Question

A circular loop in the plane of the paper lies in a 0.75 T magnetic field pointing into the paper. The loop’s diameter is changed from 20.0 cm to 6.0 cm in 0.50 s.

Determine the direction of the induced current and justify your answer.

Determine the magnitude of the average induced emf.

If the coil resistance is 2.5 Ω, what is the average induced current?

Answer 1

Giveb,

B = 0.75 T ; d1 = 20 cm = 0.2 m ; d2 = 6 cm = 0.06 m ; t = 0.5 s

We know that,

= -d/dt = -B (A2 - A1)/t

A1 = 0.0314 m^2 ; A2 = 0.002826 m^2

  = - 0.75 ( 0.002826 - 0.0314)/0.5 = 0.043 V

Hence, = 0.043 V = 43 mV.

We know from Ohm's law,

V = IR => I = V/R = 0.043/2.5 = 0.0172 A

Hence, I = 0.0172 A = 17.2 mA

Current will be counterclockwise.