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
Thepoints resembling equal potentials are
Thepoints resembling equal potentials are
If a unit positive charge is taken from one point to another over an equipotential surface, then
If a unit positive charge is taken from one point to another over an equipotential surface, then
A point charge $+Q$ is placed just outside an imaginary hemispherical surface of radius $R$ as shown in the figure. Which of the following statements is/are correct?
(IMAGE)
$[A]$ The electric flux passing through the curved surface of the hemisphere is $-\frac{\mathrm{Q}}{2 \varepsilon_0}\left(1-\frac{1}{\sqrt{2}}\right)$
$[B]$ Total flux through the curved and the flat surfaces is $\frac{Q}{\varepsilon_0}$
$[C]$ The component of the electric field normal to the flat surface is constant over the surface
$[D]$ The circumference of the flat surface is an equipotential
A point charge $+Q$ is placed just outside an imaginary hemispherical surface of radius $R$ as shown in the figure. Which of the following statements is/are correct?
(IMAGE)
$[A]$ The electric flux passing through the curved surface of the hemisphere is $-\frac{\mathrm{Q}}{2 \varepsilon_0}\left(1-\frac{1}{\sqrt{2}}\right)$
$[B]$ Total flux through the curved and the flat surfaces is $\frac{Q}{\varepsilon_0}$
$[C]$ The component of the electric field normal to the flat surface is constant over the surface
$[D]$ The circumference of the flat surface is an equipotential
- [IIT 2017]
Figure shows a set of equipotential surfaces. The magnitude and direction of electric field that exists in the region is .........
Figure shows a set of equipotential surfaces. The magnitude and direction of electric field that exists in the region is .........
Define an equipotential surface.
Define an equipotential surface.