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

Question

If the current in the solenoid is ramped at a constant rate from zero to Is= 2.20 A over a time interval of 95.0 ms, what is the magnitude of the emf in the outer coil while the current in the solenoid is changing?

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 26.0 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= 170 turns/cm lies inside a short coil of radius r2= 3.80 cm and Nc= 32 turns. A very long solenoid with a circular cross section and radius r1= 1.50 cm with ns= 170 turns/cm lies inside a short coil of radius r2= 3.80 cm and Nc= 32 turns. 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 26.0 ms, what is the magnitude of the emf in the solenoid while the current in the coil is changing? If the current in the solenoid is ramped at a constant rate from zero to Is= 2.20 A over a time interval of 95.0 ms, what is the magnitude of the emf in the outer coil while the current in the solenoid is changing?

Explanation / Answer

mutual inductance M = pi uo Ns Np rs^2/2Rp

where Ns = no. or turns in secondary coil

Np = mo. of turns per unit length in primary coil

rp is the raidu of primary coil

rs = raidus of seconday coil

so M = 4*3.14   e-7 * 170 * 32 * 3.14 * 0.015*0.015/(2* 0.038)

M = 6.35 e-5 H

so induced emfe   = M di/dt

emf e = 6.35 e-5 * 2.2/(0.095)

emf e = 1.47 mV

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mutual inductance M = pi uo Ns Np rs^2/2Rp

where Ns = no. or turns in secondary coil

Np = mo. of turns per unit length in primary coil

rp is the raidu of primary coil

rs = raidus of seconday coil

so M = 4*3.14   e-7 * 170 * 32 * 3.14 * 0.015*0.015/(2* 0.038)

M = 6.35 e-5 H

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induced emf e = 6.35 e-5*2.6/0.026

emf e = 6.35 mV

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