I've recently started studying Laplace's equation and it's solution under various simple circumstances in electrostatics. I tried to solve the equation for a parallel plate condenser system, but I couldn't meet the boundary conditions. I had two plates, one placed on xz plane at y=0 (with potential = 0), second parallel to it, at y=d (with potential [itex]V_0[/itex]). I placed them such that they're symmetrical in x and z, i.e., y axis crosses midpoints of plates; therefore the potential should be an even function of x and z. Noting that [itex]V(0,0,0) = 0[/itex] I wrote the solution:(adsbygoogle = window.adsbygoogle || []).push({});

[tex]A\cosh(kx) \cosh(lz) \sinh(my)[/tex]

with [tex]k^2 + l^2 + m^2 = 0[/tex] and let [itex]A[/itex] be any complex number.

I assumed that potential should drop to zero when [itex]x,z \to \pm \infty[/itex], and this's the boundary condition that doesn't meet with my "solution".

Can anyone help me working out the solution, or forward me to some resource on it?

Thanks!

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# Homework Help: Laplace equation for parallel plate condersers

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