Consider a system of three charges $\frac{\mathrm{q}}{3}, \frac{\mathrm{q}}{3}$ and $-\frac{2 \mathrm{q}}{3}$ placed at points $\mathrm{A}, \mathrm{B}$ and C , respectively, as shown in the figure. Take O to be the centre of the circle of radius R and angle $\mathrm{CAB}=60^{\circ}$
Select the correct option:
A
The electric field at point $O$ is $\frac{q}{8 \pi \varepsilon_0 R^2}$ 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 $\frac{q^2}{54 \pi \varepsilon_0 R^2}$
D
The potential at point O is $\frac{\mathrm{q}}{12 \pi \varepsilon_0 \mathrm{R}}$
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