk

Approved

editorial and publishing

© BSTU, 2009

Laboratory work No. 14 Study of the electrical properties of ferroelectrics

Goal of the work – study the polarization of ferroelectrics depending on the electric field strength E, get the curve E = f(E), study dielectric hysteresis, determine dielectric losses in ferroelectrics.

Brief information from the theory

As is known, dielectric molecules in their electrical properties are equivalent to electric dipoles and can have an electric moment

Where q– the absolute value of the total charge of one sign in a molecule (i.e., the charge of all nuclei or all electrons); l– a vector drawn from the “center of gravity” of negative charges of electrons to the “center of gravity” of positive charges of nuclei (dipole arm).

The polarization of dielectrics is usually described based on the concepts of hard and induced dipoles. An external electric field either orders the orientation of rigid dipoles (orientation polarization in dielectrics with polar molecules) or leads to the appearance of fully ordered induced dipoles (electronic and ion displacement polarization in dielectrics with nonpolar molecules). In all these cases, the dielectrics are polarized.

Polarization of a dielectric means that under the influence of an external electric field, the total electric moment of the dielectric molecules becomes non-zero.

A quantitative characteristic of the polarization of a dielectric is the polarization vector (or polarization vector), which is equal to the electrical moment per unit volume of the dielectric:

, (14.2)

–vector sum of the dipole electric moments of all dielectric molecules in a physically infinitesimal volume
.

For isotropic dielectrics, polarization related to the electric field strength at the same point by the relation

æ
, (14.3)

where æ is a coefficient that does not depend, to a first approximation, on and called the dielectric susceptibility of the substance; =
F/m – electrical constant.

To describe the electric field in dielectrics, in addition to the intensity and polarization , use the electric displacement vector , defined by equality

. (14.4)

Taking into account (14.3), the displacement vector can be represented as

, (14.5)

Where
æ is a dimensionless quantity called the dielectric constant of the medium. For all dielectrics æ > 0 and ε > 1.

Ferroelectrics are a special group of crystalline dielectrics that, in the absence of an external electric field in a certain temperature and pressure range, have spontaneous (spontaneous) polarization, the direction of which can be changed by an electric field and, in some cases, mechanical stresses.

Unlike conventional dielectrics, ferroelectrics have a number of characteristic properties that were studied by Soviet physicists I.V. Kurchatov and P.P. Kobeko. Let us consider the basic properties of ferroelectrics.

Ferroelectrics are characterized by very high dielectric constants , which can reach values ​​of the order
. For example, the dielectric constant of Rochelle salt NaKC 4 H 4 O 6 ∙4H 2 O at room temperature (~20°C) is close to 10,000.

A special feature of ferroelectrics is the nonlinear nature of the polarization dependence R, and hence the electrical displacement D on field strength E(Fig. 14.1). In this case, the dielectric constant ε of ferroelectrics turns out to depend on E. In Fig. Figure 14.2 shows this dependence for Rochelle salt at a temperature of 20°C.

All ferroelectrics are characterized by the phenomenon of dielectric hysteresis, which consists in a delay in the change in polarization R(or offsets D) when the field strength changes E. This delay is due to the fact that the value R(or D) is not only determined by the field value E, but also depends on the previous state of polarization of the sample. With cyclic changes in field strength E addiction R and offsets D from E is expressed by a curve called a hysteresis loop.

In Fig. 14.3 shows the hysteresis loop in coordinates D, E.

With increasing field E bias D in a sample that was not initially polarized, changes along the curve OAV. This curve is called the initial or main polarization curve.

As the field decreases, the ferroelectric initially behaves like an ordinary dielectric (in the region VA there is no hysteresis), and then (from the point A) the change in displacement lags behind the change in tension. When the field strength E= 0, the ferroelectric remains polarized and the magnitude of the electrical displacement is equal to
, is called residual bias.

To remove the residual bias, it is necessary to apply an electric field of the opposite direction to the ferroelectric with a strength of – . Size is usually called a coercive field.

If the maximum value of the field strength is such that the spontaneous polarization reaches saturation, then a hysteresis loop is obtained, called a limit cycle loop (solid curve in Fig. 14.3).

If, at maximum field strength, saturation is not achieved, then a so-called private cycle loop is obtained, lying inside the limit cycle (dashed curve in Fig. 14.3). There can be an infinite number of partial repolarization cycles, but the maximum displacement values D private cycles always lie on the main polarization curve OA.

Ferroelectric properties are highly dependent on temperature. For every ferroelectric there is such a temperature , above which its ferroelectric properties disappear and it turns into an ordinary dielectric. Temperature called the Curie point. For barium titanate BaTi0 3 the Curie point is 120°C. Some ferroelectrics have two Curie points (upper and lower) and behave like ferroelectrics only in the temperature range between these points. These include Rochelle salt, for which the Curie points are +24°C and –18°C.

In Fig. Figure 14.4 shows a graph of the temperature dependence of the dielectric constant of a BaTi0 3 single crystal (The BaTi0 3 crystal in the ferroelectric state is anisotropic. In Fig. 14.4, the left branch of the graph refers to the direction in the crystal perpendicular to the axis of spontaneous polarization.) In a sufficiently large temperature range, the values BaTi0 3 significantly exceed the values ordinary dielectrics, for which
. Near the Curie point there is a significant increase (anomaly).

All characteristic properties of ferroelectrics are associated with the existence of spontaneous polarization. Spontaneous polarization is a consequence of the intrinsic asymmetry of the unit cell of the crystal, leading to the appearance of an electric dipole moment in it. As a result of the interaction between individual polarized cells, they are positioned so that their electrical moments are oriented parallel to each other. The orientation of the electrical moments of many cells in the same direction leads to the formation of regions of spontaneous polarization, called domains. It is obvious that each domain is polarized to saturation. The linear dimensions of the domains do not exceed 10 -6 m.

In the absence of an external electric field, the polarization of all domains is different in direction, so the crystal as a whole is unpolarized. This is illustrated in Fig. 14.5, A, where the domains of the sample are schematically depicted, arrows indicate the directions of spontaneous polarization of various domains. Under the influence of an external electric field, a reorientation of spontaneous polarization occurs in a multidomain crystal. This process is carried out: a) displacement of domain walls (domains whose polarization is an acute angle with an external field, grow due to domains in which
); b) rotation of electrical moments - domains - in the direction of the field; c) the formation and germination of nuclei of new domains, the electrical moments of which are directed along the field.

The restructuring of the domain structure, which occurs when an external electric field is applied and increases, leads to the appearance and growth of the total polarization R crystal (nonlinear section OA in Fig. 14.1 and 14.3). In this case, the contribution to the total polarization R, in addition to spontaneous polarization, also introduces induced polarization of electronic and ion displacement, i.e.
.

At a certain field strength (at the point A) a single direction of spontaneous polarization is established throughout the crystal, coinciding with the direction of the field (Fig. 14.5, b). The crystal is said to become single-domain with the direction of spontaneous polarization parallel to the field. This state is called saturation. Field increase E upon reaching saturation, it is accompanied by a further increase in the overall polarization R crystal, but now only due to induced polarization (section AB in Fig. 14.1 and 14.3). At the same time, polarization R and offset D almost linearly depend on E. Extrapolating a linear section AB on the y-axis, one can estimate the spontaneous saturation polarization
, which is approximately equal to the value
, cut off by the extrapolated section on the ordinate axis:
. This approximate equality follows from the fact that for most ferroelectrics
And
.

As noted above, at the Curie point, when a ferroelectric is heated, its special properties disappear and it turns into an ordinary dielectric. This is explained by the fact that at the Curie temperature, a phase transition of the ferroelectric occurs from a polar phase, characterized by the presence of spontaneous polarization, to a nonpolar phase, in which spontaneous polarization is absent. In this case, the symmetry of the crystal lattice changes. The polar phase is often called ferroelectric, and the nonpolar phase is often called paraelectric.

In conclusion, we will discuss the issue of dielectric losses in ferroelectrics due to hysteresis.

Energy losses in dielectrics located in an alternating electric field, called dielectric, can be associated with the following phenomena: a) time lag in polarization R on field strength E due to molecular thermal motion; b) the presence of small conduction currents; c) the phenomenon of dielectric hysteresis. In all these cases, an irreversible conversion of electrical energy into heat occurs.

Dielectric losses result in the fact that in the section of the AC circuit containing the capacitor, the phase shift between the current and voltage fluctuations is never exactly equal
, but always turns out to be less than
, to the corner , called the loss angle. Dielectric losses in capacitors are estimated by the loss tangent:

, (14.6)

Where – capacitor reactance; R– loss resistance in the capacitor, determined from the condition: the power released at this resistance when alternating current passes through it is equal to the power loss in the capacitor.

The loss tangent is the reciprocal of the quality factor Q:
, and to determine it, along with (14.6), the expression can be used

, (14.7)

Where
– energy losses during the oscillation period (in a circuit element or in the entire circuit); W– vibration energy (maximum for a circuit element and total for the entire circuit).

Let us use formula (14.7) to estimate the energy losses caused by dielectric hysteresis. These losses, like the hysteresis itself, are a consequence of the irreversible nature of the processes responsible for the reorientation of spontaneous polarization.

Let us rewrite (14.7) in the form

, (14.8)

Where – energy loss of an alternating electric field due to dielectric hysteresis per unit volume of a ferroelectric during one period; – maximum electric field energy density in a ferroelectric crystal.

Since the volumetric energy density of the electric field

(14.9)

then with an increase in field strength by
it changes accordingly to . This energy is spent on repolarizing a unit volume of the ferroelectric and goes to increase its internal energy, i.e. to heat it up. Obviously, over one full period, the value of dielectric losses per unit volume of a ferroelectric is determined as

(14.10)

and is numerically equal to the area of ​​the hysteresis loop in coordinates D, E. The maximum energy density of the electric field in the crystal is:

, (14.11)

Where And
– amplitudes of electric field strength and displacement.

Substituting (14.10) and (14.11) into (14.8), we obtain the following expression for the dielectric loss tangent in ferroelectrics:

(14.12)

Ferroelectrics are used to manufacture capacitors of large capacity, but small sizes, to create various nonlinear elements. Many radio devices use variconds - ferroelectric capacitors with pronounced nonlinear properties: the capacitance of such capacitors strongly depends on the voltage applied to them. Varicondes are characterized by high mechanical strength, resistance to vibration, shaking, and moisture. The disadvantages of variconds are a limited range of operating frequencies and temperatures, high values ​​of dielectric losses.

9. Enter the data obtained in the upper half of Table 2, presenting the results in the form.

10. Press switch 10, which will allow you to make measurements according to the diagram in Fig. 2 (accurate voltage measurement). Carry out the operations specified in paragraphs. 3-8, replacing in paragraph 6 the calculation using formula (9) with the calculation using formula (10).

11. Enter the data obtained during calculations and measurements with switch 10 pressed (see paragraph 10) in the lower half of Table 2, presenting the measurement results in the form Operating mode Accurate current measurement Accurate voltage measurement 1. What is the purpose of the work?

2. What methods of measuring active resistance are used in this work?

3. Describe the working setup and the flow of the experiment.

4. Write down the working formulas and explain the physical meaning of the quantities included in them.

1. Formulate Kirchhoff’s rules for calculating branched electrical circuits.

2. Derive working formulas (9) and (10).

3. At what ratios R, RA and RV do they use the first measurement scheme? Second? Explain.

4. Compare the results obtained in this work using the first and second methods. What conclusions can be drawn regarding the accuracy of measurements using these methods? Why?

5. Why in step 4 is the regulator set in such a position that the voltmeter needle deviates by at least 2/3 of the scale?

6. Formulate Ohm's law for a homogeneous section of the chain.

7. Formulate the physical meaning of resistivity. What factors does this value depend on (see work No. 32)?

8. On what factors does the resistance R of a homogeneous isotropic metal conductor depend?

DETERMINATION OF SOLENOID INDUCTANCE

The purpose of the work is to determine the inductance of the solenoid by its resistance to alternating current.

Instruments and accessories: test solenoid, sound generator, electronic oscilloscope, AC milliammeter, connecting wires.

The phenomenon of self-induction. Inductance The phenomenon of electromagnetic induction is observed in all cases when the magnetic flux passing through a conducting circuit changes. In particular, if an electric current flows in a conducting circuit, then it creates a magnetic flux F penetrating this circuit.

When the current strength I changes in any circuit, the magnetic flux Ф also changes, as a result of which an electromotive force (EMF) of induction appears in the circuit, which causes an additional current (Fig. 1, where 1 is a conducting closed circuit, 2 are the lines of force of the magnetic field created circuit current). This phenomenon is called self-induction, and the additional current caused by the self-induction EMF is called extra self-induction current.

The phenomenon of self-induction is observed in any closed electrical circuit in which electric current flows, when this circuit is closed or opened.

Let's consider what the value of self-induction emf s depends on.

The magnetic flux F penetrating a closed conducting circuit is proportional to the magnetic induction B of the magnetic field created by the current flowing in the circuit, and the induction B is proportional to the strength of the current.

Then the magnetic flux Ф is proportional to the current strength, i.e.

where L is the circuit inductance, H (Henry).

From (1) we obtain: Circuit inductance L is a scalar physical quantity equal to the ratio of the magnetic flux Ф penetrating a given circuit to the magnitude of the current flowing in the circuit.

Henry is the inductance of a circuit in which, at a current of 1A, a magnetic flux of 1Wb appears, i.e. 1 Gn = 1.

According to the law of electromagnetic induction, substituting (1) into (3), we obtain the self-induction emf:

Formula (4) is valid for L=const.

Experience shows that with increasing inductance L in an electrical circuit, the current in the circuit increases gradually (see Fig. 2), and with decreasing L, the current decreases just as slowly (Fig. 3).

The current strength in the electrical circuit changes when closed. The current strength change curves are shown in Fig. 2 and 3.

The inductance of the circuit depends on the shape, size and deformation of the circuit, on the magnetic state of the environment in which the circuit is located, as well as on other factors.

Let's find the inductance of the solenoid. A solenoid is a cylindrical tube made of a non-magnetic, non-conducting material on which a thin metal conductive wire is wound tightly, turn to turn. In Fig. Figure 4 shows a cross-section of the solenoid along the diameter of a cylindrical tube (1 - magnetic field lines).

The length l of the solenoid is much greater than the diameter d, i.e.

l d. If l d, then the solenoid can be considered as a short coil.

The diameter of the thin wire is much smaller than the diameter of the solenoid. To increase the inductance, a ferromagnetic core with magnetic permeability is placed inside the solenoid. If ld, then when current flows inside the solenoid, a uniform magnetic field is excited, the induction of which is determined by the formula where o = 4·10-7 H/m – magnetic constant; n = N/l – number of turns per unit length of the solenoid; N – number of solenoid turns.

Outside the solenoid, the magnetic field is practically zero. Since the solenoid has N turns, the total magnetic flux (flux linkage) passing through the cross section S of the solenoid is equal to where Ф = BS is the flux passing through one turn of the solenoid.

Substituting (5) into (6) and taking into account the fact that N = nl, we obtain On the other hand, Comparing (7) and (8), we obtain The cross-sectional area of ​​the solenoid is equal Taking into account (10), formula (9) will be written in the form Determine The inductance of the solenoid can be achieved by connecting the solenoid to an AC electrical circuit with a frequency. Then the total resistance (impedance) is determined by the formula where R is active resistance, Ohm; L = xL – inductive reactance; = xc – capacitive resistance of a capacitor with capacitance C.

If there is no capacitor in the electrical circuit, i.e.

the electrical capacity of the circuit is small, then xc xL and formula (12) will look like Then Ohm’s law for alternating current will be written in the form where Im, Um are the amplitude values ​​of the current and voltage.

Since = 2, where is the frequency of alternating current oscillations, then (14) will take the form From (15) we obtain a working formula for determining inductance:

To complete the work, assemble the circuit according to the diagram in Fig. 5.

1. Set the sound generator to the oscillation frequency indicated by the teacher.

2. Measure the voltage amplitude Um and frequency using an oscilloscope.

3. Using a milliammeter, determine the effective value of the current in the circuit I e ; using the relation I e I m / 2 and solving it relative to I m 2 Ie, determine the amplitude of the current in the circuit.

4. Enter the data into the table.

Reference data: active resistance of the solenoid R = 56 Ohm; solenoid length l = 40 cm; solenoid diameter d = 2 cm; number of solenoid turns N = 2000.

1. Formulate the purpose of the work.

2. Define inductance?

3. What is the unit of measurement for inductance?

4. Write down the working formula for determining the inductance of the solenoid.

1. Obtain a formula for determining the inductance of a solenoid based on its geometric dimensions and the number of turns.

2. What is impedance?

3. How are the maximum and effective values ​​of current and voltage related to each other in an alternating current circuit?

4. Derive the working formula for the solenoid inductance.

5. Describe the phenomenon of self-induction.

6. What is the physical meaning of inductance?

BIBLIOGRAPHY

1. Savelyev I.G. General physics course. T.2, T. 4. – M.: Higher.

school, 2002. – 325 p.

Higher school, 1970. – 448 p.

3. Kalashnikov S.G. Electricity. – M.: Higher. school, 1977. – 378 p.

4. Trofimova T.I. Physics course. – M.: “Academy”., 2006. – 560 p.

5. Purcell E. Electricity and magnetism. - M.: Nauka, 1971.p.

6. Detlaf A.A Physics course: A textbook for college students. – M.: “Academy”, 2008. – 720 p.

7. Kortnev A.V. Workshop in physics.- M.: Higher. school, 1968. p.

8. Iveronova V.I. Physical workshop. - M.: Fizmatgiz, 1962. - 956 p.

Fundamental physical constants Atomic unit a.u.m 1.6605655(86) 10-27 kg 5, tare mass Specific charge -1.7588047(49) 1011 C/kg electron Compton K, n=h/ 1.3195909(22 )·10-15m 1, Compton waves K,p=h/ 1.3214099(22)·10-15m 1, Compton waves K,е=h/ 2.4263089(40)·10-12m 1, electron waves K ,e/(2) 3.8615905(64) ·10-13m 1, Bohr Magneton B=e/ 9.274078(36) ·10-24J/T 3, Nuclear Magne- Poison=e/ 5.050824(20 ) ·10-27J/T 3, ment neutron Mass of electron 0.9109534(47) ·10-30kg of ideal gas po under normal conditions (T0=273.15 K, p0=101323 Pa) Constant Avo- 6.022045(31 ) · 1023 mol- Boltzmann gas constant 8.31441(26) J/(mol·K) universal grap- constant G, 6.6720(41) · 10-11 N m2/kg2 vita- tion constant magico 12, 5663706144·10-7Gn/m nit Quantum magnetic- F o = 2.0678506(54) ·10-15Wb 2, radiation first radiation second radia electric (0с2) classical (4me) standard neutron proton electron 1 a.u.m .

Note: Numbers in parentheses indicate the standard error in the last digits of the given value.

Introduction

Basic safety requirements when conducting laboratory work in the educational laboratory of electricity and electromagnetism

Electrical Measurement Basics

Laboratory work No. 31. Measuring the value of electrical resistance using an R-Whitson bridge.................. Laboratory work No. 32. Studying the dependence of the resistance of metals on temperature

Laboratory work No. 33. Determining the capacitance of a capacitor using a Wheatstone C-bridge

Laboratory work No. 34. Study of the operation of an electronic oscilloscope

Laboratory work No. 35. Study of the operation of a vacuum triode and determination of its static parameters

Laboratory work No. 36. Electrical conductivity of liquids.

Determination of Faraday number and electron charge

Laboratory work No. 37. Study of the operating mode of an RC generator using an electronic oscilloscope

Laboratory work No. 38. Study of the electrostatic field

Laboratory work No. 40. Determination of the horizontal component of the earth's magnetic field strength

Laboratory work No. 41. Studying the zener diode and taking its characteristics

Laboratory work No. 42. Study of a vacuum diode and determination of the specific charge of an electron

Laboratory work No. 43. Study of the operation of semiconductor diodes

Laboratory work No. 45. Removing the magnetization curve and hysteresis loop using an electronic oscilloscope

Laboratory work No. 46. Damped electrical oscillations

Laboratory work No. 47. Study of forced electrical oscillations and reading a family of resonance curves...... Laboratory work No. 48. Measuring resistivity

Laboratory work No. 49. Determination of solenoid inductance

Bibliography

Appendix …………………………………………………… Dmitry Borisovich Kim Alexander Alekseevich Kropotov Lyudmila Andreevna Gerashchenko Electricity and electromagnetism Laboratory workshop Academic ed. l. 9.0. Conditional oven l. 9.0.

Printed in the publishing house BrGU 665709, Bratsk, st. Makarenko,

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