The work done to assemble the three charges i | vedclass

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(C) The work done to assemble a system of point charges is equal to the electrostatic potential energy of the system.For a system of three charges $q_

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$\frac{-q^2}{4 \pi \varepsilon_0 a}$

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(C) The work done to assemble a system of point charges is equal to the electrostatic potential energy of the system.For a system of three charges $q_1, q_2,$ and $q_3$ placed at distances $r_{12}, r_{23},$ and $r_{13}$ from each other,the potential energy $U$ is given by:$U = \frac{1}{4 \pi \varepsilon_0} \left( \frac{q_1 q_2}{r_{12}} + \frac{q_2 q_3}{r_{23}} + \frac{q_1 q_3}{r_{13}} \right)$Given the charges $q_1 = -q$,$q_2 = +q$,and $q_3 = -2q$,and the distance between each pair is $a$:$U = \frac{1}{4 \pi \varepsilon_0} \left( \frac{(-q)(q)}{a} + \frac{(q)(-2q)}{a} + \frac{(-q)(-2q)}{a} \right)$$U = \frac{1}{4 \pi \varepsilon_0 a} (-q^2 - 2q^2 + 2q^2)$$U = \frac{-q^2}{4 \pi \varepsilon_0 a}$

The work done to assemble the three charges in a configuration as shown in the figure is

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