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?

Answer 1

Let
Side of the equilateral triangle = l 
As
Work done in assembling the charges = Net potential energy of the system

\[\Rightarrow W =  U_{12}  +  U_{13}  +  U_{23} \] 

\[ \Rightarrow W = \frac{1}{4\pi \epsilon_0}\left( \frac{q_1 q_2}{l} + \frac{q_1 q_3}{l} + \frac{q_2 q_3}{l} \right)\] 

\[                 = \frac{9 \times {10}^3}{{10}^{- 1}} \times  {10}^{- 10} [4 \times 2 + 4 \times 3 + 3 \times 2]\] 

\[                 = 9 \times (8 + 12 + 6)\] 

\[                 = 9 \times 26 = 234  \] J