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 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?
Draw the equipotential surfaces due to an electric dipole. Locate the points where the potential due to the dipole is zero.
Depict the equipotential surfaces for a system of two identical positive point charges placed a distance(d) apart?
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.
Depict the equipotential surface due to
(i) an electric dipole,
(ii) two identical positive charges separated by a distance.
Statement - 1: For practical purpose, the earth is used as a reference at zero potential in electrical circuits.
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)`.
S1 and S2 are the two imaginary surfaces enclosing the charges +q and -q as shown. The electric flux through S1 and S2 are respectively ______.
- 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 ______.
Consider a uniform electric field in the ẑ direction. The potential is a constant ______.
- in all space.
- for any x for a given z.
- for any y for a given z.
- on the x-y plane for a given z.
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.
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?
