Question

if the electric field intensity is zero at a point.Will the electric potential be necessarily zero at that point?

Answer 1

if electric field intensity zero then no say potential is also zero , but potential difference may be zero .
example:-a hollow spherical body configured own charge in outer surface of spherical body . hence inside no charge available . hence electric field intensity is zero because according to guass theorem E.A=q/€ .e.g E =q/A €
hence electric field intensity related to charge, if charge zero then electric field intensity is zero but in the case of potential this is not valid , potential means workdone by external force bring a test charge from infinite to certain point .so, potential is constant when electric field intensity is zero.

Answer 2

Ans. We can only define electric potential difference between two points .so if the potential between two points is zero the field intensity also will be zero otherwise we are free to assign potential of any point as zero and that will not indicate field intensity is also zero

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