R o000000000000 N turns Figure P31.16 17. A coil formed by wrapping 50 turns of wire in the shape of a square is positioned in a magnetic field so that the normal to the plane of the coil makes an angle of 30.0° with the direction of the field. When the magnetic field is increased uniformly from 200 uT to 600 uT in 0.400 s, an emf of magnitude 80.0 mV is induced in the coil. What is the total length of the wire in the coil? 18. When a wire carries an AC current with a known fre- quency, you can use a Rogowski coil to determine the

R o000000000000 N turns Figure P31.16 17. A coil formed by wrapping 50 turns of wire in the shape of a square is positioned in a magnetic field so that the normal to the plane of the coil makes an angle of 30.0° with the direction of the field. When the magnetic field is increased uniformly from 200 uT to 600 uT in 0.400 s, an emf of magnitude 80.0 mV is induced in the coil. What is the total length of the wire in the coil? 18. When a wire carries an AC current with a known fre- quency, you can use a Rogowski coil to determine the

Principles of Physics: A Calculus-Based Text

5th Edition

ISBN:9781133104261

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter23: Faraday’s Law And Inductance

Section: Chapter Questions

Problem 53P

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A conducting rod is pulled with constant speed v on a smooth conducting rail as shown in Figure P32.77. A constant magnetic field B is directed into the page. If the speed of the bar is doubled, by what factor does the rate of heat dissipation change? FIGURE P32.77
Figure P32.21 shows a circular conducting loop with a 5.00-cm radius and a total resistance of 1.30 placed within a uniform magnetic field pointing into the page. a. What is the rate at which the magnetic field is changing if a counterclockwise current I = 4.60 102 A is induced in the loop? b. Is the induced current caused by an increase or a decrease in the magnetic field with time?
A uniform magnetic field B=5.44104iT passes through a closed surface with a slanted top as shown in Figure P31.59. a. Given the dimensions and orientation of the closed surface shown, what is the magnetic flux through the slanted top of the surface? b. What is the net magnetic flux through the entire closed surface?
A 200-turn flat coil of wire 30.0 cm in diameter acts as an antenna for FM radio at a frequency of 100 MHz. The magnetic field of the incoming electromagnetic wave is perpendicular to the coil and has a maximum strength of 1.001012T . (a) What power is incident on the coil? (b) What average emf is induced in the coil over one-fourth of a cycle? (c) If the radio receiver has an inductance of 2.50H, what capacitance must it have to resonate at 100 MHz?
A square coil with a side length of 12.0 cm and 34 turns is positioned in a region with a horizontally directed, spatially uniform magnetic field of 82.0 mT and set to rotate about a vertical axis with an angular speed of 1.20 102 rev/min. a. What is the maximum emf induced in the spinning coil by this field? b. What is the angle between the plane of the coil and the direction of the field when the maximum induced emf occurs?
A coil of area 0.100 m2 is rotating at 60.0 rev/s with the axis of rotation perpendicular to a 0.200-T magnetic field. (a) If the coil has 1 000 turns, what is the maximum emf generated in it? (b) What is the orientation of the coil with respect to the magnetic field when the maximum induced voltage occurs?
A parallel-plate capacitor with plate separation d is connected to a source of emf that places a time-dependent voltage V(t) across its circular plates of radius r0and area (a) Write an expression for the time rate of change of energy inside the capacitor in terms of V(t) and dV(t)/ dt. (b) Assuming that V(t) is increasing with time, identify the directions of the elecuic field lines inside the capacitor and of the magnetic field lines at the edge of the region between the plates, and then the direction of the Poynting vector S at this location. (c) Obtain expressions for the time dependence of E(t), for B(t) from the displacement current, and for the magnitude of the Poynting vector at the edge of the region between the plates. (d) From S , obtain an expression In terms of ‘(t) and dV(t)/dt for the rate at which electromagnetic field energy the region between the plates. (e) Compare the results of pails (a) and (d) and explain the relationship between them.
A square conducting loop with side length a = 1.25 cm is placed at the center of a solenoid 40.0 cm long with a current of 4.30 A flowing through its 420 turns, and it is aligned so that the plane of the loop is perpendicular to the long axis of the solenoid. The radius of the solenoid is 5.00 cm. a. What is the magnetic flux through the loop? b. What is the magnitude of the average emf induced in the loop if the current in the solenoid is increased from 4.30 A to 10.0 A in 1.75 s?
Figure P31.13 shows a uniform magnetic field. a. Can you find a (nonzero area) loop through which the magnetic flux is zero? If so, draw the loop and the field. If not, explain why not. b. Can you find a loop through which the magnetic flux is nonzero? If so, draw the loop and the field. If not, explain why not.
A solenoid with n turns per unit length has radius a. It is connected to a power supply that drives a current increasing linearly with time as I(t) = Ct, where C is a constant. Assume the magnetic field is uniform inside the solenoid. a. Find an expression for the magnetic field inside the solenoid as a function of time, and determine the magnitude of the induced electric field just inside the solenoid. b. What is the magnitude of the electric field induced just inside a solenoid that has exactly 10 turns/cm and a radius of 1.5 cm if the current increases at a rate of 0.50 A/s?
A metal rod of mass M and length L is pivoted about a hinge at point O as shown in Figure P32.80. The axis of rotation passes through O into the page. A constant magnetic field B is applied into the page. Find the ratio of the maximum electric field inside the rod to the applied magnetic field when the rod is rotated with angular speed . Assume the speed of the rod is determined by the linear speed of its center of mass, and its mass is uniformly distributed. FIGURE P32.80
Suppose a uniform magnetic field is perpendicular to the 81211-in. page of your homework and a rectangular metal loop lies on the page. The loops sides line up with the edges of the page. The magnetic field is changing with time as described by B = 3.75 103 t, where B is in teslas and t is in seconds. a. Is the magnetic field increasing or decreasing? b. Find the magnitude of the emf induced in the loop.