Re: vector products

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

Ludwik Kowalski wrote:
> > The fact is that the laws of electromagnetism are entirely
> > reflection-symmetric. ... In particular, the Maxwell
> > equations are commonly written using vector cross
> > products, which depend on the right-hand rule.

Magnetostatics directly requires the right-hand rule.
I moved the mention of Maxwell's equations to a footnote.

> 1) In other words a bivector is a scalar, not a vector.

A bivector is not a scalar.  It is the next step beyond
vector in a logical progression.  I added a table making
this explicit.  Remember to hit RELOAD on your browser.
http://www.monmouth.com/~jsd/physics/pierre-answer.htm

> We use a vector to represent a force but we use a bivector
> to represent a torque. Is this correct?

Right.

> 2) Also E is a vector but B is not a vector. Right?

E is a bivector.  One edge of E is in the timelike direction,
so for electroSTATICS you can represent the interesting part
of E by a vector, but as soon as you try to do electrodynamics
the bivector character of E becomes significant.

> 3) How would the magnetic flux be defined without
> the idea that B is a vector ?

The flux through a surface of area A is just
        flux = A dot B
where B is the magnetic field bivector.  Flux is a scalar.
(It's not a Lorentz scalar, since the notion of
dividing F in to an electric piece an a magnetic
piece is a dodgy, frame-dependent notion.  A dot F
would be a Lorentz scalar.)