Solved: PHYSICS Question for NEET

NEET PHYSICSEasy

The angle between the electric lines of force and the equipotential surface is:

180°

0°

45°

90°

Definition: An equipotential surface is a region where the electric potential ( $V$ ) is constant at every point. Therefore, the potential difference ( $dV$ ) between any two points on the surface is zero.
Work Done: The work done to move a charge $q$ on an equipotential surface is $dW = q dV = 0$ .
Relation to Field: Work is also defined as the dot product of force and displacement: $dW = \mathbf{F} \cdot d\mathbf{r} = q \mathbf{E} \cdot d\mathbf{r} = q E dr \cos \theta$ , where $\theta$ is the angle between the electric field ( $\mathbf{E}$ ) and the displacement ( $d\mathbf{r}$ ) along the surface.
Conclusion: For $dW$ to be zero (where $q, E, dr \neq 0$ ), $\cos \theta$ must be zero. This implies $\theta = 90^\circ$ . Thus, electric field lines are always perpendicular to equipotential surfaces.

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