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
$(a)$ Equidistant planes parallel to the $x -y$ plane are the equipotential surfaces.
$(b)$ Planes parallel to the $x -y$ plane are the equipotential surfaces with the exception that when the planes get closer, the field increases.
$(c)$ Concentric spheres centered at the origin are equipotential surfaces.
$(d)$ A periodically varying shape near the given grid is the equipotential surface. This shape gradually reaches the shape of planes parallel to the grid at a larger distance.
Draw an equipotential surface for a point charge.
Draw an equipotential surface of two identical positive charges for small distance.
A uniform electric field pointing in positive $x$-direction exists in a region. Let $A$ be the origin, $B$ be the point on the $x$-axis at $x = + 1$ $cm$ and $C$ be the point on the $y$-axis at $y = + 1\,cm$. Then the potentials at the points $A$, $B$ and $C$ satisfy
Draw an equipotential surface for dipole.
Prove that a closed equipotential surface with no charge within itself must enclose an equipotential volume.