Question

Two fixed charges 1.07 micro Coulomb and -3.29micro Coulomb are 61.8cm apart where may a third charge be located so that no net force act on it?

Answer 1

The net force on the third charge will be zero when the magnitudes of the electric forces are equal to each other:

$$F_1=F_2,$$ $$\dfrac{k|Q_1Q_3|}{(x)^2}=\dfrac{k|Q_2Q_3|}{(x+d)^2},$$ $$\dfrac{|Q_1|}{(x)^2}=\dfrac{|Q_2|}{(x+d)^2},$$ $$\dfrac{x}{x+d}=\sqrt{\dfrac{|Q_1|}{|Q_2|}},$$ $$x=\dfrac{d\sqrt{\dfrac{|Q_1|}{|Q_2|}}}{1-\sqrt{\dfrac{|Q_1|}{|Q_2|}}},$$ $$x=\dfrac{0.618\ m\cdot\sqrt{\dfrac{|1.07\cdot10^{-6}\ C|}{|-3.29\cdot10^{-6}\ C|}}}{1-\sqrt{\dfrac{|1.07\cdot10^{-6}\ C|}{|-3.29\cdot10^{-6}\ C|}}}=0.82\ m=82\ cm.$$