A very long solenoid with a circular cross section and radius r 1 = 1.90 cm with

Question

A very long solenoid with a circular cross section and radius r1= 1.90 cm with ns= 300 turns/cm lies inside a short coil of radius r2= 4.30 cm and Nc= 33 turns.

A) If the current in the solenoid is ramped at a constant rate from zero to Is= 2.80 A over a time interval of 76.0 ms, what is the magnitude of the emf in the outer coil while the current in the solenoid is changing?

B)What is the mutual inductance between the solenoid and the short coil?

C) Now reverse the situation. If the current in the short coil is ramped up steadily from zero to Ic= 3.00 A over a time interval of 16.0 ms, what is the magnitude of the emf in the solenoid while the current in the coil is changing?

Explanation / Answer

Given that

A very long solenoid with a circular cross section and radius r1= 1.90 cm =0.019m with ns= 300 turns/cm=30000turns/m lies inside a short coil of radius r2= 4.30 cm=0.0430m and Nc= 33 turns.

If the current in the solenoid is ramped at a constant rate from zero to Is= 2.80 A over a time interval of (t) =76.0 ms =76*10-3s

The induced emf in the coil is e =N dQ/dt =NA2dB/dt =NcA2uonsdi/dt

The area of the coil is (A2) =pir22 =3.14(0.0430)2 =0.00580586 =5.805*10-3m2

uo =4pi*10-7H/m

e =N dQ/dt =NAdB/dt =NcAuonsdi/dt =33*30000*5.805*10-3m2*4pi*10-7H/m*2.80/76*10-3s =0.0041V

b)

The mutual inductance is given by

M =uoN1N2A2/L =uonsNcA2 =33*30000*5.805*10-3m2*4pi*10-7H/m=7.218*10-3H =7.218mH

c)

The area of the coil is A1 =pir2 =3.14*(0.019m)2 =1.133*10-3m2

The induced emf in the solenoid is =A1uonsNcdi/dt =1.133*10-3m2*33*30000**4pi*10-7H/m*3/16*10-3s=0.264V

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