Consider a circular wire loop that is getting warmer and is expanding slightly, so that its diameter can be written as \( D = D_0 + vt \). There is a magnetic field perpendicular to the plane of the loop that is increasing, so that this uniform \( B \) field has strength \( B = B_0(1 + kt) \), where \( t \) is time. (a) Find the EMF induced in the wire loop and the current induced in the loop assuming that its resistance is equal to \( R \).(b) Find the electric field inside the wire of the loop at the time \( t \).

Answered: Image /qna-images/answer/334eee38-dda1-42e8-a8df-5be36494e203.jpg

Answered: Consider a circular wire loop that is…

Similar questions

A power line carries a current I = 100 sin(380t), where I is in amps and t is in seconds. A clever engineering student wants to steal power by inducing emf in a rectangular loop of copper wire as shown below. If the student wants to induce a maximum emf in the loop equal to 1.7 V, what should be the length L of the loop? Assume that the magnetic field produced by the power line is uniform inside of the rectangular loo and equal to the magnetic field at the center of the loop. 5 mi To equipment I 0.5 m
The conducting loop of the shape shown in the figure is being pulled out of a constantBext magnetic field at a constant speed v. The left part of the loop KN is a semicircle ofradius a. The top and the bottom parts of the loop are equal, KL=NM=b. Theresistance per unit length of the conductor is r (Ω/m). During the time intervalbetween when line LM and then KN are at the border of the magnetic field,a) What is the direction ofthe induced current? Explainyour choice of direction.b) What is the EMFproduced in the loop?c) What is the size of theinduced current?
(d) Calculate the magnitude of torque (in Nm) exerted by the magnetic field on the coil at the instant when the emf is a maximum. N.m (e) What is the maximum power delivered to the coil (in W)? W (f) What If? If the coil is constructed from aluminum wire, what is the cross-sectional area of the wire (in m²)? The resistivity of aluminum is 2.82 x 10-8 Q. m. m² (g) What If? Suppose the coil now has the same number of turns, dimensions, and resistance, but the maximum current that the wire can now safely carry is 4.50 A. What now is the maximum angular speed (in rad/s) with which the coil can be rotated in the same 2.20 T magnetic field? rad/s
Shown below is a conducting rod that slides along metal rails. The apparatus is in a uniform magnetic field of strength 0.2 T, which is directly into the page. The rod is pulled to the right at a constant speed of 6 m/s by a force F. The only significant resistance in the circuit comes from the 2-Q resistor shown. (a) What is the voltage induced in the circuit? (b) What is the induced current? (c) What is the magnitude of F? (d) What are the power output of F and the power dissipated in the resistor? 2.0 2 4.0 cm Hint a. Voltage of is induced. b. An induced current of mA flows in Select an answer v direction. c. Force F of magnitude mN is needed to maintain the constant speed. d. Force F does work at the rate of mW; power of mW is dissipated in the resistor.
At the instant a current of 0.90 A is flowing through a coil of wire, the energy stored in its magnetic field is 4.0 x 10 J. What is the self-inductance of the coil (in H)?
A loop of wire enclosing an area A is placed in a region, where the magnetic field is perpendicular to the plane of the loop. The magnetic field of B varying in time according to the expression B=Be", where a is some -at constant. (a) Find the induced EMF in the loop as a function of time. (b) Find the expression for maximum induced EMF. (c) Using the following diagrams, show the directions [in Figure] of Induced-Current and Induced Magnetic Field for the circular loop 10
A uniform magnetic field B is perpendicular to the plane of a circular wire loop of radius r and with resistance R. The magnitude of the field varies with time according to B = B0e-t/T, where B0and T are constants (T is time constant). (a) Find an expresssion for the emf induced in the loop as a function of time. (b) If the loop lies in the plane of the page and the magnetic field initially points out of the page, then what is the magnitude and direction of the induced current in the loop, i.e., is it clockwise, counter-clockwise, or is there no current induced in the loop? Include a diagram for this situation.
A single-turn circular loop of wire that has a radius of 2.0 cm lies in the plane perpendicular to a spatially uniform magnetic field. During a 0.12-s time interval, the magnitude of the field increases uniformly from 0.2 T to 0.5 T. 1)Determine the magnitude of the emf induced in the loop during the time interval. (Express your answer to two significant figures.)
A circular coil of wire has radius 0.37 m, with 979 turns of wire in the coil. It is located in a magnetic field of 1.90 T, directed perpendicular to the plane of the loop. (a) What is the magnetic flux through the loop (in T m²)? (b) Now suppose the coil is attached to a 160 ohm resistor, and the magnetic field decreases to 0 in 1 second. What is the induced current in the circuit?