A very long, straight solenoid with a diameter of 3.0 is wound with 40 turns of

Question

A very long, straight solenoid with a diameter of 3.0 is wound with 40 turns of wire per centimeter, and the windings carry a current of 0.275A . A second coil having turns and a larger diameter is slipped over the solenoid so that the two are coaxial. The current in the solenoid is ramped down to zero over a period of 0.2 Part A What average emf is induced in the second coil if it has a diameter of 3.2 and 8? Express your answer in microvolts to two significant figures. e 18 Previous Answers Request Answer ncarect Try Part B What is the induced emf if the diameter is 6.4 and 16? Express your answer in microvolts to two significant figures.

Explanation / Answer

The B field of the solenoid is :

B = u0 n I

mutual inductance between the coil

M21 = N2 phi21/I1

phi = BA = B pi r^2 = u0 n I

M21 = N2 (u0 n I) pi r^2/I1

M21 = 8 x 4 x 3.14 x 10^-7 x 4000 x 0.275 x 3.14 x 0.016^2/0.275 = 3.23 x 10^-5

e2 = N2 d(phi)/dt = M2 d(i)/dt

e2 = 3.23 x 10^-5 x 0.2 = 6.46 x 10^-6 V

Hence, e = 6.46 x 10^-6 V = 6.46 uV

b)M21 = 16 x 4 x 3.14 x 10^-7 x 4000 x 0.275 x 3.14 x 0.032^2/0.275 = 2.58 x 10^-4

e = 2.58 x 10^-4 x 0.2 = 51.6 x 10^-6 V

Hence, e = 51.6 uV

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