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Potential Inside a Box

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A rectangular box with x dimension a, y dimension b, and z dimension c is depicted in the diagram. If the electric potential on all sides except z=c is zero, and the potential on the side z=c is V(x,y), Find the potential inside the box.

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A rectangular box with x dimension a, y dimension b, and z dimension c is depicted in the diagram. If the electric potential on all sides except z=c is zero, and the potential on the side z=c is V(x,y), Find the potential inside the box.

We must solve the Laplace equation:
(please see the attached file)

Subject to the following boundary conditions:
(please see the attached file)

Where (please see the ...

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