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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?
Solution
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
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