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# Re: [femm] BELA electrostatic force calc

- To: femm@yahoogroups.com
- Subject: Re: [femm] BELA electrostatic force calc
- From: "iaaeinc" <iaaeinc@yahoo.com>
- Date: Fri, 11 Apr 2003 16:51:48 -0000
- User-agent: eGroups-EW/0.82

    >Equation (9) should have be:
    >
    >df = (1/2)(D*(E.n)+E*(D.n)-(D.E)*n)

    I still have some doubt about this equ :)

    >From a pure mechanicl POV, Since the charge only exists on the
    conductor surface, so the traction/stress due to the conductor
    surface charge in such E filed is the surface integral of Maxwell
    stress tensor Tij

    SurfInt{Tij*n(dS)}

    As far as why this is the same for a closed surface path, it is just
    the Gauss divergence manipulation,

    VolInt{F(dV)} = VolInt{Div(Tij)(dV)} = CloseSurfaceInt{Tij*n(dS)}

    since the force is the divergence of the traction (Maxwell stress
    tensor in this case). However, this is from the POV that the electric
    charge is assume to be eps*E everywhere - but make no sense since
    there is no actual charge in the dielectric media or the conductor.
    It just explains why the number is the same for any closed surface
    path.

    I guess this is only important if you want to subsequently apply the
    force to the conductor.

    ted

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