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physics
electricity and magnetism

Questions and Answers of Electricity and Magnetism

Find a potential difference φ1 €“ φ2 between points 1 and 2 of the circuit shown in Fig. 3.39 if R1 = 10 Ω, R2 = 20Ω, ε1 = 5.0 V, and ε2 = 2.0 V. The
Two sources of current of equal emf are connected in series and have different internal resistances R1 and R2. (R2 > R1) Find the external resistance R at which the potential difference across the
N sources of current with different emf's are connected as shown in Fig. 3.40.The emf's of the sources are proportional to their internal resistances, i.e. ε = aR, where a is an assigned
In the circuit shown in Fig. 3.41 the sources have emf's ε1 = 1.0 V and ε2 = 2.5 V and the resistances have the values R1 = l0 Ω and R2 = 20 Ω. The internal resistances of
In the circuit shown in Fig. 3.42 the emf of the source is equal to ε = 5.0 V and the resistances are equal to R 1 = 4.0 Ω and R2 = 6.0 Ω. The internal resistance of the source
Fig. 3.43 illustrates a potentiometeric circuit by means of which we can vary a voltage V applied to a certain device possessing a resistance R. The potentiometer has a length l and a resistance R0,
Find the emf and the internal resistance of a source which is equivalent to two batteries connected in parallel whose emf's are equal to ε1 and ε2 and internal resistances to R1 and R2.
Find the magnitude and direction of the current flowing through the resistance R in the circuit shown in Fig. 3.44 if the emf's of the sources are equal to ε1= 1.5 V and ε2 = 3.7 V
In the circuit shown in Fig. 3.45 the sources have emf's ε1 = 1.5 V, ε2 = 2.0 V, ε3 = 2.5 V, and the resistances are equal to R1 = 10Ω, R2 = 20Ω, B3 = 30Ω.
Find the current flowing through the resistance R in the circuit shown in Fig. 3.46. The internal resistances of the batteries are negligible.
Find a potential difference φA €“ φB between the plates of a capacitor C in the circuit shown in Fig. 3.47 if the sources have emf's ε1 = 4.0 V and ε 2 = 1.0 V and
Find the current flowing through the resistance R1 of the circuit shown in Fig. 3.48 if the resistances are equal to R1 = 10Ω, R2 = 20 Ω, and R3 = 30 Ω, and the potentials of points
A constant voltage V = 25 V is maintained between points A and B of the circuit (Fig. 3.49). Find the magnitude and direction of the current flowing through the segment CD if the resistances are
Find the resistance between points A and B of the circuit shown in Fig. 3.50.
Find how the voltage across the capacitor C varies with time t (Fig. 3.51) after the shorting of the switch Sw at the moment t = 0.
What amount of heat will be generated in a coil of resistance R due to a charge q passing through it if the current in the coil (a) Decreases down to zero uniformly during a time interval At; (b)
A dc source with internal resistance R 0 is loaded with three identical resistances R interconnected as shown in Fig. 3.52. At what value of R will the thermal power generated in this circuit be the
Make sure that the current distribution over two resistances Rl and R2 connected in parallel corresponds to the minimum thermal power generated in this circuit.
A storage battery with emf ε = 2.6 V loaded with an external resistance produces a current l = 1.0 A. In this case the potential difference between the terminals of the storage battery equals V
A voltage V is applied to a dc electric motor. The armature winding resistance is equal to R. At what value of current flowing through the winding will the useful power of the motor be the highest?
How much (in per cent) has a filament diameter decreased due to evaporation if the maintenance of the previous temperature required an increase of the voltage by η = 1.0%? The amount of heat
A conductor has a temperature-independent resistance R and a total heat capacity C. At the moment t = 0 it is connected to a dc voltage V. Find the time dependence of a conductor's temperature T
A circuit shown in Fig. 3.53 has resistances R1 = 20Ω and R2 = 30Ω. At what value of the resistance Rx will the thermal power generated in it be practically independent of small
In a circuit shown in Fig. 3.54 resistances R1, and R2 are known, as well as emf's ε1, and ε2. The internal resistances of the sources are negligible. At what value of the resistance
A series-parallel combination battery consisting of a large number N = 300 of identical cells, each with an internal resistance r = 0.3Ω, is loaded with an external resistance R = 10Ω.
A capacitor of capacitance C = 5.00 μF is connected to a source of constant emf ε = 200 V (Fig. 3.55). Then the switch Sw was thrown over from contact 1 to contact 2. Find the amount of
Between the plates of a parallel-plate capacitor there is a metallic plate whose thickness takes up η = 0.60 of the capacitor gap. When that plate is absent the capacitor has a capacity C =
A glass plate totally fills up the gap between the electrodes of a parallel-plate capacitor whose capacitance in the absence of that glass plate is equal to C = 20 nF. The capacitor is connected to a
A cylindrical capacitor connected to a dc voltage source V touches the surface of water with its end (Fig. 3.56). The separation d between the capacitor electrodes is substantially less than their
The radii of spherical capacitor electrodes are equal to a and b, with a < b. The interelectrode space is filled with homogeneous substance of permittivity e and resistivity p. Initially the
The electrodes of a capacitor of capacitance C = 2.00μF carry opposite charges q0 = 1.00 mC. Then the electrodes are inter- connected through a resistance R = 5.0 MΩ. Find: (a) The charge
In a circuit shown in Fig. 3.57 the capacitance of each capacitor is equal to C and the resistance, to R. One of the capacitors was connected to a voltage Vo and then at the moment t = 0 was shorted
A coil of radius r = 25 cm wound of a thin copper wire of length l = 500 m rotates with an angular velocity w = 300 rad/s about its axis. The coil is connected to a ballistic galvanometer by means of
Find the total momentum of electrons in a straight wire of length l = 1000 m carrying a current I = 70 A.
A straight copper wire of length l = 1000 m and cross-sectional area S = 1.0 mm2 carries a current I = 4.5 A. Assuming that one free electron corresponds to each copper atom, find: (a) The time it
A homogeneous proton beam accelerated by a potential difference V = 600 kV has a round cross-section of radius r = 5.0 ram. Find the electric field strength on the surface of the beam and the
Two large parallel plates are located in vacuum. One of them serves as a cathode, a source of electrons whose initial velocity is negligible. An electron flow directed toward the opposite plate prod
Two large parallel plates are located in vacuum. One of them serves as a cathode, a source of electrons whose initial velocity is negligible. An electron flow directed toward the opposite plate
The air between two parallel plates separated by a distance d = 20 mm is ionized by X-ray radiation. Each plate has an area S = 500 cm2. Find the concentration of positive ions if at a voltage V =
A gas is ionized in the immediate vicinity of the surface of plane electrode 1 (Fig. 3.58) separated from electrode 2 by a distance l. An alternating voltage varying with time t as V = Vo sin wt is
The air between two closely located plates is uniformly ionized by ultraviolet radiation. The air volume between the plates is equal to V = 500 cm a, the observed saturation current is equal to I, =
Having been operated long enough, the ionizer producing nt = 3.5.109 cm-3 ∙ s-1 of ion pairs per unit volume of air per unit time was switched off. Assuming that the only process tending to
A parallel-plate air capacitor whose plates are separated by a distance d = 5.0 mm is first-charged to a potential difference V = 90 V and then disconnected from a dc voltage source. Find the time
The gap between two plane plates of a capacitor equal to d is filled with a gas. One of the plates emits v0 electrons per second which, moving in an electric field, ionize gas molecules; this way
The gas between the capacitor plates separated by a distance d is uniformly ionized by ultraviolet radiation so that electrons per unit volume per second are formed. These electrons moving in the
A current I = 1.00 A circulates in a round thin-wire loop of radius R = 100 mm. Find the magnetic induction (a) At the centre of the loop; (b) At the point lying on the axis of the loop at a distance
A current I flows along a thin wire shaped as a regular polygon with n sides which can be inscribed into a circle of radius R. Find the magnetic induction at the centre of the polygon. Analyze the
Find the magnetic induction at the centre of a rectangular wire frame whose diagonal is equal to d = 16 cm and the angle between the diagonals is equal to φ = 30°; the current flowing in the
A current I = 5.0 A flows along a thin wire shaped as shown in Fig. 3.59. The radius of a curved part of the wire is equal to R =120 mm, the angle 2φ = 90°. Find the magnetic induction of the
Find the magnetic induction of the field at the point O of a loop with current I, whose shape is illustrated(a) In Fig. 3.60a, the radii a and b, as well as the angle φ are known;(b) In Fig.
A current I flows along a lengthy thin-walled tube of radius R with longitudinal slit of width h. Find the induction of the magnetic field inside the tube under the condition h
A current I flows in a long straight wire with cross-section having the form of a thin half-ring of radius R (Fig. 3.61). Find the induction of the magnetic field at the point O.
Find the magnetic induction of the field at the point O if a current-carrying wire has the shape shown in Fig. 3.62 a, b, c. The radius of the curved part of the wire is TI, the linear parts are
A very long wire carrying a current I = 5.0 A is bent at right angles. Find the magnetic induction at a point lying on a perpendicular to the wire, drawn through the point of bending, at a distance l
A very long wire carrying a current I = 5.0 A is bent at right angles. Find the magnetic induction at a point lying on a perpendicular to the wire, drawn through the point of bending, at a distance l
(a) Of an infinite plane carrying a current of linear density i; the vector i is the same at all points of the plane; (b) Of two parallel infinite planes carrying currents of linear densities i and
A uniform current of density j flows inside an infinite plate of thickness 2d parallel to its surface. Find the magnetic induction induced by this current as a function of the distance x from the
A direct current I flows along a lengthy straight wire. From the point O (Fig. 3.64) the current spreads radially all over an infinite conducting plane perpendicular to the wire. Find the magnetic
A current I flows along a round loop. Find the integral f B dr along the axis of the loop within the range from → ∞ to + → ∞. Explain the result obtained.
A direct current of density j flows along a round uniform straight wire with cross-section radius R. Find the magnetic induction vector of this current at the point whose position relative to the
Inside a long straight uniform wire of round cross-section there is a long round cylindrical cavity whose axis is parallel to the axis of the wire and displaced from the latter by a distance I. A
Find the current density as a function of distance r from the axis of a radially symmetrical parallel stream of electrons if the magnetic induction inside the stream varies as B = bra, where b and a
A single-layer coil (solenoid) has length l and cross-section radius R, A number of turns per unit length is equal to n. Find the magnetic induction at the centre of the coil when a current I flows
A very long straight solenoid has a cross-section radius R and n turns per unit length. A direct current I flows through the solenoid. Suppose that x is the distance from the end of the solenoid,
A thin conducting strip of width h = 2.0 cm is tightly wound in the shape of a very long coil with cross-section radius R = 2.5 cm to make a single-layer straight solenoid. A direct current I =5.0 A
N = 2.5∙103 wire turns are uniformly wound on a wooden toroidal core of very small cross-section. A current I flows through the wire. Find the ratio η of the magnetic induction inside the
A direct current I = 10 A flows in a long straight round conductor. Find the magnetic flux through a half of wire's cross-section per one meter of its length.
A very long straight solenoid carries a current I. The cross-sectional area of the solenoid is equal to S; the number of turns per unit length is equal to n. Find the flux of the vector B through the
A very long straight solenoid carries a current I. The cross-sectional area of the solenoid is equal to S; the number of turns per unit length is equal to n. Find the flux of the vector B through the
Find the magnetic moment of a thin round loop with current if the radius of the loop is equal to R = 100 mm and the magnetic induction at its centre is equal to B = 6.0μT.
Calculate the magnetic moment of a thin wire with a current I = 0.8 A, wound tightly on half a tore (Fig. 3.66). The diameter of the cross-section of the tore is equal to d = 5.0 cm, the number of
A thin insulated wire forms a plane spiral of N = 100 tight turns carrying a current I = 8 mA. The radii of inside and outside turns (Fig. 3.67) are equal to a = 50 mm and b = 100 ram. Find:(a) The
A non-conducting thin disc of radius R charged uniformly over one side with surface density σ rotates about its axis with an angular velocity w. Find: (a) The magnetic induction at the centre
A non-conducting sphere of radius R = 50 mm charged uniformly with surface density σ = 10.0μC/m2 rotates with an angular velocity w = 70 rad/s about the axis passing through its centre.
A charge q is uniformly distributed over the volume of a uniform ball of mass m and radius R which rotates with an angular velocity w about the axis passing through its centre. Find the respective
A long dielectric cylinder of radius R is statically polarized so that at all its points the polarization is equal to P = ar, where a is a positive constant, and r is the distance from the axis. The
Two protons move parallel to each other with an equal velocity v = 300 km/s. Find the ratio of forces of magnetic and electrical interaction of the protons.
Find the magnitude and direction of a force vector acting on a unit length of a thin wire, carrying a current I =8.0 A, at a point O, if the wire is bent as shown in(a) Fig. 3.68a, with curvature
A coil carrying a current I =10 mA is placed in a uniform magnetic field so that its axis coincides with the field direction. The single-layer winding of the coil is made of copper wire with diameter
A copper wire with cross-sectional area S = 2.5 mm a bent to make three sides of a square can turn about a horizontal axis OO' (Fig. 3.69). The wire is located in uniform vertical magnetic field.
A small coil C with N = 200 turns is mounted on one end of a balance beam and introduced between the poles of an electromagnet as shown in Fig. 3.70. The cross-sectional area of the coil is S = 1.0
A square frame carrying a current I = 0.90 A is located in the same plane as a long straight wire carrying a current I0 = 5.0 A. The frame side has a length a = 8.0 cm. The axis of the frame passing
Two long parallel wires of negligible resistance are connected at one end to a resistance R and at the other end to a dc voltage source. The distance between the axes of the wires is η = 20
A direct current I flows in a long straight conductor whose cross-section has the form of a thin half-ring of radius R. The same current flows in the opposite direction along a thin conductor located
Two long thin parallel conductors of the shape shown in Fig. 3.71 carry direct currents I1 and I2. The separation between the conductors is a, the width of the right-hand conductor is equal to b. I1
A system consists of two parallel planes carrying currents producing a uniform magnetic field of induction B between the planes. Outside this space there is no magnetic field. Find the magnetic force
A conducting Current-carrying plane is placed in an external uniform magnetic field. As a result, the magnetic induction becomes equal to B1 on one side of the plane and to B2, on the other. Find the
In an electromagnetic pump designed for transferring molten metals a pipe section with metal is located in a uniform magnetic field of induction B (Fig. 3.73). A current I is made to flow across this
A current I flows in a long thin-walled cylinder of radius R. What pressure do the walls of the cylinder experience?
What pressure does the lateral surface of a long straight solenoid with n turns per unit length experience when a current I flows through it?
A current I flows in a long single-layer solenoid with cross-sectional radius R. The number of turns per unit length of the solenoid equals n. Find the limiting current at which the winding may
A parallel-plate capacitor with area of each plate equal to S and the separation between them to d is put into a stream of con-ducting liquid with resistivity p. The liquid moves parallel to the
A straight round copper conductor of radius R = 5.0 mm carries a current I = 50 A. Find the potential difference between the axis of the conductor and its surface. The concentration of the conduction
In Hall effect measurements in a sodium conductor the strength of a transverse field was found to be equal to E = 5.0μV/cm with a current density j = 200 A/cm2 and magnetic induction B = = 1.00
Find the mobility of the conduction electrons in a copper conductor if in Hall effect measurements performed in the magnetic field of induction B = 100 mT the transverse electric field strength of
A small current-carrying loop is located at a distance r from a long straight conductor with current I. The magnetic moment of the loop is equal to Pm,. Find the magnitude and direction of the force
A small current-carrying coil having a magnetic moment Pm, is located at the axis of a round loop of radius R with current I flowing through it. Find the magnitude of the vector force applied to the
Find the interaction force of two coils with magnetic moments P1m, = 4.0 mA ∙ m2 and P2m, = 6.0 mA ∙ m2 and collinear axes if the separation between the coils is equal to 1 = 20 cm which
A permanent magnet has the shape of a sufficiently thin disc magnetized along its axis. The radius of the disc is R = 1.0 cm. Evaluate the magnitude of a molecular current I' flowing along the rim of
The magnetic induction in vacuum at a plane surface of a uniform isotropic magnetic is equal to B, the vector B forming an angle a with the normal of the surface. The permeability of the magnetic is

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