A very long solenoid with a circular cross section and radius r1= 1.70 cm with n
ID: 1454997 • Letter: A
Question
A very long solenoid with a circular cross section and radius r1= 1.70 cm with ns= 250 turns/cm lies inside a short coil of radius r2= 3.50 cm and Nc= 26 turns.
1) If the current in the solenoid is ramped at a constant rate from zero to Is= 1.20 A over a time interval of 62.0 ms, what is the magnitude of the emf in the outer coil while the current in the solenoid is changing?
2) What is the mutual inductance between the solenoid and the short coil?
3) Now reverse the situation. If the current in the short coil is ramped up steadily from zero to Ic= 2.80 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? PLEASE I NEED THIS ASAP
Explanation / Answer
given data
r1= 1.70 cm
,ns= 250 turns/cm ,
r2= 3.50 cm,
Nc= 26 turns,
Is= 1.20 A,
t= 62.0 ms,
1. 250 turns/cm = 25000 turns/metre
The field from the solenoid is B = 0.n.I
So the rate of change of this field. dB/dt = 0.n.dI/dt
= 4x10^-7 x 25000 x 1.2/(62x10^-3)
=6.077 T/s
The area of the outer coil = x 0.0350² = 3.84x10^-3 m²
Induced emf = rate of change of flux linkage
NA(dB/dt) =26*3.84x10^-3 *6.077 =0.606 V
2.
What is the mutual inductance between the solenoid and the short coil?
The mutual inductance = o*A1*ns*Nc
4*3.14*10^-7*3.84*10^-3*25000*26 = 0.003135 Henry
3.E =o*A1*ns*Nc *Ic / t
E=4*3.14*10^-7*25000*26*250*2.8/0.015 = 38098 V