How do Eddy Currents Affect a Magnet's Motion in a Copper Tube?

[Student149]

Homework Statement

In one of the most common examples of Lenz's Law a magnet is dropped inside a copper tube and due the induced emf and the eddy currents generated in the copper tube the magnet falls through it with constant velocity. The external force that the eddy currents oppose is obviously the acceleration due to gravity. So, the tube acts like a brake.

I have a simple doubt:

If the magnet travels towards a copper tube from left side (tube is at rest w.r.t. our reference frame), with a constant initial velocity v₀ (with no external force i.e. no acceleration due to gravity present) I assume the magnet will still 'fall' slowly due to eddy currents (since even with 0 acceleration there is still motion w.r.t. the tube).

1. But, how would the output velocity change when the magnet emerges from the other end of the tube?

Homework Equations

The Attempt at a Solution

I was told that the magnet would come to rest w.r.t. the tube if the tube is long enough. So, I assume we can tailor the length of the copper tube appropriately. This in turn would change the relative velocity of the tube and magnet w.r.t. to each other (when the magnet emerges from right side of the tube)?

Is the above interpretation correct?

 

[cnh1995]

So, I assume we can tailor the length of the copper tube appropriately. This in turn would change the relative velocity of the tube and magnet w.r.t. to each other (when the magnet emerges from right side of the tube)?

Is the above interpretation correct?

Yes. Either you make the tube small enough or you make v₀ high enough so that the magnet won't come to rest inside the tube.

 

[Student149]

Yes. Either you make the tube small enough or you make v₀ high enough so that the magnet won't come to rest inside the tube.

Thank you [Dr. Cooper :) ].

 

[Student149]

Yes. Either you make the tube small enough or you make v₀ high enough so that the magnet won't come to rest inside the tube.

One more follow up. If I am correct the tube would also move rightwards as it acts as a classical brake or barrier?

 

[cnh1995]

If I am correct the tube would also move rightwards

Yes. That would reduce the relative velocity between the two. It is consistent with the principle of Lenz's law.