# Small magnets and Lenz's Law

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1. Feb 15, 2015

### gildomar

In all demonstrations of Lenz's Law that I've seen about the falling magnet, the diameter of the magnet is roughly the same size as that of the tube. Would there be any difference if the magnet was significantly smaller?

2. Feb 15, 2015

### jasonleroy

I think the proximity of the magnet to the metal helps the cutting of the magnetic flux. If you think of the extreme, a pea sized magnetic falling through a tube with a diameter of 1 meter would need to be VERY strong to see any effect. I am by far no expert though.

3. Feb 15, 2015

Staff Emeritus
The tube produces a magnetic field in response to the change in magnetic field from the falling magnet. To produce a large force, you want those magnetic field sources near each other, and that argues for a large magnet. Additionally, all other things being equal, you get a stronger field from a bigger magnet.

4. Feb 18, 2015

### vanhees71

More precisely the time-varying magnetic field of the falling magnet leads to an electromotive force, according to Faraday's Law,
$$\frac{1}{c} \dot{\vec{B}}+\vec{\nabla} \times \vec{E}=0.$$
This leads to a current in the tube (or coil). This current leads to a magnetic field, according to the Ampere-Maxwell Law,
$$-\frac{1}{c} \dot{\vec{E}}+\vec{\nabla} \times \vec{B}' = \frac{1}{c} \vec{j}.$$
The so "induced" magnetic field acts back on the magnetic moment of falling magnet in such a way to hinder it falling (Lenz's Law).