Question

A+2uc is placed at x=+2m and a second charge+6uc is placed x=-2cu.
Where can a third charge be placed so that the net electric force experienced by the third charge is zero

Answer 1

$$E_1+E_2=0\\\frac{kq_1}{(x-x_1)^2}-\frac{kq_2}{(x-x_2)^2}=0\\\frac{q_1}{(x-x_1)^2}=\frac{q_2}{(x-x_2)^2}\\\frac{2}{(x-2)^2}=\frac{6}{(x-(-2))^2}\\x=0.536\ m$$