### Today is Fara Day

It’s been my job to wind coils in the lab, and at some point I acquired a strong rare-earth magnet, so I decided to play around with Faraday’s law: A changing magnetic fields will induce a potential difference in a loop of wire, and with many turns present in a coil each turn can contribute, so this can be be a significant effect. I set up an oscilloscope to measure the voltage in the coil and took some movies, which allowed me to grab good still shots and do this without needing more than two hands or a prehensile appendage.

Faraday’s law tells us that
$$V = -Nfrac{dphi}{dt}$$

So lots of windings (N) helps, and the driving effect is the rate at which the flux changes.

Here’s what the signal looks like when I pushed the magnet in and the pulled it out after a short delay (and repeated as necessary); you can see the pulse as the coil sees an increasing field (and therefore flux) as it gets closer to (and enters) the coil, and then the signal drops back to zero when the magnet stops moving.

But that’s not the only way for the coil to see a changing magnetic field. You can flip the magnet, and this actually induces a larger voltage in the coil

You can see that this gives a signal about 4x as large as the simple motion; flipping the magnet with my fingers happened quickly, and changing the direction by 180º gives you the maximum change in the flux that you can achieve, and you get a change in sign as well — the flux starts out at a maximum inside the coil, and the rotation causes it to decrease, increase again, and is a constant when the rotation stops. Decreasing and increasing flux give opposite signs for the induced voltage.

So what happens if you combine the two motions? Here’s the signal from dropping a spinning magnet through the coil

I think the signal here can be broken up into two parts: the drop and spin is before the center division, and the behavior from ~50 milliseconds before that division is from the magnet bouncing off of the carpeted floor and coming to rest. The drop & spin, show the envelope of the motion we see in the first plot with the oscillating behavior of the spinning. It looks like there are 5 rotations during the drop, which was from ~1 meter (though the coil itself is shorter), which would take ~450 ms. In the first part of the curve the magnet is still outside the coil, so the flux is getting bigger, which means the signal size increases. I’m not exactly sure why the signal amplitude levels off in the second half of the drop; it’s entirely possible the magnet’s rotation axis was changing direction as it fell, and any component along the axis of the cylinder won’t contribute to the signal we see here. It would be nice to have an independent way of measuring the spin effects to match them up with the electronic signal; this might be a reasonable physics-101 lab measurement to do.

## 1 Comment so far

1. Uncle Al on July 5th, 2011

Supermagnet bullets (jacketed – they’re brittle) magnetized normal to their spin axis, fired through a rifled barrel (large electrical resistance helps) into a finely thickly wound coil. Compare exit speed with coil open or closed. This looks like a job for Mythbusters! – the bullet-proof vacuum.

Second case: The control, magnetized parallel to spin. This will detect spin precession, especially for elongated bullets. Third case: Spark gap the coil’s ends. Breakdown, then sudden braking.

http://en.wikipedia.org/wiki/M16_rifle
http://en.wikipedia.org/wiki/Rifling
M16A2 rifle, 5.56x45mm cartridge, 3110 ft/s muzzle velocity, 1-in-7 twist, 321,000 rpm, 5353 Hz.

Limiting equatorial velocity for a rotating solid sphere (independent of the sphere’s radius!) is v_lim = sqrt[(2S)/(rho)] where S is the yield strength and rho the density.