The voltage at any point is zero. At that point the electric field strength will be zero?
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An electric field exists between two points when there is a difference in potential between those two points.
So you could have two points which are both at a potential of zero in which case there would be no electric field.
But the two points could both have potentials of 4 V. Again no electric field between them.
But you could have one point at zero potential and one point at 4 V so there would be a field between them.
So the answer is that there might or might not be a field where the potential is zero as it depends on the potential of the points around it.
There has to be a difference in potential to get an electric field.
Mathematically:
E = - d V / dx
Electric field strength, E, measured in volt per metre
x measured in metres.
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