RE: [SI-LIST] : question electrostatic solvers

Date: Tue Aug 29 2000 - 14:42:38 PDT

Jan,

you described the physics perfectly right.

div D = 0 (Maxwell eq.)
Since D=E+4*pi*P, div(E+4*pi*P)=0. But divE=4*pi*rho, where rho is charge
surface density at the dielectric interface. Therefore, div P = - rho.

> -----Original Message-----
> From: [email protected] [mailto:[email protected]]
> Sent: Tuesday, August 29, 2000 8:12 AM
> To: [email protected]
> Subject: [SI-LIST] : question electrostatic solvers
>
>
> hello si-list,
>
> I have a question concerning method of moments electrostatic solvers.
>
> Some (I think most) general-purpose electrostatic solvers replace the
> dielectric-dielectric interfaces with an unknown surface
> charge. So these solvers
> atack a free-space problem.
>
> My question is: on what is this based? Why is one allowed to
> remove the dielectra
> and replace them by a surface charge?
>
> I do understand (better I think) the following: the
> divergence of the polarization P
> equals the polarization charge in the dielectric material. A
> volume integral of div P
> can be reduced to a surface integral over the enclosed volume
> (divergence theorem). So
> it seems likely that the potential for a location outside the
> dielectric volume can
> be calculated using the surface charge and a volume
> integration is avoided. Is this
> correct or am I wrong?
>
> I have checked Paul's book (Analysis of Multiconductor Lines)
> (Electromagnetic Fields, page 73+). Paul discusses the matter
> briefly but gives no
> details. Van Bladel is, as usual, thourough, but I am missing
> some points in his
> derivation. It will take somewhile to digest this matter.
>
> It would be great if someone could, in plain simple words,
> explain the physics behind
> this matter or direct me to some detailed exposition or reference(s).
>
> regards,
>
> Jan Vercammen
> Agfa-Gevaert NV
>
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