Question

An eight-turn coil is tightly wrapped around the outside of the long solenoid as shown below. The radius of the solenoid is 2.0 cm and it has 10 turns per centimeter. The current through the solenoid increases according to 1 Zo (1-e-at), where Γ0 4.0 A and α 2.0 x 10-2 s-1. What is the emf induced in the coil when t1.0 x 102 s? Report your answer in units of microvolts. Enter answer here 0.968 -0.968 μνο Your Answer

Answer 1

The magnetic field due to solenoid is B(t) = mu_0 n l_0 (1 - e^-infinity) The emf induced in the coil is epsilon = -d(NAB(t)/dt) = -(pi (2.0 times 10^-2)^2) d/dt (N mu_0 n l_0 (1 - e^-at)) = (pi (2.0 times 10^-2)^2) N mu_0 n l_0 (alpha e^-infinity) = (pi (2.0 times 10^-2)^2) (8) (4 pi times 10^-7) (1000) (4.0) ((2.0 times 10^-2) e^-(2.0 times 10^-2) (10 times 10^2)) = 1.37 times 10^-7 V = 0.137 mu V