Question: 5: The angle between the electric lines of force and the equipotential surface is
(1) 90^{\circ}
(2) 180^{\circ}
(3) 0^{\circ}
(4) 45^{\circ}
Answer: Option (1)
Explanation:
An equipotential surface is a surface on which the electric potential remains constant at every point.
The electric field \vec{E} is related to electric potential V
by the relation \vec{E} = -\nabla V.
This relation shows that the electric field is directed along the direction of maximum decrease of
potential and is normal to the equipotential surface.
If an electric field had any component along the equipotential surface,
work would be done in moving a charge along the surface,
which contradicts the definition of an equipotential surface.
Therefore, electric lines of force always intersect equipotential surfaces at right angles.
Hence, the angle between the electric lines of force and the equipotential
surface is 90^{\circ}.