As its name suggest a
line of equipotential is a line joining points of equal potential just like a contour line on a
mountainside. Since E = -dV/dx the closer the lines of equipotential are the greater is the field
strength.
An equipotential surface is a surface which joins points of equal potential and
therefore a surface on which the potential does not vary. This means that if you connected a
wire between two points on the surface no current would flow between them. The analogy with
gravity could be two small lakes at equal height on a mountain side - if a pipe connected the two
together no water would flow along it in either direction.
Looking at it in another way on the surface of a conducting solid
electric currents are free to flow - they would do this until the potential at all points is the same
and so the surface of the solid would become an equipotential surface.
A line of force is
always at right angles to an equipotential surface it shows the "downhill" motion of a positive
charge.
