Cross product of magnetic fields

1. Jan 14, 2010

wofsy

Is there any physical meaning to the cross product of two magnetic fields e.g. two fields generated in two different current loops?

2. Jan 14, 2010

Born2bwire

I do not think so, I am at a lost as to a situation where we would take the cross of two different magnetic fields. There is of course the usual geometrical interpretation of the cross product, indicating the anti-parallelism of the vectors, a normal to the vectors, etc., but that applies to any pair of vectors independent of their physical interpretations.

3. Jan 14, 2010

Phrak

Two loops will interact, if that's what you mean, so that the results are more than the sum of each.

4. Jan 14, 2010

wofsy

The reason I asked is that the cross product of the fields of two current loops tells you the work that one field would do on a magnetic monopole moving uniformly along the other loop.

5. Jan 14, 2010

Born2bwire

But work is a scalar quantity, not a vector.

6. Jan 14, 2010

wofsy

True. The work is a scalar factor in the cross product. If you divide out by the work you get a fundamental generator of the second cohomology of R^3 minus the two loops. For instance if the work is zero the the cross product is the curl of another vector.

7. Jan 15, 2010

Phrak

What do you mean by "moving uniformly along the other loop." Are these loops supposed to be electric-current loops or magnetic monopole-current loops?

8. Jan 16, 2010

wofsy

Sorry - the monopole doesn't need to move uniformly. It just needs to make a complete circuit of the second loop. It's just that I am used to doing the integral using the unit of arc length.