What is the net electrostatic force of the sphere at the origin?

[Rijad Hadzic]

Homework Statement

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 )

Homework Equations

kqQ/r^2

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 CSo 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

http://imgur.com/a/5PeJM

 

[Eclair_de_XII]

I'm not exactly following your train of thought, but I felt like drawing a picture to get a better idea of what you want to do. Basically, you want to find the sum of the vectors in this picture.

Start by identifying what distance to use for Coulomb's law.

 

[haruspex]

Three charged metal spheres

Bad question. If they are conducting spheres the charge distributions on them will not remain uniform. The radii matter, and the problem becomes extremely difficult. It should specify either uniformly charged non-conducting spheres or point charges.

the angles are 90 for each vertex, which should be implied when the problem said equilateral

I think you mean 60.

F_y = cos(30)8.58x10^-6 N

Check the sign. Other than that, all looks good.

 

[Rijad Hadzic]

Bad question. If they are conducting spheres the charge distributions on them will not remain uniform. The radii matter, and the problem becomes extremely difficult. It should specify either uniformly charged non-conducting spheres or point charges.

I think you mean 60.

Check the sign. Other than that, all looks good.

Haha sorry. Yes I meant 60 degrees.

Ohh gotcha not sure how I didn't catch that. of course its going to be negative because its in the -j hat direction!

Thanks a lot.