Equipotential Surfaces

The work done to move a charge along an equipotential from A to B ______.

1. cannot be defined as `- int_A^B E.dl`
2. must be defined as `- int_A^B E.dl`
3. is zero.
4. can have a non-zero value.

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.

Draw the equipotential surfaces due to an electric dipole. Locate the points where the potential due to the dipole is zero.

Find the amount of work done in rotating an electric dipole of dipole moment 3.2 x 10^{- 8}Cm from its position of stable equilibrium to the position of unstable equilibrium in a uniform electric field if intensity 10⁴ N/C.  

Why is there no work done in moving a charge from one point to another on an equipotential surface?

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?

Find the equation of the equipotentials for an infinite cylinder of radius r₀, carrying charge of linear density λ.

Equipotential surfaces ______.

1. are closer in regions of large electric fields compared to regions of lower electric fields.
2. will be more crowded near sharp edges of a conductor.
3. will be more crowded near regions of large charge densities.
4. will always be equally spaced.