Three point charges of $1C, 2Cand3C$ are placed at the corners of an equilateral triangle of side 1 m. The work required to move these charges to the corners of a smaller equilateral triangle of sides 0.5 m as shown in Figure is  $99\times {10}^{x}J$. Find x

Initial potential energy of system

$U_1=\frac{1}{4\pi {\in }_0}\left[\frac{q_1{q}_2}{r_{12}}+\frac{q_2{q}_3}{r_{23}}+\frac{q_3{q}_1}{r_{13}}\right]$

$\Rightarrow U_1=q\times {10}^9\left[\frac{2\times 3}{1}+\frac{3\times 1}{1}+\frac{2\times 1}{1}\right]$

$\Rightarrow U_1=9\times {10}^9\times 11$

$\Rightarrow U_1=99\times {10}^{9}J$

Final potential energy of system

$U_2=\frac{1}{4\pi {\in }_0}\left[\frac{q_1{q}_2}{r_{23}^{\text{'}}}+\frac{q_2{q}_3}{r_{23}^{\text{'}}}+\frac{q_3{q}_1}{r_{13}^{\text{'}}}\right]$

$\Rightarrow U_2=9\times {10}^9\left[\frac{2\times 3}{0.5}+\frac{3\times 1}{0.5}+\frac{2\times 1}{0.5}\right]$

$\Rightarrow U_2=9\times {10}^9\times 22=198\times {10}^{9}J$

So, work done $W=U_2-U_1$

$\Rightarrow W=198\times {10}^9-99\times {10}^9$

$\Rightarrow W=99\times {10}^{9}J$

$\Rightarrow x=9$