Three point charges of 1C, 2C and 3C are placed at the corners of an equilateral triangle of side 1m. 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 $11x\times {10}^9$  J. Find x.
 

The initial energy of system  $u_1=\frac{1}{4\pi {\in }_0}[\frac{q_1{q}_2}{r_{12}}+\frac{q_2{q}_3}{r_{23}}+\frac{q_3{q}_1}{r_{13}}]$
$\Rightarrow u_1=q\times {10}^9[\frac{2\times 3}{1}+\frac{3\times 1}{1}+\frac{2\times 1}{1}]$
$\Rightarrow u_1=9\times {10}^9\times 11=99\times {10}^{9}J$
Final energy of system  $u_2=\frac{1}{4\pi {\in }_0}[\frac{q_1{q}_2}{r_{12}^1}+\frac{q_2{q}_3}{r_{23}^1}+\frac{q_3{q}_1}{r_{13}^1}]$
$\Rightarrow u_2=9\times {10}^9[\frac{2\times 3}{0.5}+\frac{3\times 1}{0.5}+\frac{2\times 1}{0.5}]$
$\Rightarrow u_2=9\times {10}^9\times 22=198\times {10}^{9}J$
So, work done   $W=u_2-u_1$
$W=198\times {10}^9-9\times {10}^9=99\times {10}^{9}J$
$\Rightarrow x=99$