Is there a good experiment to demonstrate Gauss's Law for Magnetism? I'm trying to come up with a simple experiment that can demonstrate the properties of Gauss's Law for Magnetism.  I am aware that it is a mathematical representation of the fact that magnetic monopoles don't exist (at least as far as we know), but are there any simple experiments that I could set up that a high schooler would be able to understand (without any higher level physics)?
 A: If I understood your question correctly, then you want a simple experiment to demonstrate that magnetic monopoles cannot exist. The simplest way to explain this to a high schooler would be to actually break a small piece of magnet, and then make the student realize that the poles of the magnet haven't been 'split'; instead, both the pieces contain two poles. 
I can't think of anything simpler than this and I have myself used this experiment to explain the concept of magnetic monopoles. Maybe some of the more knowledgeable folks here can help you out.
A: A method that also applies to AC circuits is to move a magnet all the way through a loop connected to a volt meter and sum up all the measurement over time. (They should sum up to zero although the measurement errors may get in the way of a precise 0.)
A: I have a lab exercise that uses a Hall effect probe (Vernier MG-BTA, $58) interfaced to a computer. I put a magnet, held rigidly in some asymmetrical position, inside a cubical cardboard box with faces 17 cm on a side. We have a 17 cm square piece of paper with 1 cm strips marked on it. To measure the magnetic flux through each side, we orient the box with that side facing up, place the paper on top, and then collect data while sweeping the probe back and forth across the strips in a fixed rhythm set by a clock, one second per strip.
The software can be used to average the data taken over the 17 second period, and this average is a measure of the flux through that face of the cube. Rotating the box allows all six fluxes to be measured, and we then add them. To get rid of the effect of the ambient field, we do a measurement in the same location in space, with the box not present. (The ambient field varies quite a bit within my lab room, due to magnetic materials in the furniture and walls.) We subtract this background value from each of the six flux measurements.
This is a new lab that I'm just starting to test now, but it seems to work well. I get fluxes that cancel to better than 1% compared to the largest flux through any side.
It would be nice to be able to do this with an external magnet, but it seems physically awkward and I haven't worked out a method to do it. It would also be nice to make an electrical version of this.
