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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
Draw a sketch of equipotential surfaces due to a single charge (-q), depicting the electric field lines due to the charge
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!)
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 are the forms of energy into which the electrical energy of the atmosphere is dissipated during a lightning?
(Hint: The earth has an electric field of about 100 Vm−1 at its surface in the downward direction, corresponding to a surface charge density = −10−9 C m−2. Due to the slight conductivity of the atmosphere up to about 50 km (beyond which it is good conductor), about + 1800 C is pumped every second into the earth as a whole. The earth, however, does not get discharged since thunderstorms and lightning occurring continually all over the globe pump an equal amount of negative charge on the earth.)
Why is there no work done in moving a charge from one point to another on an equipotential surface?
Define equipotential surface.
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.
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 ______.
Consider the following statements and select the correct statement(s).
- Electric field lines are always perpendicular to equipotential surface.
- No two equipotential surfaces can intersect each other.
- Electric field lines are in the direction of tangent to an equipotential surface.
Equipotential surfaces ______.
Can two equipotential surfaces intersect each other?
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.
Equipotential surfaces are shown in figure. Then the electric field strength will be ______.
