Re: magnetic field of a long straight wire

[Bob LaMontagne <rlamont@POSTOFFICE.PROVIDENCE.EDU>]

I fail to see where this has clarified anything. It's hardly a tutorial.
If one doesn't know the physical significance of ^, then the arbitrary
assertion of F = 2/rho^I is just jingoism.

Cross products have handedness but give a simple mental picture of a
field, wedge products avoid handedness but leaves one with no picture
except a circulation (which certainly seems to have a handedness to me!).

It seems that it still comes down to whatever is your mnemonic of choice.
Cross products and wedge products both give the correct results, but
neither gives insight into the actual physics.

Perhaps if we had concrete examples of wedge products between a variety
of 3 dimensional vectors we could see why there is no handedness (I guess
I'm looking for a good clear definition of the wedge product). At some
point, a charge placed in a field will accelerate in a definite
direction, describable by a vector. How does a bivector field predict
this direction any better than a pseudovector field generated by a cross
product?

Bob at PC

"John S. Denker" wrote:

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