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Question

Write two properties of equipotential surfaces. Depict equipotential surfaces due to an isolated point charge. Why do the equipotential surfaces get closer as the distance between the equipotential surface and the source charge decreases ?

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Solution

Properties of equipotential surfaces:
1. The electric potential value is same across the surface.
2. The electric field is directed normal to the equipotential surface at all points.
For an isolated point charge electric potential is given by
V=kQr
So spheres centered on the charge forms an equipotential surface.
Now, E=dVdr
dr=dVE
But dV is constant for an equipotential surface. Therefore,
dr1E
Hence, the equipotential surfaces get closer as the distance between the equipotential surface and the source charge decreases.

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