Question

Three point charges are arranged along the x-axis. Charge q1 = +3.00 µC is at the origin, and charge q2 = - 5.00 µC is at x = 0.200 m. Charge q3 = - 8.00 µC. Where is q3 located if the net force on q1 is 7.00 N in the – x-direction?

Answer 1

Let the first charge there is placed between third and second charges at distance x from third. The net force on a first charge

$$F_x=-k\frac{q_1q_3}{x^2}+k\frac{q_1q_2}{0.2^2}$$

$$-7.00=9\times 10^9\left(-\frac{3.00\times 8.00}{x^2}+\frac{3.00\times 5.00}{0.2^2}\right)\times 10^{-12}$$

Solution of this equation

$$x=0.14\:\rm{m}$$

The position of third charge is denoted at the picture below