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प्रश्न
Prove that a closed equipotential surface with no charge within itself must enclose an equipotential volume.
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उत्तर
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 a potential gradient (dV/dr)
It means E ≠ 0 electric field comes into existence, which is given by as E = – dV/dr
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 originated from the charges inside. This contradicts the original assumption. Hence, the entire volume inside must be equipotential.
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संबंधित प्रश्न
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Statement - 2: The electrical potential of a sphere of radius R with charge Q uniformly distributed on the surface is given by `Q/(4piepsilon_0R)`.
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Equipotentials at a great distance from a collection of charges whose total sum is not zero are approximately.
The diagrams below show regions of equipotentials.
(i) |
(ii) |
(iii) |
(iv) |
A positive charge is moved from A to B in each diagram.
- The potential at all the points on an equipotential surface is same.
- Equipotential surfaces never intersect each other.
- Work done in moving a charge from one point to other on an equipotential surface is zero.
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