Advertisements
Advertisements
प्रश्न
Prove that a closed equipotential surface with no charge within itself must enclose an equipotential volume.
Advertisements
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.
APPEARS IN
संबंधित प्रश्न
Define an equipotential surface.
Draw a sketch of equipotential surfaces due to a single charge (-q), depicting the electric field lines due to the charge
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?
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?
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?
Depict the equipotential surfaces for a system of two identical positive point charges placed a distance(d) apart?
Depict the equipotential surface due to
(i) an electric dipole,
(ii) two identical positive charges separated by a distance.
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.
Equipotentials at a great distance from a collection of charges whose total sum is not zero are approximately.
- 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.
Equipotential surfaces ______.
Which of the following is NOT the property of equipotential surface?
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.
Find the equation of the equipotentials for an infinite cylinder of radius r0, carrying charge of linear density λ.
What is meant by an equipotential surface?
