A very long solenoid with a circular cross section and radius r_1 = 2.00 cm with

Question

A very long solenoid with a circular cross section and radius r_1 = 2.00 cm with n_s = 150 turns/cm lies Inside a short coll of radius r_2 = 3.80 cm and N_c = 38 turns. If the current in the solenoid is ramped at a constant rate from zero to I_s = 1.20 A over a time Interval of 51.0 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? Look up the definition of mutual inductance. You already did most of the work in the previous problem. Now reverse the situation. If the current in the short coil is ramped up steadily from zero to I_c = 2.20 A over a time interval of 16.0 ms, what is the magnitude of the emf in the solenoid while the current in the coil is changing? The mutual inductance is the same both ways: M12-M21. You don't need to start all over with Faraday's Law.

Explanation / Answer

b)

M = Nc*ns*uo*pi*r1^2

where,

ns = 150 turns/cm = 15000 turns/m

Nc = 38 turns

r1 = 2 cm

M = 38 x 15000 x 4pi x 10^-7 x pi x (2 x 10^-2)^2

M = 8.99 x 10^-4 H

a)

E = M*Is / (51*10^-3) Volt

E = (8.99 x 10^-4 x 1.20) / (51 x 10^-3)

E = 21.15 mV

c)

E = M*Ic/(16*10^-3)

E = (8.99 x 10^-4 x 2.2) / (16 x 10^-3)

E = 123.6 mV

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