Where is the Max Electrostatic field?

[Bloo_Mec]

Homework Statement

Consider 2 charges with value q=3[$$\mu$$C], 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? ​

 

[tomcue]

I would like to first clarify that the electrostatic field refers to the electric field created by a static charge, which is a vector quantity that represents the force per unit charge at any given point in space. The maximum electrostatic field refers to the point where the electric field has the highest magnitude.

In order to find the coordinates on the x-axis where the maximum electrostatic field occurs, we can use the formula for the electric field created by a point charge:

E = kq/r^2

where E is the electric field, k is the Coulomb's constant, q is the charge, and r is the distance from the point charge.

In this case, we have two point charges with the same magnitude (q=3[\muC]) and opposite signs, so we can calculate the electric field created by each charge separately and then add them together to find the total electric field at any given point.

Now, to find the coordinates on the x-axis where the maximum electrostatic field occurs, we can set up a distance equation using the Pythagorean theorem:

r^2 = (x-0)^2 + (y-2)^2

where x is the distance from the origin to the point on the x-axis we are trying to find and y=0 since we are only interested in the x-axis.

We can then substitute this into the electric field formula and take the derivative with respect to x to find the point where the electric field is maximum:

dE/dx = 2kq(x-0)/[(x-0)^2 + 4]

Setting this equal to 0 and solving for x, we get x=0 as the point where the electric field is maximum. This makes sense since the charges are symmetrically placed on the y-axis, so the maximum electric field will occur at the midpoint between them, which is the origin.

In summary, the coordinates on the x-axis where the maximum electrostatic field occurs are (0,0).

I hope this helps clear up any confusion and provides a solution to the problem. Keep up the good work in your studies!