Prove that a closed equipotenitial surface with no charge within itself must enclose an equipotential volume.

Prove that a closed equipotenitial surface with no charge within itsel

1.	Prove that a closed equipotenitial surface with no charge within itself must enclose an equipotential volume.
Answer» Suppose a closed equipotential surface with no charge within itself does not enclose an equipotential volume. Therefore, potential just inside the surface would be different from potential at the surface, resulting in some potential gradient. Therefore, there would be field lines pointing inwards or outwards from the surface. This is possible only if other end of the lines are at a charges inside. As there is no charge inside, therefore, the entire volume inside the equipotential surface must be the same potential.

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Prove that a closed equipotenitial surface with no charge within itself must enclose an equipotential volume.

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