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Why electric field is always at right an...

Why electric field is always at right angle to the equipotential surface ?

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Because work done in moving a test charge `(q_(0))` between two points on an equipote surface is zero.
As Work done = (Electricl force). displacement
So `W=q_(0)vecE.vec(dl)`
`impliesvecE.vec(dl)=(W)/(q_(0))=0" "[:.W=0]`
So `vecE` and `vec(dl)` are perpendicular to each other.
As the displacement `vec(dl)` is along the equipotential surface.
It means electric field `vecE` must be perpendicular to the equipotential surface.
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