Question

For any charge configuration, equipotential surface through a point is _____to the electric field at that point.

Answer 1

1. Equipotential surface is a surface in which the potential is constant at each point.
2. Therefore, the work required to move a charge along this surface will be zero.
3. The work done is given by $W=Fx\cos \theta$
4. For zero work, $$\begin{gathered} 0=Fx\cos \theta \\ \Rightarrow \cos \theta =0 \\ \Rightarrow \theta =90° \end{gathered}$$

Hence, for any charge configuration, equipotential surface through a point is perpendicular to the electric field at that point.