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A long solenoid has 1000 turns per metre. A short secondary coil of…
Question
A long solenoid has 1000 turns per metre. A short secondary coil of 200 turns and cross-sectional area 1.0 x 10^-3 m^2 is wound tightly over the solenoid (same area). The current in the solenoid is increased uniformly from 2.0 A to 6.0 A in 0.10 s. Using mu_0 = 4*pi x 10^-7, find the EMF (in millivolts) induced in the secondary coil.
✓ Verified answer: 10.053096checked by our engine — not a guess
Step-by-step solution
Mutual inductance M = mu_0 n N2 A = (4*pi x 10^-7)(1000)(200)(1.0e-3) = 4*pi x 10^-7 x 2.0e2 = 8e-5 * pi = 2.5133e-4 H. dI/dt = (6-2)/0.10 = 40 A/s. EMF = M dI/dt = 2.5133e-4 x 40 = 1.00531e-2 V = 10.0531 mV.
Final answer10.0531
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