A very long solenoid with a circular cross section and radius r 1 = 2.60 cm with

Question

A very long solenoid with a circular cross section and radius r1= 2.60 cm with ns= 170 turns/cm lies inside a short coil of radius r2= 4.10 cm and Nc= 35 turns.

If the current in the solenoid is ramped at a constant rate from zero to Is= 3.00 A over a time interval of 81.0 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= 2.10 A over a time interval of 14.0 ms, what is the magnitude of the emf in the solenoid while the current in the coil is changing?

Explanation / Answer

Here ,

time , t = 81 ms

ns = 170 turns/cm

ns = 17000 turns/m

NOw , magnitude of induced emf = rate of change of magnetic flux in outer coil

magnitude of induced emf = ns * u0*Is * pi * r1^2 * Nc/t

magnitude of induced emf = 4pi *10^-7 * 17000 * 3 *3.141* 0.026^2* 35/(0.081)

magnitude of induced emf = 0.0588 V

the magnitude of induced emf is 0.0588 V

-------------------------

for the mututal inductance , M

emf = M * di/dt

0.0588 = M * (3/.081)

M = 1.588 *10^-3 H

mutual ionductance in the coils is 1.588 *10^-3 H

-----------------------------------

For the reverse situation

emf induced in solenoid = M * di/dt

emf induced in solenoid = 1.588 *10^-3 * (2.1)/.014

emf induced in solenoid =0.238 V

the emf induced in solenoid is 0.238 V

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