1. The current I through a long solenoid with n turns per meter and radius 0.30m is changing with time as given by /= sin(120t). The magnetic field inside a solenoid is given by B = nuol where μo is the free space permeability Mo=1.26-10-6 H/m. Because of the varying current, the magnetic field inside the solenoid will also vary, and induce an electric field inside the solenoid according to Faraday's Law. In this problem you will calculate the induced electric field as a function of distance r from the central axis of the solenoid for r. a) Start by determining the magnetic flux through a through a single coil at a time of t= 1.1 s at distance r= 0.28 m from the center of the solenoid if there are, n=105 turns/m?. Hint: Is the angle for the sine function in degrees or radians? B=nuosin(120t) πr²= 1.729-10-66 Tm² b) Next determine the rate of change of the magnetic flux with time B=(nu sin(120t) ²) = 3.904-10-3 dt 3.904-10-3 Tm²/s c) The electic field can then be determined from | E-di|-|-| dl problem means the electric field is constant when integrating around the loop. E at t= 1.1 s at distance r= 0.28 m from the center of the solenoid = 2.072-10-³√ V/m Recall that the symmetry of the

1. The current I through a long solenoid with n turns per meter and radius 0.30m is changing with time as given by /= sin(120t). The magnetic field inside a solenoid is given by B = nuol where μo is the free space permeability Mo=1.26-10-6 H/m. Because of the varying current, the magnetic field inside the solenoid will also vary, and induce an electric field inside the solenoid according to Faraday's Law. In this problem you will calculate the induced electric field as a function of distance r from the central axis of the solenoid for r. a) Start by determining the magnetic flux through a through a single coil at a time of t= 1.1 s at distance r= 0.28 m from the center of the solenoid if there are, n=105 turns/m?. Hint: Is the angle for the sine function in degrees or radians? B=nuosin(120t) πr²= 1.729-10-66 Tm² b) Next determine the rate of change of the magnetic flux with time B=(nu sin(120t) ²) = 3.904-10-3 dt 3.904-10-3 Tm²/s c) The electic field can then be determined from | E-di|-|-| dl problem means the electric field is constant when integrating around the loop. E at t= 1.1 s at distance r= 0.28 m from the center of the solenoid = 2.072-10-³√ V/m Recall that the symmetry of the

College Physics

10th Edition

ISBN:9781285737027

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter20: Induced Voltages And Inductance

Section: Chapter Questions

Problem 19P

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Review. Figure P31.31 shows a bar of mass m = 0.200 kg that can slide without friction on a pair of rails separated by a distance = 1.20 m and located on an inclined plane that makes an angle = 25.0 with respect to the ground. The resistance of the resistor is R = 1.00 and a uniform magnetic field of magnitude B = 0.500 T is directed downward, perpendicular to the ground, over the entire region through which the bar moves. With what constant speed v does the bar slide along the rails?
(a) A nonferrous screwdriver is being used in a 2.00 T magnetic field. What maximum emf can be induced along its 12.0 cm length when it moves at 6.00 m/s? (b) Is it likely that this emf will have any consequences or even be noticed?
The current I through a long solenoid with n trims per meter and radius R is changing with time as given by dI/dt. Calculate the induced electric field as a function of distance r from the central axis of the solenoid.
(a) If the emf of a coil rotating in a magnetic field is zero at t = 0, and increases to its first peak at t = 0.100 ms, what is the angular velocity of the coil? (b) At what time will its next maximum occur? (c) What is the period of the output? (d) When is the output first one-fourth at its maximum? (e) When is it next one-fourth at its maximum?
A wire of length 1.0 m is wound into a single-turn planar loop. The loop carries a current of 5.0 A, and it is placed in a uniform magnetic field of strength 0.25 T. (a) What is the maximum torque that the loop will experience if it is square? (b) If it is circular? (c) At what angle relative to B would die normal to the circular coil have to be oriented so that the torque on it would be the same as the maximum torque on the square coil?
A uniform magnetic field is directed along the x axis. For what orientation of a flat, rectangular coil is the flux through the rectangle a maximum? (a) It is a maximum in the xy plane. (b) It is a maximum in the xz plane. (c) It is a maximum in the yz plane. (d) The flux has the same nonzero value for all these orientations. (e) The flux is zero in all cases.
Ail electron is moving at a speed of 1.0 104 in/s in a circular path of radius 2.0 cm inside a solenoid. The magnetic field of the solenoid is perpendicular to the plane of the electrons path. Find (a) the strength of the magnetic field inside the solenoid and (b) the current in the solenoid if it has 25 turns per centimeter.
Review. In studies of the possibility of migrating birds using the Earths magnetic field for navigation, birds have been fitted with coils as caps and collars as shown in Figure P30.1. (a) If the identical coils have radii of 1.20 cm and are 2.20 cm apart, with 50 turns of wire apiece, what current should they both carry to produce a magnetic field of 4.50 10-5 T halfway between them? (b) If the resistance of each coil is 210 . what voltage should the battery supplying each coil have? (c) What power is delivered to each coil?
Two frictionless conducting rails separated by l = 55.0 cm are connected through a 2.00- resistor, and the circuit is completed by a bar that is free to slide on the rails (Fig. P32.71). A uniform magnetic field of 5.00 T directed out of the page permeates the region, a. What is the magnitude of the force Fp that must be applied so that the bar moves with a constant speed of 1.25 m/s to the right? b. What is the rate at which energy is dissipated through the 2.00- resistor in the circuit?
A 2.00-m length of wire is held in an eastwest direction and moves horizontally to the north with a speed of 0.500 m/s. The Earths magnetic field in this region is of magnitude 50.0 T and is directed northward and 53.0 below the horizontal. (a) Calculate the magnitude of the induced emf between the ends of the wire and (b) determine which end is positive.
The homopolar generator, also called the Faraday disk, is a low-voltage, high-current electric generator. It consists of a rotating conducting disk with one stationary brush (a sliding electrical contact) at its axle and another at a point on its circumference as shown in Figure P31.33. A uniform magnetic field is applied perpendicular to the plane of the disk. Assume the field is 0.900 T, the angular speed is 3.20 103 rev/min, and the radius of the disk is 0.400 m. Find the emf generated between the brushes. When superconducting coils are used to produce a large magnetic field, a homopolar generator can have a power output of several megawatts. Such a generator is useful, for example, in purifying metals by electrolysis. If a voltage is applied to the output terminals of the generator, it runs in reverse as a homopolar motor capable of providing great torque, useful in ship propulsion.
A rectangular loop has dimensions 0.500 m by 0.300 m. The loop is hinged along the x-axis and lies in the xy-plane (Fig. P19.42). A uniform magnetic field of 1.50 T is directed at an angle of 40.0 with respect to the positive y-axis and lies parallel everywhere to the yz-plane. The loop carries a current of 0.900 A in the direction shown. (Ignore gravitation.) (a) In what direction is magnetic force exerted on wire segment ab? What is the direction of the magnetic torque associated with this force, as computed with respect to the x-axis? (b) What is the direction of the magnetic force exerted on segment cd? What is the direction of the magnetic torque associated with this force, again computed with respect to the x-axis? (c) Can the forces examined in parts (a) and (b) combine to cause the loop to rotate around the x-axis? Can they affect the motion of the loop in any way? Explain. (d) What is the direction (in the yz-plane) of the magnetic force exerted on segment bc? Measuring torques with respect to the x-axis, what is the direction of the torque exerted by the force on segment bc? (e) Looking toward the origin along the positive x-axis. Will the loop rotate clockwise or counterclockwise? (f) Compute the magnitude of the magnetic moment of the loop. (g) What is the angle between the magnetic moment vector and the magnetic field? (h) Compute the torque on the loop using the values found for the magnetic moment and magnetic field. Figure P19.42