Question

The current in a long solenoid of radius 4 cm and 19 turns/cm is varied with time at a rate of 8 A/s. A circular loop of wire of radius 6 cm and resistance 3 Ω surrounds the solenoid. Find the electrical current induced in the loop (in µA).

Answer 1

Answer:

Current induced in the loop = 0.032 mA

Explanation:

emf induced in the solenoid using Faraday law e = $\frac{-d\phi}{dt}=-\pi R^{2} \frac{dB}{dt}$

here, R is the radius of solenoid which is constant &  $\frac{dB}{dt}$ is the change in magnetic field.

Magnetic field inside the solenoid from B=μ0 n i -----(i)

Where, i is the current in the coil.

n= numbers of turn in per meter length.

n=19 x 100 turns/m

Differentiating equation (i)

$\frac{dB}{dt} =$ μ0 n $\frac{dI}{dt}$

= 4 π 10-7 x 1900 x 8 =0.019

$E = 3.14 X 0.42^{2} X 0.019$ =0.095 m V

Hence electrical current induced in the loop =  $\frac{E}{R} =\frac{0.095}{3}$ = 0.032 mA