A very long solenoid with a circular cross section and radius r 1 = 2.20 cm with

Question

A very long solenoid with a circular cross section and radius r1= 2.20 cm with ns= 100 turns/cm lies inside a short coil of radius r2= 3.60 cm and Nc= 32 turns.

If the current in the solenoid is ramped at a constant rate from zero to Is= 1.20 A over a time interval of 65.0 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 Ic= 4.00 A over a time interval of 11.0 ms, what is the magnitude of the emf in the solenoid while the current in the coil is changing?

Explanation / Answer

Ans:-

The mutual inductance between the solenoid and short coil

= o*A1*ns*Nc = (note convert ns to turns per meter)
o**0.022^2*10000*32 = 6.11x10^-4
so emf in outer coil = M*di/dt

= 6.11x10^-4*1.2/0.065 = 11.27x10^-3V

Now reverse the situation

Emf in the coil = M* di/dt = 6.11x10^-4*4/0.011 =0.222v

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