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Question

Which of the following is a property of equipotential surfaces?

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A
The direction of electrostatic field will be perpendicular to the equipotential surface
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B
The potential difference between any two points on an equipotential surface is zero
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C
For a point charge, the equipotential surfaces will be concentric spheres
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D
All the statements above are correct.
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Solution

The correct option is D All the statements above are correct.
An equipotential surface is a surface with a constant value of potential at all points on the surface. So the potential difference between any two points in an equipotential surface will be zero.

From the expression dV=E . dr

The change in potential dV will be zero when E is perpendicular to dr,

Where dr is the displacement vector in the surface. So, Electrostatic field will be always perpendicular to an equipotential surface.

As the electrostatic field due to a point charge is radial in direction, the equipotential surfaces has to be concentric spheres.

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