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The third option  is wrong.

d VG / d x = EG = 0  =  gradient of potential in distance is the field.

So  if VG = 0 then EG = 0  This is true.
If  VG ≠ 0 then EG can still be 0.
If  VG≠ 0 then it is also possible that EG ≠ 0.

But if VG = 0, then  it is not possible that EG ≠ 0.  

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