Consider an infinitely long ideal solenoid with current $I$, radius $a$, turns per unit length $n$. Put a closed conducting loop around it (radius $b > a$), on a common axis through their centers.
I understand that there will be a flux $\Phi$ through the second loop, and if the solenoid's current is changing in time, the flux will also ($\frac{d\Phi}{dt} \not= 0)$.
This will induce a current in the circular loop, and I can find that current.
What about the force on the loop though? Assume the circular loop and the solenoid are held still. Lenz's law says the the induced current will act to oppose the change in flux. Then the magnetic fields repulse I suppose?
I'm having trouble pinning down what is causing what, and how one could quantify the force applied to the circular loop.
Best Answer
I think a source of difficulty lies in the fact that the solenoid is infinitely long, so strictly speaking there shouldn't be any field lines outside the solenoid. But imagine for a minute the field that the loop sets up due to the induced current. The solenoid's windings will intersect these field lines and so there will be a force on the solenoid. By Newton's third law, one would expect an equal and opposite force on the loop.