A very long, straight solenoid with a cross-sectional area of 2.11 cm2 is wound

Question

A very long, straight solenoid with a cross-sectional area of 2.11 cm2 is wound with 86.4turns of wire per centimeter. Starting at t = 0, the current in the solenoid is increasing according to i(t)= ( 0.171 A/s2 )t2. A secondary winding of 5 turns encircles the solenoid at its center, such that the secondary winding has the same cross-sectional area as the solenoid.

What is the magnitude of the emf induced in the secondary winding at the instant that the current in the solenoid is 3.2 A ?

Express your answer with the appropriate units.

Explanation / Answer

A(t) =(0.171 A/s2 )t^2

32= (0.171 A/s2 )t^2   => t= 13.7s

e= d/dt = NA*dB/dt = 5*2.11*10^-4*[(32-0)/(13.7)] = 2.5*10^-3 V

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