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For a given charge configuration, electric field lines should intersect equipotential lines at right angles. Explain...

For a given charge configuration, electric field lines should intersect equipotential lines at right angles. Explain using math why these two sets of lines should be mutually perpendicular.

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Answer #1

At equipotential surface, surface has same potential throughout the surface.

Equipotential lines are always perpendicular to the electric field. The lines form equipotential surfaces in 3D. No work is required to move the charge because such movement is always perpendicular to the electric field.

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