For Coulomb's law could I use the distance equation for my r?

Question

I have a list of positions (about 22 in (x,y,z)), and what I would like to know is if i used the distance equation for finding the distance between two charges would that suffice as my r. I have 22 charges and 22 different positions (x,y,z), will this work?

Answer 1

Yes, use what you've got. With 22 charges, the easiest thing to do to find the force is

Sum(i) kq(1)q(i)r(i1)/|r(i1)|^3 where r(i1) is the VECTOR from charge i to the charge of interest (I called 1)

An example:

Say the location of q(1)=r(1)=(5,3,2) and the location of the next charge is r(2)=(7,-3,1) then r(1,2)=(-2,6,1) and |r|^3=(4+36+1)^(3/2)

Do this 21 more times and vectorally add the results using the above formula.