Question

How much work has to be done in assembling three charged particles at the vertices of an equilateral triangle, as shown in the figure?
Figure

Answer 1

234 J work has to be done in assembling three charged particles at the vertices of an equilateral triangle

Explanation:

Step 1:  

We know that

The amount of work done is equal to the net energy potential

Let

Side of the equilateral triangle = l

Step 2:

As we know that

Work done in assembling the charges = Net potential energy of the system

$\begin{array}{c}{P . E=U_{12}+U_{13}+U_{23}} \\\\{P \cdot E=\frac{k q_{1} q_{2}}{r_{12}}+\frac{k q_{1} q_{3}}{r_{13}}+\frac{k q_{2} q_{3}}{r_{23}}}\end{array}$

Step 3:

On substituting the values, we get

$\begin{aligned}P . E=& \frac{k \times 10^{-10}}{r}[4 \times 2+4 \times 3+3 \times 2] \\P \cdot E=& \frac{k \times 10^{-10}}{r}[8+12+6]\end{aligned}$

$\begin{aligned}P \cdot E=\frac{9 \times 10^{9} \times 10^{-10}}{10^{-1}}[26]\end{aligned}$

$\begin{aligned}&P . E=\frac{9 \times 10^{-1}}{10^{-1}}[26]\\&P . E=9 \times[26]\\&P . E=234 \mathrm{J}\end{aligned}$

234 J work has to be done in assembling three charged particles at the vertices of an equilateral triangle

Answer 2

Answer:

261 J as calculated jsjshssjjs