Question

Three identical charges each of $2\mu C$ are placed at the vertices of a triangle $ABC$ as shown in the figure. If $AB+AC=12cm$ and $AB\cdot AC=32c{m}^2$, the potential energy of the charge at $A$ is

• A. 1.53 J
• B. 5.31 J
• C. 3.15 J
• D. 1.35 J

Answer 1

Answer: (D)

Given each charge, $q=2\mu C$
or $q=2\times 10^{-6}C$
$AB+AC=12cm\dots$(i)
$AB\cdot AC=32c{m}^2\dots$ (ii)
From equation (i), $AB=12-AC$
Put the value of $AB$ in equation (ii)
$(12-AC)AC=32$ or $A{C}^2-12AC+32=0$
On solving, we get $AC=8$ or $4$
$\therefore$ If $AC=8cm,AB=4cm$ or
$AB=0.04m,AC=0.08m$
The $P.E$ of the charge at $A$ is
$U=\frac{1}{4\pi {\epsilon }_0}\left[\frac{q^2}{AB}+\frac{q^2}{AC}\right]$
$=9\times 10^9\left[\frac{4\times 10^{-12}}{0.04}+\frac{4\times 10^{-12}}{0.08}\right]=1.35J$