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 \varepsilon_0R^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 \varepsilon_0R^2} $
• D. The potential at point O is $\frac {q}{12 \pi \varepsilon_0R} $

Answer 1

Answer: (C)

Distance $BC=AB \sin 60^{\circ}=(2R) \frac {\sqrt 3}{2}= \sqrt 3 \, R $
$\therefore |Fe_{BC}|=\frac {1}{4 \pi \varepsilon_0} \frac {(q/3)(2q/3)}{(\sqrt 3 R)^2 } $
$ = \frac {q^2}{54 \pi \varepsilon_0R^2} $