Electrostatics 7 Question 10
10. Consider a system of three charges $q / 3, q / 3$ and $-2 q / 3$ 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 $C A B=60^{\circ}$
$(2008,3 M)$
(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 $\frac{q}{12 \pi \varepsilon _0 R}$.
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Solution:
- Distance $B C=A B \sin 60^{\circ}=(2 R) \frac{\sqrt{3}}{2}=\sqrt{3} R$
$$ \therefore \quad\left|F e _{B C}\right|=\frac{1}{4 \pi \varepsilon _0} \frac{(q / 3)(2 q / 3)}{(\sqrt{3} R)^{2}}=\frac{q^{2}}{54 \pi \varepsilon _0 R^{2}} $$
