A very long solenoid with a circular cross section and radius r 1 = 3.00 cm with

Question

A very long solenoid with a circular cross section and radius r1= 3.00 cm with ns= 240 turns/cm lies inside a short coil of radius r2= 3.60 cm and Nc= 41 turns.

Now reverse the situation. If the current in the short coil is ramped up steadily from zero to Ic= 3.00 A over a time interval of 23.0 ms, what is the magnitude of the emf in the solenoid while the current in the coil is changing?

A very long solenoid with a circular cross section and radius r1= 3.00 cm with ns= 240 turns/cm lies inside a short coil of radius r2= 3.60 cm and Nc= 41 turns. Now reverse the situation. If the current in the short coil is ramped up steadily from zero to Ic= 3.00 A over a time interval of 23.0 ms, what is the magnitude of the emf in the solenoid while the current in the coil is changing?

Explanation / Answer

N = 240 turns/cm = 24000 turns/m

mutual inductance M = Nc*N*uo*pir1^2 H

M = 41*24000*4pix10^-7*pi*(3x10^-2)^2

M = 3.496x10^-3 H

E = M*Ic/(70*10^-3)

E = 3.496x10^-3*3 / (23x10^-3)

E = 0.456 V

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