Discussion
True or false: a point where the electric field is zero must be at zero potential.
Answer: D
Correct answer: False, the interior of a charged conductor having zero field at finite potential
The field is the gradient of the potential, so a zero field means the potential is not changing, not that it is zero. The inside of a charged conductor is the standard counterexample: no field anywhere within it, and the whole body at whatever potential its charge gives it.
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