Answer to Question #152976 in Electricity and Magnetism for Maryam Mane

Question

A charge q1 of +8.00 × 10−9 C and a charge q2 of -4.00 × 10−9 C are separated by a distance of 60.0 cm. What is the equilibrium position for a third charge of
–12.0 × 10−9 C?

Answer 1

$F_1=\frac{k|q_1|\cdot|q_3|}{(60+x)^2},$

$F_2=\frac{k|q_2|\cdot|q_3|}{x^2},$

$F_1=F_2,$

$\frac{|q_1|}{(60+x)^2}=\frac{|q_2|}{x^2},$

$\frac{60+x}{x}=\sqrt{|\frac{q_1}{q_2}|},$

$x=\frac{60}{\sqrt{|\frac{q_1}{q_2}|}-1}\approx 145~$ cm at right from $q_2$ (or 145+60=205 cm at right from $q_1$ ) .