A very long solenoid with a circular cross section and radius r_1 = 2.90 cm with
ID: 1603367 • Letter: A
Question
A very long solenoid with a circular cross section and radius r_1 = 2.90 cm with n_s = 130 turns/cm lies inside a short coil of radius r_2 = 4.80 cm and N_c = 32 turns. If the current in the solenoid is ramped at a constant rate from zero to I_s = 1.00 A over a time interval of 40.0 ms, what is the magnitude of the emf in the outer coil while the current in the solenoid is changing? What is the mutual inductance between the solenoid and the short coil? Now reverse the situation. If the current in the short coil is ramped up steadily from zero to I_c = 3.20 A over a time interval of 24.0 ms, what is the magnitude of the emf in the solenoid while the current in the coil is changing?Explanation / Answer
Mutual inductance of the solenoid will be:
1)M = Nc n mu0 A1
M = Nc n mu0 pi r1^2
M = 32 x (130 x 10^2) x (4 pi x 10^-7) x (3.14 x 0.029^2) = 1.34 x 10^-3
e = M (di/dt)
e = 1.34 x 10^-3 (1/40 x 10^-3) = 0.0335 Volts
Hence, e = 0.0335 Volts
2)M = 1.34 x 10^-3 H
(Calculated in 1)
3)e = M (di/dt)
e = 1.34 x 10^-3 (3.2/24 x 10^-3) = 0.178 V
Hence, e = 0.178 V