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Is it probable for the electric field to be non-zero at a point in space where the electric potential is zero?
Ans:
Regard as for instance the case of an electric potential given that is only a function of x and is given by
V(x) = 5volts - (5volts/m)x
V is therefore 0 at x=1m but Ex = -dV/dx which is 5 volts/m everywhere including at x=1m. Therefore V being zero does not mean that E is zero.
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