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

In summary, the problem involves three uniformly charged non-conducting spheres arranged in an equilateral triangle. Using Coulomb's law, the net electrostatic force on the sphere at the origin is calculated by considering the forces exerted by the other two spheres. The final result is a vector sum of forces in the positive x direction and negative y direction. However, the question itself may be flawed as it does not specify the type of charged spheres and the radii of the spheres may affect the solution.

## 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 )

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

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.

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.

haruspex said:
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.

## 1. What is electrostatic force?

Electrostatic force is a fundamental force in nature that is caused by the attraction or repulsion of electrically charged particles. It is responsible for many everyday phenomena, such as static electricity and the behavior of atoms and molecules.

## 2. What is the net electrostatic force?

The net electrostatic force is the total amount of force exerted on an object by all the other charged particles in its surroundings. It takes into account both the magnitude and direction of each individual force.

## 3. How is the net electrostatic force calculated?

The net electrostatic force can be calculated using Coulomb's law, which states that the force between two charged particles is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.

## 4. What is a sphere at the origin?

A sphere at the origin refers to a spherical object that is centered at the point (0,0,0) in a three-dimensional coordinate system. This means that all points on the surface of the sphere are equidistant from the origin.

## 5. How does the location of a charged sphere affect the net electrostatic force?

The location of a charged sphere can affect the net electrostatic force by changing the distance and direction of the forces acting on it from other charged particles. As the sphere moves closer or further away from other charged objects, the net electrostatic force will change accordingly.

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