Hi, I am in grade 12 and in physics we are talking about Coulomb's law. I understand the equation Fe = kq1q2/r^2 but I am confused about the directions we assign.

For example if I have 3 spheres A, B, C in a straight line each having a charge of +2, -4, +6 respectively with a distance of 0.5m within each then what is the electrostatic force acting on C?

A B C
o ----------------------- o -------------------------- o

I know I am suppose to do forces with AC then BC then add them up. So for AC I would get a positive force. Would this be labelled Right because C is moving away? Or labelled left since A is moving away?

What about BC? I would get a negative force but how would I label it?

Thanks in advance and sorry if I wasn't clear

You're right, it's a little confusing because they both repel each other.

The best way is to label the force that the balls feel, so that's a force on A away from C and a force on C away from A, a force on B towards C and a force on C towards B. Does that help?

Sorry, I am still confused

So if I do my calculation for AC (where A is acting on C) then I get the 1.08 x 10^11 N. Would I label this as Right since I am concerned with the electrostatic force on C and C in this case is repelled by sphere A?

Yes, you just want to label what you are interested in. In this case it's the force or movement of sphere C, so just label it as a force on C.

It's hard to answer your question, because the way that the teacher wants it labeled might not be the way that I would think to label it, I'm just trying to suggest something that's as clear as possible.

All right thank you for your input, I might as well just ask my teacher then seeing there could be different ways to label the directions. Thanks again for your time

Oh, yes it would be right for the interaction from A and left for the interaction from B, then just add the vectors to get the net force.

You're welcome, feel free to stick around!

Use the following steps, then it will be very easy.
Suppose there are charges A and B. You need to find force by A on B.
Let r=distance between A and B,
q1=charge at A,
q2=charge at B

Calculate the force using formula kq1q2/r^2
Direction is from A to B.
Using above rule find all forces and do vector addition. If final result is negative, then take its absolute value and reverse the direction.

In your problem, force by A on C
= k*2*6/1.0^2
= 12k towards right
It is towards right because force is from A to C. A is on left and C is on right. So A to C becomes towards right.

Force by B on C = k*(-4)*6/0.5^2
= -96k towards right

So total force on C
= 12k - 96k = -84k towards right.
This means +84k towards left.

In regards to just your generally question about the sign (direction) of the electrical force:

Coloumb's law equation gives the unsigned MAGNITUDE of a force between two electrically charged objects.
Like charges always repel (negative force) and unlike charges attract (positive force). Sum them up for the total force.