Three charged metal spheres are arrayed in the xy plane so that they form an eqilateral triangle. What is the net electrostatic force on the sphere at the origin?
http://imgur.com/a/4XnoO (sorry I forgot to put this but the angles are 90 for each vertex, which should be implied when the problem said equilateral )
The Attempt at a Solution
Sorry guys. My book doesn't have an answer for this question and I just wanted to make sure I'm doing it right.
So first I start with the origin sphere and the other sphere on the x axis.
I use kqQ/r^2
(8.99x10^9)(5.5x10^-9)(3x10^-9) / (12x10^-2)^2 = 1.03x10^-5 C
So this will be a force vector going in the positive x axis
Now since the origin has a negative charge, and the top sphere has a negative charge, the force vector here is going to point in the opposite direction of the side of the triangle connecting the origin sphere and the top sphere, right? meaning its going to be going somewhere in the third quadrant?
I use kqQ/r^2 again
(8.99x10^9)(-5.5x10^-9)(-2.5x10^-9) / (12x10^-2)^2 = 8.58x10^-6 C
So the net electrostatic force of the sphere at the origin should be:
F_x = 1.03 x 10^-5 N - sin(30)8.58x10^-6 N
F_y = cos(30)8.58x10^-6 N
I drew a force diagram just so you guys will understand what I mean