Electrostatic Force curved beam

[Chase_md]

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!

 

[zzzoak]

For infinite plate electric field does not depend on distance.