Q.
Consider a system of three charges $\frac{q}{3},\frac{q}{3}and - \frac{2q}{3}$ placed at point 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°.
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
$\frac{q}{12\pi\varepsilon_{0}R}$
Explanation
(c) Distance
$BC = AB\sin{60{^\circ} = (2R)\frac{\sqrt{3}}{2} = \sqrt{3}R\ }$
$\therefore\left| F_{BC} \right| = \frac{1}{4\pi\varepsilon_{0}}\frac{\left( \frac{q}{3} \right)\ \left( \frac{2q}{3} \right)}{\left( \sqrt{3}R \right)^{2}} = \frac{q^{2}}{54\pi\varepsilon_{0}R^{2}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.