Can you draw an equipotential surface through a position where the electric fiel

Question

Can you draw an equipotential surface through a position where the electric field vanishes? Select the correct answer and explanation.

A) Yes. Consider the equipotential surface around two particles (that carry charges equal in magnitude and opposite in sign) that includes a point half-way between them as an example. B) No. If the electric field vanishes, it is impossible to determine the potential. Thus, it is impossible to draw an equipotential surface in this case. C) Yes. Consider the equipotential surface around two equally-charged particles that includes a point half-way between them as an example. D) No. If the electric field vanishes, the potential is zero too. Thus, it is impossible to draw an equipotential surface in this case.

Explanation / Answer

The fourth one is currect because the negative gradient of potential is the electric field. Now if the potential and its derivative both vanishes then we can not draw equi potential surface

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