a. What is the current in the loop (magnitude) at the instant when B = 1.28 T ?

Question

a. What is the current in the loop (magnitude) at the instant when B = 1.28 T ?

Express your answer with the appropriate units.

b. What is the direction of the current in the loop? (clockwise; counter clockwise)

A circular loop of wire with radius 0.0200 m and resistance 0.350 S2 is in a region of spatially uniform magnetic field, as shown in the following figure(Figure 1) The magnetic field is directed into the plane of the figure At t 0, B-0. The magnetic field then begins in th B(t) (0.360 T/s3) t creasing. w You may want to review (Pages 965-966) For related problemsolving tips and strategies, you may Figure 1 of1

Explanation / Answer

(A)

The time at which B=1.28 T is given by

1.28 = 0.360*t^3

t = (1.28/0.360)^(1/3) = 1.526 s

Using Faraday's Law, we have

emf = - d?/dt = - A dB/dt = - A d/dt ( 0.360 t^3 )

emf = - pi()*(0.0200^2)*(3*0.360)*t^2

thus, the emf at t=1.526 s is

emf = - pi()*(0.0200^2)*(3*0.360)*(1.526)^2 = -0.00315 V

if the resistance is 0.350 ohms, then the current is given by

I = V/R = 0.00315/0.350 = 0.009 A = 9mA...............Ans.

(B) Use Riht hand rule. Magnetic field is in the inward direction and current will flow in clockwise direction.

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