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# Re: [femm] BELA electrostatic force calc

- To: femm@yahoogroups.com
- Subject: Re: [femm] BELA electrostatic force calc
- From: David Meeker <dmeeker@ieee.org>
- Date: Fri, 11 Apr 2003 10:12:51 -0400
- In-reply-to: <b74ak9+q68c@eGroups.com>
- References: <b74ak9+q68c@eGroups.com>
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`iaaeinc wrote:`

>     I have a question about the BELA electrostatic force calculation of
>     the conductor dielectric analysis. If you want to get the effective
>     pressure/force due to the surface charge in the electrostastic field,
>     isn't that should be computed from the Maxwell stress equation
>     integrated on the conductor surface only ? The manual says you should
>     do the line integral away from the surface (If you do so, the there
>     is no charge in the outer dielectric media ?). Also, the equation
>     does not seems to be correct

> `df = 0.5(D(H*n)+H(D*n)-(D*E)n))`

>     Shouldn't that be the integral of Tij*n on the conductor surface
>     (line integral)? Tij is the Maxwell stress tensor from the D,E,H,B.

> `thanks`
> `ted`

`I appear to have thoroughly bolloxed this equation in the manual. Equation (9) should have be:`
`df = (1/2)(D*(E.n)+E*(D.n)-(D.E)*n)`
`This should be the same as Tij*n if the magnetic terms in the stress tensor are zero. Thanks a lot for pointing this out--I'll fix this in the manual. This appears to be an error in just the manual--the correct equation is implemented in the program.`
`Perhaps somewhat counterintuitively, the surface upon which the integral is performed doesn't /have/ to be the conductor's surface. The surface upon which the integral is performed can be any surface that encloses the conductor--the total force result is theoretically the same . Although this is a commonly cited result, I couldn't think of a way of deriving this that lends much intuitive insight into why this should be so--anyone have any good reference for this?`
`Dave`
`P.S. -- I guess that the McFee "Tunable volume integration for force calculation" paper kind of shows this, because it starts out with stress tensor applied to the surface of a body and derives a more general formulation that turns this original form into a volume integration around the region of interest, incorporating some weighting function denoted as g. By suitable choice of g, you could make this look like the stress tensor surface integral applied to an arbitrary surface in the volume around the region of interest. However, this doesn't lead a lot of "intuitive insight." The McFee paper also considers just the magnetic case, although the math ought to be similar for electrostatics.`

    --
    David Meeker
    email: dmeeker@ieee.org
    www: http://femm.berlios.de/dmeeker

- References:
  - BELA electrostatic force calc
    - From: "iaaeinc" <iaaeinc@yahoo.com>

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