A coil 4.00 cm in radius, containing 500 turns, is placed in a uniform magnetic field that varies with time according to B=(0.0120T/s)t+(3.00×10−5T/s4)t4. The coil is connected to a 600−Ω resistor, and its plane is perpendicular to the magnetic field. You can ignore the resistance of the coil. (a) Find the magnitude of the induced emf in the coil as a function of time. (b) What is the current in the resistor at time t = 5.00 s?

A. e = 0.0302 V+ (3.02 x 10-4 V/s)t3

B. I = 1.13 x 10-4 A

Explanation:

(a) Consider a coil with radius of r = 4.00 cm, and containing N = 500

turns, it is placed perpendicularly in a magnetic field of B, which is given

by,

B = (0.0120 T/s)t + (3.00 x 10-5 T/s) 14

the magnitude of the induced emf is,

|E 1 =

NdФВ

at

where

B = B A cos(0) = BA. Since the area is constant, then,

|E| = NA (B)

= NA ((0.0120 T/s)t + (3.00 x 10-6 T/s*) 4]

NA[(0.0120 T/s)+(1920 x 10-4 T/s*) t1

(500) (0.040)? [(0.0120 T/s)+ (1.20 x 10-4 T/s^) tº]

= 0.0302 V + (3.02 x 10-4 V/s°) 43

e = 0.0302 V+ (3.02 x 10-4 V/s) t3

(b) The induced emf at t = 5.00 s, is,

e = 0.0302 V +(3.02 x 10-4 V/s) (5.00 s)3

= 0.0680 V

if the resistance of the coil is R = 600 2, then the induced current at t = 5.00

s, is,

E 0.0680 V - 1.13 x 10-4 A

I= = 600 12

I = 1.13 x 10-4 A