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## Homework Statement

There are 12 electrons spread on the circumference of a circle with radius R evenly. What's the electric potential at the centre? Then the electrons are concentrated on the upper half of the circle, spread evenly. What's the electric potential at the centre now?

## Homework Equations

## The Attempt at a Solution

Since electric potential is a scalar, the potential due to one electron is V=kq/R. By superposition principle, the potential due to all the electrons is simply 12kq/R=12V. Both situations have the same potentials.

What confuses me is that the electric fields in both situations are indeed different. In the first case, the field is simply zero because they all cancel at that point, while it's nonzero in the second case. But electric field is the negative gradient of the electric potential, then how come the same potentials result in different fields?