# A doubt regarding Lenz's Law

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 falls through with a constant initial velocity $v_0$ (with no external force i.e. no acceleration due to gravity present) would it still fall slowly due to eddy currents? And I assume the answer to it is again yes since any motion should generate an eddy current. But, how would the output velocity change when the magnet emerges from the other end of the tube?
• The thing you are suppose to have noted is that the velocity is 'initially constant' even though it is 'fall'ing. How could that be? How does that affect the answer to the question? – dmckee --- ex-moderator kitten Aug 26 '17 at 17:29
• sorry what I meant is that there is no other external force, i.e. no acceleration due to gravity in my doubt. So input velocity is all we have. – J.Doe Aug 26 '17 at 17:33

## 1 Answer

The magnet falls with constant velocity only when the decelerating electromagnetic forces balance the accelerating gravitational force, resulting in no net acceleration. If there is no gravitational acceleration (say in a free-falling reference frame), there would be only a decelerating force from Lenz, and the magnet would come to a stop (asyptotically, since the electromagnetic force gets weaker as the magnet slows down). If the tube is of finite length, and there were no other drag forces, the magnet would eventually reach the other end, but it could take awhile.

• Thank you. I understand. But is there formula to predict how much distance it travels before it comes to rest or the rate of decrease in velocity ? – J.Doe Aug 26 '17 at 17:51
• There is, but I don't know it offhand. I can tell you the procedure, though: 1. Write down the force on the magnet according to the Lenz law (this will depend on velocity). 2. Use Newton's second law to write down a differential equation for the position of the magnet. 3. Solve the differential equation to find the position of the magnet as a function of time. – Gilbert Aug 26 '17 at 18:12
• Not an issue. Will look up. – J.Doe Aug 26 '17 at 18:17
• One more additional doubt: "the magnet would come to a stop (asyptotically, since the electromagnetic force gets weaker as the magnet slows down)." This would also be true if the tube and magnet are in space and not on earth or attached to some 'fixed holding point'. Am I correct? – J.Doe Aug 27 '17 at 5:36
• This is as I read a magnet trying to enter a pipe would feel repulsive force. So now I am unsure what would happen as a magnet tries to get in a hollow tube with constant velocity (in space). Lets assume we are the external observer w.r.t. whom the tube was at rest initially. – J.Doe Aug 27 '17 at 6:30