How to Find Terminal Velocity of Conducting Loop Falling into B-field

Here is a different type of induction problem. This has to do with the long aluminum tube we have in the lab, and even though it is non-magnetic, a falling magnet in the tube falls with a terminal velocity. Huh?! The reason for this is as the magnet moves, it is changing flux in the loop. This induces a voltage (Faraday) and therefore a current (Ohm). In a tube these are called eddy currents.

But those currents then feel a force since they are in a magnetic field. This is F = Il x B. The force is upward, trying to stop the motion and therefore stopping the change in flux (Lenz). The mathematics turn out to be identical to that of a sky diver with air friction! We will get an exponential solution, and a terminal velocity. Check it out!