Electrostatic Force curved beam

Chase_md
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Hi,

I'm trying to figure out what the electrostatic force between a curved beam (see picture attached) and a standard parallel plate electrode would be. I have an equation for the critical force to induce snapping between the bi-stable states of the beam, but I need to find out one for electrostatic force to induce this snapping.

I know how to obtain the electrostatic force for 2 parallel plates, but when the beam is curved I'm having an issue. Can someone point me in the right direction here?

Thanks so much!
 

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