Question

Consider a system of three charges $q/3,q/3$ and $-2q/3$ placed at points $A,B$ and $C$ respectively, as shown in the figure. Take $O$ to be the centre of the circle of radius $R$ and angle $CAB=60^{\circ }$

• A. The electric field at point O is $\frac{q}{8\pi {\epsilon }_0{R}^2}$ directed along the negative x-axis
• B. The potential energy of the system is zero
• C. The magnitude of the force between the charges at C and B is $\frac{q^2}{54\pi {\epsilon }_0{R}^2}$
• D. The potential at point O is $\frac{q}{12\pi {\epsilon }_{0}R}$

Answer 1

Answer: (C)

Distance $BC=AB\sin 60^{\circ }=(2R)\frac{\sqrt{3}}{2}=\sqrt{3}R$
$\therefore |F{e}_{BC}|=\frac{1}{4\pi {\epsilon }_0}\frac{(q/3)(2q/3)}{(\sqrt{3}R{)}^2}$
$=\frac{q^2}{54\pi {\epsilon }_0{R}^2}$