A very long solenoid with a circular cross section and radius r 1 = 1.40 cm with
ID: 1472604 • Letter: A
Question
A very long solenoid with a circular cross section and radius r1= 1.40 cm with ns= 100 turns/cm lies inside a short coil of radius r2= 4.90 cm and Nc= 48 turns.
If the current in the solenoid is ramped at a constant rate from zero to Is= 1.00 A over a time interval of 80.0 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= 2.00 A over a time interval of 30.0 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= 1.40 cm =0.014m with ns= 100 turns/cm=10000turns/m lies inside a short coil of radius r2= 4.90 cm=0.0490m and Nc= 48 turns.
If the current in the solenoid is ramped at a constant rate from zero to Is= 1.00 A over a time interval of (t) =80.0 ms =80*10-3s
The induced emf in the coil is e =N dQ/dt =NA2dB/dt =NcA2uonsdi/dt
The area of the coil is (A2) =pir2 =3.14(0.0490)2 =7.539*10-3m2
uo =4pi*10-7H/m
e =N dQ/dt =NAdB/dt =NcAuonsdi/dt =48*10000*7.539*10-3m2*4pi*10-7H/m*1/80*10-3s =0.0568V
b)
The mutual inductance is given by
M =uoN1N2A2/L =uonsNcA2 =48*10000*7.539*10-3m2*4pi*10-7H/m=4.545*10-3H =4.545mH
c)
The area of the coil is A1 =pir2 =3.14*(0.014m)2 =6.154*10-4m2
The induced emf in the solenoid is =A1uonsNcdi/dt =6.154*10-4m2*48*10000**4pi*10-7H/m*2/30*10-3s=0.0247V