Question

Three-point charges 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 side 0.5m in two different ways as in fig.(A) and (B)Calculate the work done

• A. $9\times {10}^9$
• B. $99\times {10}^9$
• C. $89\times {10}^9$
• D. $29\times {10}^9$

Answer 1

The correct option is B $99\times {10}^9$

Work done on the system is change in their potential energies in two configuration.

$q_1=1C{q}_2=2C{q}_3=3C$

So initial potential energy of arrangement

$r=1m$

$U=h(\frac{q_1{q}_2}{r}+\frac{q_2{q}_3}{r}+\frac{q_3{q}_1}{r})$[h is constant $9\times {10}^9$]

$=h\left(\frac{2+6+3}{1}\right)U_{initial}=11h\to \left(1\right)$

Initial potential energy of arrangement $r=0.5m$

$U_{final}=h(\frac{q_1{q}_2}{r}+\frac{q_2{q}_3}{r}+\frac{q_3{q}_1}{r})=h\left(\frac{2+6+3}{0.5}\right)=22h\to \left(2\right)$

Work done$=U_{final}-U_{initial}=22h-11h=11\times 9\times {10}^9=99\times {10}^{9}J$