Prove that a closed equipotential surface with no charge within itself must enclose an equipotential volume.
Prove that a closed equipotential surface with no charge within itself must enclose an equipotential volume.
Let us assume that in a closed equipotential surface with no charge the potential is changing from position to position. Let the potential just inside the surface is different to that of the surface causing in a potential gradient $\left(\frac{d \mathrm{~V}}{d r}\right)$. It means $\mathrm{E} \neq 0$ electric field comes into existence which is given by as $\mathrm{E}=-\frac{d \mathrm{~V}}{d r}$.
It means, there will be field lines pointing inwards or outwards from the surface. These lines cannot be again on the surface as the surface is equipotential. It is possible only when the other end of the field lines are originated from the charges inside. This contradicts the original assumption. Hence, the entire volume inside must be equipotential.
Similar Questions
Given below are two statements: one is labelled a
Assertion $(A)$ and the other is labelled as Reason$(R)$
$Assertion$ $(A)$ : Work done by electric field on moving a positive charge on an equipotential surface is always zero.
$Reason$ $(R)$ : Electric lines of forces are always perpendicular to equipotential surfaces.
In the light of the above statements, choose the most appropriate answer from the options given below
Given below are two statements: one is labelled a
Assertion $(A)$ and the other is labelled as Reason$(R)$
$Assertion$ $(A)$ : Work done by electric field on moving a positive charge on an equipotential surface is always zero.
$Reason$ $(R)$ : Electric lines of forces are always perpendicular to equipotential surfaces.
In the light of the above statements, choose the most appropriate answer from the options given below
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Statement $2$ : Electric lines of force at the equipotential surfaces are mutually perpendicular to each other
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