Solving Electric Field & Potential: Jack Needs Help!

[Jackoyo]

Hi everyone,
I have abit of trouble with this question. Please help!

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

 

[haruspex]

Hi everyone,
I have abit of trouble with this question. Please help!

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.