Advertisements
Advertisements
Question
Prove that a closed equipotential surface with no charge within itself must enclose an equipotential volume.
Advertisements
Solution
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.
APPEARS IN
RELATED QUESTIONS
Draw a sketch of equipotential surfaces due to a single charge (-q), depicting the electric field lines due to the charge
A regular hexagon of side 10 cm has a charge 5 µC at each of its vertices. Calculate the potential at the centre of the hexagon.
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!)
Draw equipotential surfaces:
(1) in the case of a single point charge and
(2) in a constant electric field in Z-direction. Why are the equipotential surfaces about a single charge not equidistant?
(3) Can electric field exist tangential to an equipotential surface? Give reason
Draw the equipotential surfaces due to an electric dipole. Locate the points where the potential due to the dipole is zero.
Why is there no work done in moving a charge from one point to another on an equipotential surface?
Depict the equipotential surfaces for a system of two identical positive point charges placed a distance(d) apart?
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.
A particle of mass 'm' having charge 'q' is held at rest in uniform electric field of intensity 'E'. When it is released, the kinetic energy attained by it after covering a distance 'y' will be ______.
Assertion: Electric field is discontinuous across the surface of a spherical charged shell.
Reason: Electric potential is continuous across the surface of a spherical charged shell.
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.
The work done to move a charge along an equipotential from A to B ______.
- cannot be defined as `- int_A^B E.dl`
- must be defined as `- int_A^B E.dl`
- is zero.
- can have a non-zero value.
Draw equipotential surfaces for (i) an electric dipole and (ii) two identical positive charges placed near each other.
What is meant by an equipotential surface?
