Basic electrical engineering question! pls help?

Question

can anyone help: 2 positive charges Q1 = 5x10^-9 and Q2=2x10^-9 are fixed and separated at a distance. a 3rd charge, negative Q3=-2x10^-9 is introduced between them. determine ratio between Q3 & Q2 and Q3 & Q1 such that Q3 will not move. answer is 0.6325 but how do i set it up for solution??? thanks!

Answer 1

you call this basic?

Answer 2

You want the pull on Q3 due to Q1 to equal the pull on Q3 due to Q2.

Using (I think its coulomb's law?)  F = k* (Q1*Q2 / r^2)....that's coulomb's law.  Now to apply it to the problem

equalising the magnitude of the force (as its in opposite directions)

Q1*Q3 / r(13)^2 = Q2*Q3 / r(23)^2

where r(23) is the distance between Q2 and Q3 etc.

Note the the constant k was divided through in this step, eliminating it.

You should be able to pull a ratio of distances out of that, see if it matches your answer.  Been a while since I did straight electrostatics.