Posted: Tue Feb 12, 2008 3:04 am Post subject: Reply with quote

Okay, the above probably sounds a bit too "sure of myself," which I'm not. But still, the notion of "circuits" with respect to magnetic fields occurred to me a while back. Today I just happened to recall that someone had mentioned that magnetic fields MUST be closed and can't just amorphously "end." Hence, they can't reconnect, hence any point source of a field has to have both a start and and end at the body. No so much a start / end, as a circuit which intersects at least two points on the surface of the object.

Maybe it's too simple a conception, but it seems to make sense to me...

Seems to make sense to them too:

http://farside.ph.utexas.edu/teaching/e ... ode35.html

Happened to google "magnetic field divergence" and it was like the 4th or 5th result. Heh. They seem to say the exact same thing. Which isn't to say we should succumb to any kind of confirmation bias. But they seem to have maths to back it up! Are their maths correct? I'm pretty sure that someone could look into it. I'd assume they would be (but, better safe than sorry)? They even say that magnetism is due to electric currents on the atomic / sub-atomic scale.

Ha! Love it!

Quote:

Can we produce an isolated North or South magnetic pole: for instance, by snapping a bar magnet in two? A compass needle would always point towards an isolated North pole, so this would act like a negative "magnetic charge." Likewise, a compass needle would always point away from an isolated South pole, so this would act like a positive "magnetic charge."

Figure 32

It is clear from Fig. 32 that if we take a closed surface S containing an isolated magnetic pole, which is usually termed a magnetic monopole, then : the flux will be positive for an isolated South pole, and negative for an isolated North pole. It follows from Gauss' theorem that if then . Thus, the statement that magnetic fields are solenoidal, or that , is equivalent to the statement that there are no magnetic monopoles.

[...]

In conclusion, all steady magnetic fields in the Universe are generated by circulating electric currents of some description. Such fields are solenoidal: that is, they never begin or end, and satisfy the field equation

This, incidentally, is the second of Maxwell's equations. Essentially, it says that there is no such thing as a magnetic monopole. We have only proved that for steady magnetic fields, but, in fact, this is also the case for time-dependent fields (see later).