Electric Potential over Conducting Surface is Constant

Theorem

Let $S$ be a conducting surface.

The electric potential $V$ over $S$ is constant.

This can be expressed using the Laplacian:

$\nabla^2 V = 0$

and is thus seen to satisfy Laplace's equation.

Proof

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Sources

• 1961: Ian N. Sneddon: Special Functions of Mathematical Physics and Chemistry (2nd ed.) ... (previous) ... (next): Chapter $\text I$: Introduction: $\S 1$. The origin of special functions