work done in moving the charge from one point to another in an equipotential surface is zero. since the work is done is zero when the direction of force (electric field) and displacement is normal. Thus, electric field is perpendicular to the plane in an equipotential surface.
In mathematics and physics, equipotential or isopotential refers to a region of space in which all points have the same potential. This term usually refers to a scalar potential, but it can also refer to vector potentials.
The equipotential surface is the surface that is the locus of all points with the same potential. On the equipotential surface, moving a charge from one point to another requires no work.
An equipotential surface is one on which all of the points on it have the same electric potential. This means that a charge has the same potential energy at all points along the equipotential surface.
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