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 !

 

[Nickie]

The potential would be the same at all four points since the distance from the origin is the same. Therefore, the potential is the same at all points on the periphery of the circle.