Question

Consider a system of three charges $\frac{q}{3},\frac{q}{3}$ and $-\frac{2q}{3}$ 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 $CAB={60}^o$

• 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

The correct option is C The magnitude of the force between the charges at $C$ and $B$ is $\frac{q^2}{54\pi {\epsilon }_0{R}^2}$

Given that,

Three charges = $\frac{q}{3},\frac{q}{3},\frac{-2q}{3}$

Radius of circle = R

Angle CAB = ${60}^0$

Now, the electric force between the charges at C and B

$\overrightarrow{F}=\frac{1}{4\pi {\epsilon }_0}\frac{\frac{q}{3}\times \left(\frac{-2q}{3}\right)}{{\left(R\sqrt{3}\right)}^2}$

$\overrightarrow{F}=\frac{-q^2}{54\pi {\epsilon }_0{R}^2}$

$F=\frac{q^2}{54\pi {\epsilon }_0{R}^2}$

Hence, the magnitude of the force between the charges at C and B is $\frac{q^2}{54\pi {\epsilon }_0{R}^2}$