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My textbook gives what seems to be a simple mathematical explanation, but the logic is escaping me.

It states that dV= -

**E**.d

**s**= 0, (where the "." appears to be dot product of the two vectors

**-E**and d

**s**and so

**E**must be perpendicular to the displacement of the equipotential surface.

I can understand that the dot product=0 means two vectors are perpendicular. I am looking for a more intuitive explanation to really understand what is going on.