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physics
electricity and magnetism

Questions and Answers of Electricity and Magnetism

Determine the potential difference φA €“ φB between points A and B of the circuit shown in Fig. 3.23. Under what condition is it equal to zero?
A capacitor of capacitance C1 = 1.0μF charged up to a voltage V = 110 V is connected in parallel to the terminals of a circuit consisting of two uncharged capacitors connected in series and
What charges will flow after the shorting of the switch Sw in the circuit illustrated in Fig. 3.24 through sections 1 and 2 in the directions indicated by the arrows?
In the circuit shown in Fig. 3.25 the emf of each battery is equal to ε = 60 V, and the capacitor capacitances are equal to C1 = 2.0μF and C2 = 3.0μF. Find the charges which will flow
Find the potential difference φA €“ φB between points A and B of the circuit shown in Fig. 3.26.
Determine the potential at point 1 of the circuit shown in Fig. 3.27, assuming the potential at the point O to be equal to zero. Using the symmetry of the formula obtained, write the expressions for
Find the capacitance of the circuit shown in Fig. 3.28 between points A and B.
Determine the interaction energy of the point charges located at the corners of a square with the side a in the circuits shown in Fig. 3.29.
There is an infinite straight chain of alternating charges q and – q. The distance between the neighbouring charges is equal to a. Find the interaction energy of each charge with all the others.
A point charge q is located at a distance l from an infinite conducting plane. Find the interaction energy 6f that charge with chose induced on the plane.
Calculate the interaction energy of two balls whose charges ql and q2 are spherically symmetrical. The distance between the centers of the balls is equal to l. Instruction. Start with finding the
A capacitor of capacitance C1 = 1.0μF carrying initially a voltage V = 300 V is connected in parallel with an uncharged capacitor of capacitance C2: = 2.0μF. Find the increment of the
What amount of heat will be generated in the circuit shown in Fig. 3.30 after the switch Sw is shifted from position I to position 2?
What amount of heat will be generated in the circuit shown in Fig. 3.31 after the switch Sw is shifted from position 1 to position 2?
A system consists of two thin concentric metal shells of radii R1 and R2 with corresponding charges ql and q2. Find the self-energy values W1 and W2 of each shell, the interaction energy of the
A charge q is distributed uniformly over the volume of a ball of radius R. Assuming the permittivity to be equal to unity, find: (a) The electrostatic self-energy of the ball; (b) The ratio of the
A point charge q = 3.0μC is located at the centre of a spherical layer of uniform isotropic dielectric with permittivity e = 3.0. The inside radius of the layer is equal to a = 250 ram, the
A spherical shell of radius R1 with uniform charge q is expanded to a radius R21. Find the work performed by the electric forces in this process.
A spherical shell of radius R12 with a uniform charge q has a point charge q0 at its centre. Find the work performed by the electric forces during the shell expansion from radius R1 to radius R2.
A spherical shell is uniformly charged with the surface density σ, using the energy conservation law find the magnitude of the electric force acting on a unit area of the shell.
A point charge q is located at the centre O of a spherical uncharged conducting layer provided with a small orifice (Fig. 3.32). The inside and outside radii of the layer are equal to a and b
Each plate of a parallel-plate air capacitor has an area S. What amount of work has to be performed to slowly increase the distance between the plates from xl to x2 if? (a) The capacitance of the
Inside a parallel-plate capacitor there is a plate parallel to the outer plates, whose thickness is equal to η = 0.60 of the gap width. When the plate is absent the capacitor capacitance equals
A parallel-plate capacitor was lowered into water in a horizontal position, with water filling up the gap between the plates d = t.0 mm wide. Then a constant voltage V = 500 V was applied to the
A parallel-plate capacitor is located horizontally so that one of its plates is submerged into liquid while the other is over its surface (Fig. 3.33). The permittivity of the liquid is equal to e,
A cylindrical layer of dielectric with permittivity e is inserted into a cylindrical capacitor to fill up all the space between the electrodes. The mean radius of the electrode a equals R, the gap
A capacitor consists of two stationary plates shaped as a semi-circle of radius R and a movable plate made of dielectric with permittivity e and capable of rotating about an axis O between the
A flat, rectangular coil consisting of 50 turns measures 25.0 cm by 30.0 cm. It is in a uniform, 1.20-T, magnetic field, with the plane of the coil parallel to the field. In 0.222 s, it is rotated so
In a physics laboratory experiment, a coil with 200 turns enclosing an area of 12 cm2 is rotated in 0.040 s from a position where its plane is perpendicular to the earth's magnetic field to a
In a physics laboratory experiment, a coil with 200 turns enclosing an area of 12 cm2 is rotated in 0.040 s from a position where its plane is perpendicular to the earth's magnetic field to a
A closely wound search coil (Exercise 29.3) has an area of 3.20 cm2, 120 turns, and a resistance of 60.0 Ω. It is connected to a charge-measuring instrument whose resistance is 45.0 Ω.
A circular loop of wire with a radius of 12.0 cm and oriented in the horizontal xy-plane is located in a region of uniform magnetic field. A field of 1.5 T is directed along the positive z-direction,
A coil 4.00 cm in radius, containing 500 turns, is placed in a uniform magnetic field that varies with time according to B = (0.0120 T/s)t + (3.00 x 10-5 T/s4)t4. The coil is connected to a 600-0
A coil 4.00 cm in radius, containing 500 turns, is placed in a uniform magnetic field that varies with time according to B = (0.0120 T/s)t + (3.00 x 10-5 T/s4)t4. The coil is connected to a 600-0
A flat, circular, steel loop of radius 75 cm is at rest in a uniform magnetic field, as shown in an edge-on view in Fig. 29.28. The field is changing with time, according to B (t) = (1.4T)e -(0?057
Shrinking Loop A circular loop of flexible iron wire has an initial circumference of 165.0 cm, but its circumference is decreasing at a constant rate of 12.0 cm/s due to a tangential pull on the
A rectangle measuring 30.0 cm by 40.0 cm is located inside a region of a spatially uniform magnetic field of 1.25 T, with the field perpendicular to the plane of the coil (Fig. 29.29). The coil is
In a region of space, a magnetic field points in the + x-direction (toward the right). Its magnitude varies with position according to the formula Bx = B0 + bx, where Bo and b are positive constants,
A motor with a brush-and-commutators arrangement, as described in Example 29.5 has a circular coil with radius 2.5 cm and 150 turns of wire. The magnetic field has magnitude 0.060 T, and the coil
The armature of a small generator consists of a flat, square coil with 120 turns and sides with a length of 1.60 cm. The coil rotates in a magnetic field of 0.0750 T. What is the angular speed of the
A flat, rectangular coil of dimensions l and w is pulled with uniform speed v through a uniform magnetic field B with the plane of its area perpendicular to the field (Fig. 29.30).(a) Find the emf
A circular loop of wire is in a region of spatially uniform magnetic field, as shown in Fig. 29.31. The magnetic field is directed into the plane of the figure. Determine the direction (clockwise or
The current in Fig. 29.32 obeys the equation I(t) = I0e??bt, where b > O. Find the direction (clockwise or counterclockwise) of the current induced in the round coil fort >O.
Using Lenz's law, determine the direction of the current in resistor ab of Fig. 29.33 when(a) Switch S is opened after having been closed for several minutes;(b) Coil B is brought closer to coil A
A cardboard tube is wrapped with two windings of a insulated wire wound in opposite directions, as shown in Fig. 29.34. Terminals a and b of winding A may be connected to a battery through a
A sma1l, circular ring is inside a larger loop that is connected to a battery and a switch, as shown in Fig. 29.35. Use Lenz's law to find the direction of the current induced in the small ring(a)
A 1.50-m-Iong metal bar is pulled to the right at a steady 5.0 m/s perpendicular to a uniform, 0.750-T magnetic field. The bar rides on parallel metal rails connected through a 25.0-n resistor, as
In Fig. 29.37 a conducting rod of length L = 30.0 cm moves in a magnetic field B of magnitude 0.450 T directed into the plane of the figure. The rod moves with speed v = 5.00 m/s in the direction
For the situation in Exercise 29.20, find (a) The motional emf in the bar and (b) The current through the resistor.
Are Motional emfs a Practical Source of Electricity? How fast (in m/s and mph) would a 5.00-cm copper bar have to move at right angles to a 0.650-T magnetic field to generate 1.50 V (the same as a AA
Motional emfs in Transportation Airplanes and trains move through the earth's magnetic field at rather high speeds, so it is reasonable to wonder whether this field can have a substantial effect on
The conducting rod ab shown in Fig. 29.38 makes contact with metal rails ca and db. The apparatus is in a uniform magnetic field of 0.800 T, perpendicular to the plane of the figure(a) Find the
A square loop of wire with side length L and resistance R is moved at constant speed v across a uniform magnetic field confined to a square region whose sides are twice the length of those of the
A1.41-m bar moves through a uniform, 1.20-T magnetic field with a speed of 2.50 m/s (Fig. 29.40). In each case, find the emf induced between the ends of this bar and identify which, if any, end (a or
A long, thin solenoid has 900 turns per meter and radius 250 cm. The current in the solenoid is increasing at a uniform rate of 60.0 A/s. What is the magnitude of the induced electric field at a
The magnetic field within a long, straight solenoid with a circular cross section and radius R is increasing at a rate of dB/dt.(a) What is the rate of change of flux through a circle with radius r1
The magnetic field B at all points within the colored circle shown in Fig. 29.31 has an initial magnitude of 0.750 T. (The circle could represent approximately the space inside a long, thin
A long, thin solenoid has 400 turns per meter and radius 1.10 cm. The current in the solenoid is increasing at a uniform rate di/dt. The induced electric field at a point near the center of the
A metal ring 4.50 cm in diameter is placed between the north and south poles of large magnets with the plane of its area perpendicular to the magnetic field. These magnets produce an initial uniform
A long, straight solenoid with a cross-sectional area of 8.00 cm2 is wound with 90 turns of wire per centimeter, and the windings carry a current of 0.350 A. A second winding of 12 turns encircles
A dielectric of permittivity 3.5 x l0-l1 F/m completely fills the volume between two capacitor plates. For t > 0 the electric flux through the dielectric is {8.0 x 103 V· m/s3) t3. The dielectric is
The electric flux through a certain area of a dielectric is (8.76 x l03 V · m/s4)t4. The displacement current through that area is 12.9 pA at time t = 26.1 ms. Calculate the dielectric constant for
A parallel-plate, air-filled capacitor is being charged as in Fig. 29.23. The circular plates have radius 4.00 cm, and at a particular instant the conduction current in the wires is 0.280 A. (a) What
Displacement Current in a Dielectric Suppose that the parallel plates in Fig. 29.23 have an area of 3.00 cm2 and are separated by a 2.50-mm-thick sheet of dielectric that completely fills the volume
In Fig. 29.23 the capacitor plates have area 5.00 cm2 and separation 2.00 mm. The plates are in vacuum. The charging current ic has a constant value of 1.80mA. At t = 0 the charge on the plates is
Displacement Current in a Wire A long, straight, copper wire with a circular cross-sectional area of 2.1 mm2 carries a current of16 A. The resistivity of the material is 2.0 X 10-8Ω ∙
A long, straight wire made of a type-I superconductor carries a constant current I along its length. Show that the current cannot be uniformly spread over the wire's cross section but instead must
A type-II superconductor in an external field between Be1 and Bc2 has regions that contain magnetic flux and have resistance, and also has superconducting regions. What is the resistance of a long,
At temperatures near absolute zero, Bc approaches 0.142 T for vanadium, a type-I superconductor. The normal phase of vanadium has a magnetic susceptibility close to zero. Consider a long, thin
The compound SiV3, is a type-II superconductor At temperatures near absolute zero the two critical fields are Be1 = 55.0 mT and Bc2 = 15.0 T. The normal phase of SiV3 has a magnetic susceptibility
A Changing Magnetic Field you are testing a new data acquisition system. This system allows you to record a graph of the current in a circuit as a function of time. As part of the test, you are using
(a) Find the current in the large circuit 200?s after S is closed.(c) Find the direction of the current in the small circuit.(d) Justify why we can ignore the magnetic field from all the wires of the
A flat coil is oriented with the plane of its area at right angles to a spatially uniform magnetic field. The magnitude of this field varies with time according to the graph in Fig. 29.42. Sketch a
A circular wire loop of radius a and resistance R initially bas a magnetic flux through it due to an external magnetic field. The external field then decreases to zero. A current is induced in the
A coil is stationary in a spatially uniform, external, time-varying magnetic field. The emf induced in this coil as a function of time is shown if Fig. 29.43. Sketch a clear qualitative graph of the
In Fig. 29.44 the loop is being pulled to the right at constant speed v. A constant current I flows in the long wire in the direction shown.(a) Calculate the magnitude of the net emf ? induced in the
Suppose the loop in Fig. 29.45 is(a) Rotated about the y-axis;(b) Rotated about the x-axis;(c) Rotated about an edge parallel to the z-axis. What is the maximum induced emf in each case if A = 600
As a new electrical engineer for the local power company, you are assigned the project of designing a generator of sinusoidal ac voltage with a maximum voltage of 120 V. Besides plenty of wire, you
Make a Generator? You are shipwrecked on a deserted tropical island. You have some electrical devices that you could operate using a generator but you have no magnets. The earth's magnetic field at
A flexible circular loop 6.50 cm in diameter lies in a magnetic field with magnitude 0.950 T, directed into the plane of the page as shown in Fig. 29.46. The loop is pulled at the points indicated by
A Circuit within a Circuit Fig. 29.47 shows a small circuit within a larger one, both lying on the surface of a table. The switch is closed at t = 0 with the capacitor initially uncharged. Assume
Terminal Speed A conducting rod with length L, mass m, and resistance R moves without friction on metal rails. A uniform magnetic field B is directed into the plane of the figure. The rod starts from
Terminal Speed A bar of length L = 0.8 m is free to slide without friction on horizontal rails, as shown in Fig. 29.48. There is a uniform magnetic field B = 1.5 T directed into the plane of the
Antenna emf A satellite, orbiting the earth at the equator at an altitude of 400 km. has an antenna that can be modeled as a 2.0-m-long rod. The antenna is oriented perpendicular to the earth's
At the equator, the earth's magnetic field is approximately horizontal, is directed toward the north, and has a value of 8 X 10-5 T. (a) Estimate the emf induced between the top and bottom of a
A very long, cylindrical wire of radius R carries a current 10 uniformly distributed across the cross section of the wire. Calculate the magnetic flux through a rectangle that has one side of length
(c) Because of the internal resistance of the ring, the current through R at the time given in part (b) is only 3.00mA. Determine the internal resistance of the ring. (d) Determine the emf in the
The long, straight wire shown in Fig. 29.51a carries constant current 1. A metal bar with length L is moving at constant velocity V, as shown in the figure. Point a is a distance d from the wire.(a)
The cube shown in Fig. 29.52, 50.0 cm on a side, is in a uniform magnetic field of 0.120 T, directed along the positive y-axis. Wires A, C, and D move in the directions indicated, each with a speed
A slender rod, 0.240 m long, rotates with an angular speed of 8.80 rad/s about an axis through one end and perpendicular to the rod. The plane of rotation of the rod is perpendicular to a uniform
A Magnetic Exercise Machine you have designed a new type of exercise machine with an extremely simple mechanism (Fig. 29.36). A vertical bar of silver (chosen for its low resistivity and because it
A rectangular loop with width L and a slide wire with mass m are as shown in Fig. 29.53. A uniform magnetic field B is directed perpendicular to the plane of the loop into the plane of the figure.
A 25.0-cm-long metal rod lies in the xy-plane and makes an angle of 36.90 with the positive x-axis and an angle of 53.10 with the positive y-axis. The rod is moving in the + x- direction with a speed
The magnetic field B, at all points within a circular region of radius R, is uniform in space and directed into the plane of the page as shown in Fig. 29.54. (The region could be a cross section
An airplane propeller of total length L rotates around its center with angular speed '" in a magnetic field that is perpendicular to the plane of rotation Modeling the propeller as a thin, uniform
It is impossible to have a uniform electric field that abruptly drops to zero in a region of space in which the magnetic field is constant and in which there are no electric charges. To prove this
Falling Square Loop A vertically oriented, square loop of copper wire falls from a region where the field B is horizontal, uniform, and perpendicular to 1he plane of 1he loop, into a region where 1he
In a region of space where there are no conduction or displacement currents. it is impossible to have a uniform magnetic field that abruptly drops to zero. To prove this statement, use the method of
A capacitor has two parallel plates with area A separated by a distance d. The space between plates is filled with a material having dielectric constant K. The material is not a perfect insulator but
(b) Assuming E = EO, find the maximum displacement current density in the wire, and compare with 1he result of part (a). (c) At what frequency f would the maximum conduction and displacement

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