Equipotential Surfaces

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 equipotential surfaces for (i) an electric dipole and (ii) two identical positive charges placed near each other.

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

Consider a uniform electric field in the ẑ direction. The potential is a constant ______.

1. in all space.
2. for any x for a given z.
3. for any y for a given z.
4. on the x-y plane for a given z.

Draw the equipotential surfaces due to an electric dipole.

Two charges 2 μC and −2 µC are placed at points A and B 6 cm apart.

1. Identify an equipotential surface of the system.
2. What is the direction of the electric field at every point on this surface?

Prove that a closed equipotential surface with no charge within itself must enclose an equipotential volume.

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