Question

A very long solenoid with a circular cross section and radius r1= 1.50 cm with ns= 100 turns/cm lies inside a short coil of radius r2= 3.70 cm and Nc= 33 turns.

If the current in the solenoid is ramped at a constant rate from zero to I_s= 2.30 A over a time interval of 72.0 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 I_c= 3.10 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?

Answer 1

1)

a) given :

for solenoid :

radius= r1= 1.50 cm = 0.015 m

ns= 100 turns/cm = 10000 turns/m

for coil :

radius=r2= 3.70 cm = 0.037 m

Nc= 33 turns

When there is current through solenoid say is.

the magnetic field inside solenoid is = Bs = .

The magnetic flux through the coil is = [the magnetic field is eclosed within the crossection of solenoid]

The mutual inductance is = [answer]

The e.m.f induced in the coil is

when current in the solenoid changes from 0 to in time t = 72ms, the em.f induced in the coil is [answer]

b) Suppose instead of solenoid the current in the coil increases from 0 to   in time t=30 ms.

Also, value of mutual inductance does not depend on current, it will remain as calculated above M = 0.00029H.

therefore, the e.m.f induced in the solenoid is [answer]