Where is the Max Electrostatic field?

[Bloo_Mec]

Homework Statement

Consider 2 charges with value q=3[\muC], situated on the xOy plane at (0;2) and (0;-2) [cm]. Obtain the coordinates on the x-axis (y=0) where the modulo of the electrostatic field is maximum.

Homework Equations

The Attempt at a Solution

I am trying to do this but I keep failing.. I know that as both charges are positive, the maximum value of the electrostatic field will be in both sides of the origin, but i need to get that distance from the origin to the max electrostatic field point. My biggest question is what am suposed to do with the value of the electrostatic field in its formula? And is there any relation with another quantity when the electrostatic field is max? The potential does not have anything to do with that, i think, but the electrostatic force may have, but i can´t get it! I also tried to do this by finding the point where the gradient of r (I call "r" the distance from a charge to the point I'm trying to find) on the x direction is max, but i can't translate this mathematicaly. I'm stuck.

By the way, this is my first post! Hi everyone! Great forum you have here=)

 

[tiny-tim]

Welcome to PF!

Hi Bloo_Mec! Welcome to PF!

(have a mu: µ )

Either find the field at r (remember, you'll only need the x coordinate ), and then find its maximum

or find the potential at r, and use the fact that its gradient is the field.

What do you get? ​