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Equipotential surfaces are surfaces of constant scalar potential. They are used to visualize an (n)-dimensional scalar potential function in (n-1) dimensional space. The gradient of the potential, denoting the direction of greatest increase, is perpendicular to the surface.
In electrostatics, the work done to move a charge from any point on the equipotential surface to any other point on the equipotential surface is zero since they are at the same potential. Furthermore, equipotential surfaces are always perpendicular to the net electric field lines passing through it.
Since all points on a sphere around a test charge are equidistant, using the formula V= KQ/r it can be concluded that the charges will have the same potential difference. for the equipotential surface v2-v1=0 V2-V1=-E.dl=0 neither E nor dl is zero so E must be perpendicular to dl or perpendicular to equpotential line. The term is used in electrostatics, fluid mechanics, and geodesy.
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