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# Capacitance with Permittivity (Laplace's Equation)

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A parallel plate capacitor has its plates at x = o and x = d. The space between the plates is filled with an inhomogenous material with permittivity: {see attachment}.

The plate at x = d is maintained at Vo while the plate at x = o is grounded.

(a) Solve Laplace's Equation for V(x)

(b) Find the field {see attachment} between the plates.

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##### Solution Summary

The solution provides calculations for a parallel plate capacitor. Calculations for Laplace's Equation and the field between plates are included.

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