Question

In the figure, a 120-turn coil of radius 1.6 cm and resistance 4.4 Ω is coaxial with a solenoid of 230 turns/cm and diameter 2.6 cm. The solenoid current drops from 1.8 A to zero in time interval Δt = 27 ms. What current is induced in amperes in the coil during Δt?

Answer 1

here,

number of turns in solenoid , N = 230 turns/cm

N = 23000 turns/m

diameter , d2 = 2.6 cm

radius , r2 = 0.013 m

the magnetic feild due to solenoid , B = u0 * N * I

B = 1.26 * 10^-6 * 120000 * 1.8 = 0.272 T

number of turns in the circular coil , n1 = 120 turns

radius , r = 0.016 m

resistance , R = 4.4 ohm

the current induced in the circular coil , I' = N * area * ( B - B(0)) /(t * R)

I' = 120 * pi * 0.016^2 * ( 0.272 - 0) /( 4.4 * 0.027)

I' = 0.22 A

the induced current during the time dt is 0.22 A