Question

A charge of +q is located at the origin, while an identical charge is located on the x axis at x = 0.45 m. A third charge of +4q is located on the x axis at such a place that the net electrostatic force on the charge at the origin doubles, its direction remaining unchanged. Where should the third charge be located?

I am just supposed to be using Coulombs law. I tried in relation to origin charge where the charge at .45 would be F=kq/.45^2 and in relation with charge 4q F-k4q/X^2. Then since q1=q2 the formula was kq/.45^2 = k4q/x^2. simplified that into x^2=4/.45^2. Then took the square root of the answer. it was like 4.444 totally wrong. I cannot figure out this problem at all please some guidance!

Answer 1

To double the force at the origin, the +4q charge must have the same effect upon the charge as the +q charge at x=0.45 m

Making the distance x = 0.9 (twice that of the second charge) will result in the same force produced by the +4q particle, because of the the inverse square law.

You were OK with this equation
q/(0.45)^2 = 4q/(0.9)^2

Your mistake was algebra in the next step.
k*q/.45^2 = k*4q/x^2.
leads to
x^2 = 4*(0.45)^2
x = 0.9