Question

Two charges q1 = 5 µC, q2 = -26 µC, are L = 19 cm apart. A third charge is to be placed on the line between the two charges. How far from q1 should the third charge be placed so that the net electric force on the third charge is minimized?

Answer 1

well if we set both forces to zero it is as small as it gets so

kq1q3/r^2+ kq2q3/(.19-r)^2=0
cancel out k's and q3's
q1/r^2=-q2/(.19-r)^2
take the square root of both sides
end up with 7.62x=.19 x=.025m

Answer 2

Something that has really helped me in physics is if they don't give you something you need, accept that its going to cancel out and move on with it as a variable.