Question

Three particles, each having a charge of $10\mu \text{C}$ are placed at the vertices of an equilateral triangle of side $10\text{cm}$. Find the work done by a person in pulling them apart to infinite separation.

• A. $0\text{J}$
• B. $27\text{J}$
• C. $-54\text{J}$
• D. $-27\text{J}$

Answer 1

The correct option is B $27\text{J}$

Given that,
Length of each side of the triangle, $r=10\text{cm}=0.1\text{m}$
Charge, $q=10\mu \text{C}$

The potential energy ($U$) of a system of two charges ($q_1$ and $q_2$) is given by

$U=\frac{k{q}_1{q}_2}{r}$

In the case of system of multiple charges, the potential energy is

$U=\frac{k{q}_1{q}_3}{r_2}+\frac{k{q}_2{q}_3}{r_1}+\frac{k{q}_1{q}_2}{r_3}$

Here, $q_1=q_2=q_3=q=10\times {10}^{-6}\text{C}$
$r_1=r_2=r_3=r=0.1\text{m}$
Substituting the values,
$U=\frac{9\times {10}^9\times 10\times {10}^{-6}\times 10\times {10}^{-6}\times 3}{0.1}$

$\Rightarrow U=27\text{J}$

This is the initial potential energy. So, $U_i=27\text{J}$

Now, when charges are infinitely separated, the potential energy is reduced to zero. So, $U_f=0$

Work done by electric force is
$W=U_f-U_i=-27\text{J}$

Thus, work done by a person on the system is $27\text{J}$.

$\begin{array}{c}\text{Why this question ?}\\ \text{Tip:When charges are infinitely separated}\\ (r\to \infty )\text{then the potential energy of}\\ \text{the system reduces to zero.}\end{array}$