Finding the point where the net electric field is 0

[012983]

Homework Statement

Three charges of equal magnitude q reside at the corners of an equilateral triangle of side length a. The topmost charge is positive while the charges at the bottom left and bottom right of the triangle are negative. If point P is midway between the negative charges, at what distance above point P along the +y axis must a -8q charge must be placed so that any charge located at point P experiences no net electric force? The distance from point P to the positive charge is 9 meters.

Homework Equations

E = (kq)/r^2

The Attempt at a Solution

No clue. I think you would find the the electrical field for one of the points and then, using that, find the x and y components of the magnitude. Then solve for 0 = sqrt{(Ex)^2 - (Ey)^2}... but the "any charge located at point P" is confusing me. Or else I'm not thinking correctly.

 

[ideasrule]

It just means that the electric field at P has to be 0. So assume that the third charge is a distance "a" from P, calculate the electric field at P, and set the result to 0.

 

[012983]

It just means that the electric field at P has to be 0. So assume that the third charge is a distance "a" from P, calculate the electric field at P, and set the result to 0.

If the electric field at P is equal to (-4*ke*q)/(3a^2), where ke = 8.99 * 10^9, do I proceed by plugging in -8q for q and setting equal to 0?

If so, how would I solve for a? a could be any number so long as the numerator is 0.

 

[ideasrule]

If the electric field at P is equal to (-4*ke*q)/(3a^2), where ke = 8.99 * 10^9, do I proceed by plugging in -8q for q and setting equal to 0?

That's not the total electric field. There are 3 charges, not just one, and the electric field has both an x and a y component.

 

[rwisz]

As a scientist, my response to this content would be as follows:

To find the point where the net electric field is 0, we need to use the principle of superposition to calculate the electric field at point P due to each of the three charges individually, and then add them together. Since the positive charge at the top of the triangle and the negative charges at the bottom are equal in magnitude, they will cancel each other out and result in a net electric field of 0 at point P.

To ensure that any charge located at point P experiences no net electric force, we need to place an -8q charge at a distance above point P along the +y axis. Using the equation E = (kq)/r^2, we can calculate the distance at which this charge must be placed. By setting the net electric field at point P to 0, we can solve for the distance r, which in this case is 9 meters.

Therefore, to find the point where the net electric field is 0, we need to place an -8q charge at a distance of 9 meters above point P along the +y axis. This will result in a net electric field of 0 at point P, ensuring that any charge located at this point experiences no net electric force.