Question

Two point charges Q₁ = -25 micro coulombs and Q₂ = +50 micro coulombs are separated by a distance of 12 cm. The electric field at the point P is zero (and is to the left of Q₁). How far from (Q₁) is P?

Answer 1

Write the fields from both charges:

$$E_1=\frac{kq_1}{r^2},\\\space\\ E_2=\frac{kq_2}{(x+r)^2},\\\space\\ E_1+E_2=0,\\\space\\ \frac{kq_1}{r^2}+\frac{kq_2}{(x+r)^2}=0,\\\space\\ q_1x^2+2q_1rx+(q_1+q_2)r^2=0,\\\space\\ r_{1,2}=\frac{-q_1x\pm\sqrt{(q_1x)^2-q_1(q_1+q_2)x^2}}{q_1+q_2}=\pm0.17\text{ m}.$$