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## 19 February 2011

### Magnetic force on a wire demonstration

The force on a current-carrying wire is given by F = ILB, where I is the current, L is the length of the wire in the magnetic field, and B is the value of the magnetic field.  The direction of that force is given by a right-hand rule.

This seems like an easy enough concept to demonstrate in a classroom setting:  set up a horseshoe magnet, connect a wire to a battery, run the wire between the magnet poles, and watch the wire jump.  (Or, watch the wire hug the desktop, if you set the magnet poles the wrong way.)

Here's a seven-second youtube video of someone doing this very demonstration:

Now, I didn't do this demonstration at all for the first 14 years I taught.  Why not?  It seems so easy...

To get this to work, the magnetic force has to be bigger than (approximately) the weight of the wire.  Even with some big-butt magnets, this still requires a current through the wire in the neighborhood of 5-30 A.  The variable-voltage power supplies I use for circuit labs won't give out that current -- for safety reasons, they're fused somehow so that the max current they can provide is in the neighborhood of a few hundred mA.  I could use a car battery, but I don't have one around, and I don't really *want* one around... the last thing I need is to shock myself or a careless student.

But last year, when I was cleaning out part of a sputnik-era storeroom, I found this classroom-use variable-voltage power supply from 1960 or 1970.  It even had a two-pronged, non-polarized plug.  Sure enough, the current-limiting feature was absent.  I can get 10-12 amps through a single alligator-clipped wire.

I'm less concerned about frying myself with this than I am with a car battery, for two reasons -- (1) the car battery has enormous electrodes intended for contact with jumper cables, while the power supply has 1 cm diameter poles intended for alligator or banana plugs; it's hard to make accidental contact with the power supply.  (2) The power supply is plugged in to a fused power strip, and so can be easily shut off manually or automatically.  The battery keeps on rollin' no matter what.

Perfect!  I clipped two alligator wires to a long, thin piece of aluminum foil -- this reduces the weight of the wire, so the wire should "jump" more easily.  The aluminum foil wire was strung between the poles of a strong magnet.  I asked the class which way I should connect the other end of the alligator clips to the power supply.  They had to use the right hand rule to figure out what direction of current we wanted to provide an upward force on the wire.  Then I connected the wires to the power supply, flipped the switch... and the wire jumped, just like in the video.

I used the same power supply and a compass the next day to show the direction of the magnetic field created by a current-carrying wire.  Since the current in the wire is ~10 A, the magnetic field generated 1 cm away from the wire is about 10-3 T. That's 100 times the earth's magnetic field, so the compass "ignores" the earth's field and just points in the direction of the wire's field.

GCJ