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One of the educational demos often shown in schools is to drop a high strength neodymium magnet down a length of copper tube. It takes a considerable time to exit the tube because as it falls it induces a current in the copper walls that opposes the field of the magnet and slows it.

The question is how to calculate that current. So, one might start with various parameters:

(a) The thickness of the copper in the walls of the tube

(b) The tube diameter/circumference

(c) The strength of the magnet

(d) The mass of the magnet

(e) Rate of travel of the magnet

Now, working out the field interaction with the copper is rather too hard for me, so I made some approximations. It also turns out (apparently) that knowing the magnet field strength is not necessary.

I assumed that rate of travel is 10cm/s, the wall thickness is 2mm, the magnet mass is 0.1kg

When that magnet is falling at 0.1 m/s we get a power dissipation of 0.1W (P = mgh/t )

Now comes the BIG assumption - that the walls of the tube can be approximated by 2mm diameter copper loops. The resistance of each loop is 250 microOhms for a circumference of 5cm.

Using P = I^2 * R = 0.1W we get a value for I of about 6 Amps ("correct to within an order of magnitude" as physicists often say)

Does all this sound plausible?

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    $\begingroup$ Two comments - (1) is it correct to assume current circulates around the tube? - this will be the case I guess in the magnet goes in 'pole' first e.g. N at bottom and S at top. and (2) I think the mass of the magnet might normally be lower - 0.04 kg is my guess, but you may have measured it to be 0.1 kg. - Finnally I think your power dissipation method of calculation is very nice as a method for figuring out what is happening. A good approach. $\endgroup$
    – tom
    Commented Nov 26, 2014 at 13:16
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    $\begingroup$ The strength of the magnet (an input) is absent of your calculations because you're using the speed (an output) which is dependant on the strength of the magnet. $\endgroup$
    – TZDZ
    Commented Nov 26, 2014 at 13:26
  • $\begingroup$ I wonder if you could maybe calculate the power with $p=u*i$, and evaluating the voltage with lenz's law. So the big assumption is no longuer needed. $\endgroup$
    – TZDZ
    Commented Nov 26, 2014 at 13:31
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    $\begingroup$ Can you read french ? Here is some homework about this very topic. $\endgroup$
    – TZDZ
    Commented Nov 26, 2014 at 13:45
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    $\begingroup$ I've also thought about what the equations of motion would be. I built the same device, but instead of a ball on the inside of the tube I use a ring magnet on the outside so you can see it fall. Although I'm not sure how to start writing the equations I have observed that the magnet reaches a terminal velocity where the weight of the magnet reaches dynamic equilibrium with the induced Lenz force. Your equations should be able to predict what the terminal velocity would be. $\endgroup$
    – docscience
    Commented Nov 26, 2014 at 15:39

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