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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
Define an equipotential surface.
Two charges 2 μC and −2 µC are placed at points A and B 6 cm apart.
- Identify an equipotential surface of the system.
- What is the direction of the electric field at every point on this surface?
Describe schematically the equipotential surfaces corresponding to
(a) a constant electric field in the z-direction,
(b) a field that uniformly increases in magnitude but remains in a constant (say, z) direction,
(c) a single positive charge at the origin, and
(d) a uniform grid consisting of long equally spaced parallel charged wires in a plane.
The top of the atmosphere is at about 400 kV with respect to the surface of the earth, corresponding to an electric field that decreases with altitude. Near the surface of the earth, the field is about 100 Vm−1. Why then do we not get an electric shock as we step out of our house into the open? (Assume the house to be a steel cage so there is no field inside!)
A man fixes outside his house one evening a two metre high insulating slab carrying on its top a large aluminium sheet of area 1 m2. Will he get an electric shock if he touches the metal sheet next morning?
The discharging current in the atmosphere due to the small conductivity of air is known to be 1800 A on an average over the globe. Why then does the atmosphere not discharge itself completely in due course and become electrically neutral? In other words, what keeps the atmosphere charged?
What is the geometrical shape of equipotential surfaces due to a single isolated charge?
Why is there no work done in moving a charge from one point to another on an equipotential surface?
Define equipotential surface.
Two identical point charges, q each, are kept 2m apart in the air. A third point charge Q of unknown magnitude and sign is placed on the line joining the charges such that the system remains in equilibrium. Find the position and nature of Q.
Draw the equipotential surfaces due to an electric dipole.
Write two important characteristics of equipotential surfaces.
Find the amount of work done in rotating an electric dipole of dipole moment 3.2 x 10- 8Cm from its position of stable equilibrium to the position of unstable equilibrium in a uniform electric field if intensity 104 N/C.
Can two equipotential surfaces intersect each other?
Equipotential surfaces ______.
- are closer in regions of large electric fields compared to regions of lower electric fields.
- will be more crowded near sharp edges of a conductor.
- will be more crowded near regions of large charge densities.
- will always be equally spaced.
Draw equipotential surfaces for (i) an electric dipole and (ii) two identical positive charges placed near each other.
