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).

Current induced in the loop = 0.032 mA

Explanation:

emf induced in the solenoid using Faraday law e =

here, R is the radius of solenoid which is constant &   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)

μ0 n

= 4 π 10-7 x 1900 x 8 =0.019

=0.095 m V

Hence electrical current induced in the loop =   = 0.032 mA