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