Where Is the Electric Potential Minimum on a Circle in a Uniform Electric Field?

[Epiclightning]

The electric field at the origin is along the positive x axis. A small circle is drawn with the center at the origin cutting the axes at points A, B, C, and D having coordinates (a,0), (0,a), (-a,0), (0,-a), respectively. Out of the points on the periphery of the circle, the potential is minimum at _______?
(a) A (b) B (c) C (d) D

After drawing the diagram, I see that the electric field is directed towards the right along the x-axis (towards A). However, electric potential = KQ/r, and here Q and r are constant for all four points. I don't see how any point could have "minimum" potential.

 

[BvU]

Hello Epic, welcome to PF :)

Did you notice the template ? Better use it.

However:
Your electric potential expression isn't applicable here. There is no mention of Q !

You want to make use of a different relationship between E and V.
In the template, there is room for such equations under 2) relevant equations.

 

[Epiclightning]

Homework Statement

The electric field at the origin is along the positive x axis. A small circle is drawn with the center at the origin cutting the axes at points A, B, C, and D having coordinates (a,0), (0,a), (-a,0), (0,-a), respectively. Out of the points on the periphery of the circle, the potential is minimum at _______?
(a) A (b) B (c) C (d) D

Homework Equations

V = -E dr

The Attempt at a Solution

After drawing the diagram, I see that the electric field is directed towards the right along the x-axis (towards A). But how will integrating the above equation give me the "minimum" potential necessary?
Thanks for the help

 

[BvU]

Much better !
Actually, it's ${\bf d}V = -\vec E\cdot d\vec r\,$. You integrate and get $\Delta V$, which happens to be just the one you are after !