Re: [Phys-l] solenoidal and cylindrical EM sourced magnetic fields.

[John Denker <jsd@av8n.com>]

On 06/10/2011 09:38 AM, Bernard Cleyet wrote:
> My solid coil is many (to fill space) solenoids inside each other
> (co-axial)  does this make a difference?

In the far field, it does not matter.  The right answer in this case
is 1/r^3 in the far field.  There is no magnetic system on earth that
goes like 1/r^2 in the far field.

> bc again not clear.

Expand the field using a multipole series:  monopole, dipole, quadrupole, 
et cetera.

The Maxwell equation ∇•B = 0 tells us the monopole term is identically
zero.  The next leading term is the dipole term.  It falls off like 1/r^3.
In the given geometry, this term is nonzero, so in the far field it is
the dominant term.

The multipole series is used in 3 dimensions the way a Fourier series
is used in 1 dimension.  Multipole series have been used in physics
since the late 1700s (which actually makes them 50 years older than
Fourier series).

Here is an animation that shows the angular dependence of the various
terms in the multipole series:
  http://www.av8n.com/physics/wavefunctions.htm#fig-sphere-ylm-3