Question

An equipotential line and a line of force are:
A) Perpendicular to each other
B) Parallel to each other
C) In any direction
D) At an angle of $45^\circ $

Answer 1

Hint: An equipotential line is a line for a given configuration of charges such that the potential due to the charges will be equal for the entire line. A line of force indicates the direction of the force that will be exerted on another charge when it is placed near the original configuration of charges.

Complete step by step answer:
Electric field lines and equipotential lines are both helpful for visualizing electric fields. The electric field lines correspond to the line of force as it indicates the force that will be exerted on any external charge that is placed in the field of a given configuration of charges. While an equipotential line is formed by a set of points at which the electric potential due to the configuration of a given charge configuration is the same. An equipotential surface can be a line, a curve, or any locus of points. To answer this question, let us think of an example of a point charge. The electric lines of force due to a point charge will be facing inwards or outwards but always in a radial direction. In contrast, the equipotential surface due to a point charge will always be a circle as the potential due to a point charge only depends on the distance of the point from the charge. As a result, a locus of all points at an equal distance from the point charge will form a circle. So, the lines of force that are inwards or outwards will always be tangential to the circular equipotential surface.
Hence the equipotential line and the line of force will be perpendicular to each other. So, the correct choice is option (A).

Note: In order to answer such questions, we need to be familiar with the concepts of electric fields and electric potentials. While electric potential by itself is scalar, the curve formed by the set of points with equal potentials will have a specific shape and the tangent to the curve will indicate the direction of the equipotential surface. So in case of a point charge, the tangent to the circle will indicate the direction of the equipotential surface.