Equipotential Surface Property

Question

Electric field is ______ to equipotential surfaces.

RankGuru · Accepted Answer

1. **Definition**: An equipotential surface is a surface where every point has the same electric potential ($V$).
2. **Energy Logic**: To move a charge along such a surface, work done must be zero ($W = q \Delta V = 0$).
3. **Work Formula**: $W = \vec{F} \cdot \vec{d} = q \vec{E} \cdot \vec{d} = 0$.
4. **Geometric Implication**: Since $q$ and $d$ are non-zero, the dot product $\vec{E} \cdot \vec{d}$ must be zero ($\cos 	heta = 0$).
5. **Conclusion**: $	heta = 90^\circ$. The electric field lines are always **perpendicular (normal)** to the equipotential surfaces at every point.

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Equipotential Surface Property

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