Question

The work done to assemble the three charges in a configuration as shown in the figure below is

• A. $\frac{-3 q^{2}}{4 \pi \varepsilon_{0} a}$
• B. $\frac{-2 q^{2}}{4 \pi \varepsilon_{0} a}$
• C. $\frac{-q^{2}}{4 \pi \varepsilon_{0} a}$
• D. $0$

Answer 1

Answer: (C)

Work done,
$W=U_{12}+U_{23}+U_{13} $
$=\frac{k q_{1} \,q_{2}}{r_{12}}+\frac{k q_{2} \,k q_{3}}{r_{23}}+\frac{k q_{1} \,q_{3}}{r_{13}}$
$=\frac{1}{4 \,\pi\, \varepsilon_{0} a}\left[-2 q^{2}+2 q^{2}-q^{2}\right] $
$=-\frac{q^{2}}{4 \,\pi\, \varepsilon_{0} a}$