Question

Three point charges of $1\text{C},2\text{C}$ and $3\text{C}$ are placed at the corners of an equilateral triangle of side $1\text{m}$. The work required to move these charges to the corners of a smaller equilateral triangle of side $0.5\text{m}.$ is $x\times {10}^9\text{J}$, Find $x$

• A. 99.0
• B. 99.00
• C. 99

Answer 1

Answer: (A), (B), (C)

Given,

$q_1=+1\text{C},q_2=+2\text{C},q_3=+3\text{C}$

Side of an equilateral triangle , $r=1\text{m}$

Workdone by the electrostatic force $W=U_i-U_f$

For three charge distribution we know that ,

$\Delta U=\frac{[q_1{q}_2+q_2{q}_3+q_3{q}_1]}{4\pi {\epsilon }_0}(\frac{1}{r_f}-\frac{1}{r_i})$

$\therefore W=|\frac{[q_1{q}_2+q_2{q}_3+q_3{q}_1]}{4\pi {\epsilon }_0}(\frac{1}{r_f}-\frac{1}{r_i})|$

Substituting the given values we get,

$W=\frac{(9\times {10}^9)[3\times 2+3\times 1+2\times 1](1-0.5)}{0.5\times 1}$

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

Acceptable answers : $99,99.0,99.00$