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If the current in the solenoid is ramped at a constant rate from zero to I s = 2

ID: 1554277 • Letter: I

Question


If the current in the solenoid is ramped at a constant rate from zero to Is= 2.10 A over a time interval of 98.0 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= 2.60 A over a time interval of 15.0 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= 1.50 cm with ns= 270 turns/cm lies inside a short coil of radius r2= 3.20 cm and Nc= 32 turns.

Explanation / Answer

rate of change in magnetic flux through solenoid is d(phi_B) = A*(dB/dt) = A*mu_o*n*(dI/dt) = 3.142*(0.015^2)*4*3.142*10^-7*27000*(2.1/0.098) = 5.14*10^-4 Wb/sec

this same rate of change in flux can be observed in coil also


so induced emf is e = rate of change of magnetic flux

e = 5.14*10^-4 V

Mutual inductance

e2 = M*dI1/dt

M = e2/(dI1/dt) = (5.14*10^-4)/(2.1/0.098) = 24*10^-6 H

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if rate of change of current in coil is dI/dt = 2.6/0.015 = 173.34 A/sec

rate of change of flux is d(phi_B)/dt = A*dB/dt =A*mu_o*n*(dI/dt) = 3.142*(0.015^2)*4*3.142*10^-7*32*(2.6/0.015) = 4.93*10^-6 Wb/sec

emf is e = 4.93*10^-6 V

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