If the current in the solenoid is ramped at a constant rate from zero to I s = 1

Question

If the current in the solenoid is ramped at a constant rate from zero to Is= 1.70 A over a time interval of 61.0 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= 2.70 A over a time interval of 27.0 ms, what is the magnitude of the emf in the solenoid while the current in the coil is changing?
4.94×10-2 V

A very long solenoid with a circular cross section and radius r1= 1.30 cm with ns= 200 turns/cm lies inside a short coil of radius r2= 4.50 cm and Nc= 37 turns.

Explanation / Answer

here,

r1 = 0.013 m

ns = 20000 turns/m

r2 = 0.045 m

Nc = 37 turns

Is = 1.7 A

(a)

the magnitude of the emf in the outer coil while the current in the solenoid is changing , EMF = u0 * ns * dIs/dt * Nc * pi * r2^2

EMF = 1.26 * 10^-6 * 20000 * 1.7/0.061 * 37 * pi * 0.045^2

EMF = 0.165 V

(b)

let the coefficient of mutual inductance be M

EMF = - M * di/dt

0.165 = - M * 1.7 /0.065

M = - 6.3 * 10^-3 H

(c)

on reversing ,

the emf induced in the solenoid , EMF = ((u0 * nc * dI/2r2) /dt) * pi * r1^2 * Ns

EMF = ( 1.26 * 10^-6 * 37 * 2.7 * 3.14 * 0.013^2 * 2000)/( 0.027 * 2 * 0.045)

EMF = 5.5 V

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