# How to verify the relation between electric potential and electric field

Moved from a technical forum, so homework template missing
Hi everyone,

Given charges +q, +2q, −5q and +2q are placed at the four corners ABCD of a square of side a, taken in cylic order from the bottom left corner. Find the electric field E and the potential V at the centre and verify that they are related by E = −∇V.

I can do the first part which gives 12kq/a^2, and 0, but how do I verify E= −∇V.

Cheers,
Jack

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haruspex
Homework Helper
Gold Member
Hi everyone,

Given charges +q, +2q, −5q and +2q are placed at the four corners ABCD of a square of side a, taken in cylic order from the bottom left corner. Find the electric field E and the potential V at the centre and verify that they are related by E = −∇V.

I can do the first part which gives 12kq/a^2, and 0, but how do I verify E= −∇V.

Cheers,
Jack
First, the equation to be verified is a vector equation, so you need the field as a vector.
Secondly, Del is a differential operator, so you need to consider how the potential changes as you move around near the centre.