- #1

TheDemx27

Gold Member

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I was reading this paper, and was confused by a result in section 2-A. (Heck they even mention they weren't expecting it themselves). The purpose of the paper is to find the linear charge density for a wire and they use several models, the first of which treats the wire like an ellipsoid. They end up with an expression that doesn't depend on ##x##, ##y##, or ##z##, but only on ##Q## and ##a##:

##\lambda(x)=\frac{Q}{2a}##

Meaning that the charge density is constant as you move along the x-axis.

Its pretty crazy how nicely things simplify in the paper.

Certainly there must be something wrong with this ellipsoid model, since we

*know*that the charge is supposed to collect at the ends of an object. (right?) I mean, that's how static wicks on planes operate. Not only that, but

*every other*model used in the paper produces a charge distribution you would expect: Higher charge density near the ends of the object.

I'm pretty sure that using ellipsoids like they did isn't a good way to model this judging by the discrepancy in the results. This is also coupled with the fact that it is counter intuitive for me.

Is this model really correct?

Are ellipsoids really mathematically special objects that have linear charge distributions?

Thanks in advance to anyone who can clear things up.