magnetic field of a long straight wire

["John S. Denker" <jsd@MONMOUTH.COM>]

Ludwik Kowalski wrote:
> I second Robert's plead for a little tutorial "for the rest of us."
...
> Please assume that the reader is going to be a student in the
> first semester of the first physics course without calculus.

1) As you may have noticed, the way I start a tutorial
is by doing lots of examples.

2) The example du jour is the magnetic field of a long
straight wire, calculated from scratch using Clifford
Algebra.  No nasty cross products anywhere to be seen.
Just start from
        del F = 4pi J
and turn the crank.

This doesn't entirely comply with Ludwik's "without calculus"
request ... but it's not much calculus.  To carry out the
calculation, you need to be able to differentiate x/(x^2+y^2)
with respect to x.

It's not tricky or even laborious.  I worked out the whole
thing on about half a page of paper.  With diagrams and
explanations and remarks it comes out to just over two pages.

The final expression for the field is
        F = (2/rho) I
which is just amazingly elegant.


http://www.monmouth.com/~jsd/physics/straight-wire.htm
http://www.monmouth.com/~jsd/physics/straight-wire.djvu
http://www.monmouth.com/~jsd/physics/straight-wire.pdf