The Equipotential surfaces

As the electric field can be represented graphically by lines of force, the potential distribution in an electric field may be represented graphically by equipotential surfaces.

The equipotential surface is a surface such that the potential has the same value at all points on the surface. i.e. V_B -V_A = zero for any two points on one surface.

The work is required to move a test charge between any two points on an equipotential surface is zero. (Explain why?)

In all cases the equipotential surfaces are at right angles to the lines of force and thus to E. (Explain why?)

Figure 1.1 shows the equipotential surfaces (dashed lines) and the electric field lines (bold lines), (a) for uniform electric field and (b) for electric field due to a positive charge.