On Sun, 26 Sep 1999 00:06:51 -0400 Brian Kraut wrote:

>Is it theoretically possible to have a spherical magnet that
>has the north pole on the outside and south on the inside?

Though I'm no expert, I think the answer is yes and no (sounds like an
expert answer, doesn't it?)

Yes - you could complete your ping-pong ball with all the north poles on
the outside and all the south poles on the inside.  In the theoretical
case you could do this perfectly well and achieve exactly what you
requested.

No - this would no longer be a magnet.  Let me explain what I mean,
because what I said may not be quite true in the most literal sense.  A
magnet (my definition) is an object that creates a magnetic field.  This
field is often described by 'lines of flux' which travel through space
from one pole (let's say north) of the magnet to the other (south).
Maxwell's equations require that these lines actually be closed loops,
and this happens because the lines travel through the magnet from south
to north to close the loop.  For your sphere, any flux lines going out of
the sphere (north) must also come back into the sphere in order to reach
the south pole.  Spherical symmetry requires that the flux density be the
same at all points on the sphere.  Since the 'out' and 'in' must total
the same, and must be uniform, the only possible answer is that they
cancel completely.  This argument holds true at any point on a sphere
centered at the center of your magnet, with any radius.  Since that
includes all the known universe, your magnet does not meet my definition
at any point in the known universe!

Can anyone see a flaw in my logic?

Don

'Perpetual motion is impossible, but it perpetually moves people to try.'