What is an equipotential surface? Draw equipotential surfaces for:
$(1)$ $A$ single point charge
$(2)$ $A$ dipole (charges $+q$ and $-q$ at a small distance)
$(3)$ Two $+q$ charges at a small distance
$(4)$ $A$ uniform electric field.

(N/A) An equipotential surface is an imaginary surface in an electric field where the electric potential is the same at every point.
$(1)$ For a single point charge $q$,the potential at a distance $r$ is $V = \frac{kq}{r}$. Since $V$ is constant for a constant $r$,the equipotential surfaces are concentric spheres centered at the charge.
$(2)$ For a dipole ($+q$ and $-q$),the potential is zero at the mid-plane. The equipotential surfaces are distorted spheres,closer together near the charges and further apart in the middle.
$(3)$ For two like charges ($+q$ and $+q$),the potential is high near the charges. The equipotential surfaces are distorted spheres that do not intersect the mid-plane.
$(4)$ For a uniform electric field,the equipotential surfaces are a set of parallel planes perpendicular to the direction of the electric field lines.