Question
Mon April 20, 2015 By: Subhashree Lenka

why the electric field at every point is normal to the equipotential surface?

Expert Reply
Jyothi Nair
Mon April 20, 2015

Any surface on which the electric potential is the same everywhere is called an equipotential surfaces. 

Hence the potential difference between any two points on an equipotential surface will be, dV= 0

begin mathsize 12px style straight i. straight e space minus straight E with rightwards arrow on top. dl with rightwards arrow on top equals 0 or space minus space straight E space dl space cos space straight theta space equals 0 straight E space and space dl space cannot space be space zero. straight E space not equal to 0 space and space dl with rightwards arrow on top space not equal to space 0 So space cos space straight theta space equals 0 comma rightwards double arrow space straight theta space equals space 90 degree This space implies space that space straight E with rightwards arrow on top space is space normal space to space the space equipotential space surfaces space end style
Hence the electric field at every point is normal to the equipotential surface.
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