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Re: Energy density; the correct one



At 2:15 PM -0700 9/25/02, David Rutherford wrote:

Bob LaMontagne wrote:
>
> Whoa!
>
> David Rutherford wrote:
>
> >
> >
> > W = \int{q*(-d(phi)/dr)*dr}
> >
> > or
> >
> > W = \int{q*(-d(phi)}
> >
>
> IMHO - The scond equations is incorrect! - because the second dr
in the first
> equation is 0.

Please check your local calculus book

(d(phi)/dr)dr = d(phi)

This may or may not be true depending on what you mean by d(phi)/dr.
(What *do* you mean by that?) However, it has nothing to do with the
integral in question which is certainly not

integral of {q*(-d(phi)/dr)*dr}

but rather

integral from initial pos to final pos of {q*(-grad(phi)) dot dr_vector}

where dr_vector is an infinitesimal element of the path along which
the charge moves. If the charge doesn't move, there is no path to
integrate over, and the integral = 0.

--
John Mallinckrodt mailto:ajm@csupomona.edu
Cal Poly Pomona http://www.csupomona.edu/~ajm