Chapter 18, Problem 1CQ

Why must electric field lines be perpendicular to equipotential surfaces?

To determine

The reason for which the electric field lines must be perpendicular to equipotential surfaces.

Answer to Problem 1CQ

There will be no change in potential when a charge moves perpendicular to the field lines, and hence no work done. The equipotential surface is thus along the direction perpendicular to the field line. Since the work done on a charge in an equipotential surface is zero, it is thus along the direction perpendicular to the field line.

Explanation of Solution

The tangent to the electric field line at a point gives the direction of electric force at that point. This results the absence of any component of electric force in the direction perpendicular to the field line.

The work done on a charge when it moves in an equipotential surface is zero. There will be no change in potential when a charge moves perpendicular to the field lines, and hence no work done. The equipotential surface is thus along the direction perpendicular to the field line.