Induced Current Problem from the professor not in our textbook

[stevencarlover]

Homework Statement

A long straight solenoid of cross-sectional area 400 cm^2 is wound with 10 turns of wire per centimeter, and the winding carry a current in the direction shown (downward). A small ring of radius 5.00 cm and resistance 0.300 ohms is placed at the center of the solenoid. If the current in the solenoid increases from 20.0 Amps to 60.0 Amps in 2.50 seconds, find the direction and magnitude of the current induced in the ring during this period.

Homework Equations

M = (Mu0)(A)(N1)(N2)/L
emf = M(di/dt)
emf = I *R

The Attempt at a Solution

Since the question does not give values for N1, N2, and L I do not know how to find the mutual inductance and thus the induced current in the ring.

 

[cnh1995]

If you know the current through the solenoid, can you find the magnetic flux passing through the ring?

 

[rude man]

M = (Mu0)(A)(N1)(N2)/L
emf = M(di/dt)
emf = I *R
Since the question does not give values for N1, N2, and L I do not know how to find the mutual inductance and thus the induced current in the ring.

Your formula assumes no flux coupled into the solenoid from the ring, i.e. ring current is assumed small (L_ring I_ring << M I_solenoid to be precise. Strictly speaking your ring emf = M(di/dt) - L_ring(di_ring/dt). But you have the right formula for emf since computing the second term is exceedingly difficult. I mention it only for the record.

In which case the question does give N1, N2 and l (your L should be rewritten l to diIstinguish it from inductance). All you need do is find A.

Or, better, follow cnh1995's suggestion, again assuming the solenoid flux is independent of the ring current.