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(D) The total electrostatic potential energy $U$ of a system of point charges is the sum of the potential energies of all distinct pairs of charges.Fo

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$\frac{-\sqrt{2}q}{\sqrt{2}+1}$

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(D) The total electrostatic potential energy $U$ of a system of point charges is the sum of the potential energies of all distinct pairs of charges.For the given configuration,the pairs are $(Q, +q)$,$(+q, +q)$,and $(Q, +q)$ with distances $l$,$l$,and $\sqrt{2}l$ respectively.The total potential energy is given by:$U = \frac{kQq}{l} + \frac{kq^2}{l} + \frac{kQq}{\sqrt{2}l} = 0$Dividing by $k/l$ (assuming $k 
eq 0$ and $l 
eq 0$):$Qq + q^2 + \frac{Qq}{\sqrt{2}} = 0$$Qq(1 + \frac{1}{\sqrt{2}}) = -q^2$$Qq(\frac{\sqrt{2}+1}{\sqrt{2}}) = -q^2$$Q = -q^2 \cdot \frac{\sqrt{2}}{q(\sqrt{2}+1)}$$Q = -\frac{\sqrt{2}q}{\sqrt{2}+1}$

Three charges $Q$,$+q$,and $+q$ are placed at the vertices of a right-angled triangle as shown. The net electrostatic potential energy of the configuration is zero. The value of $Q$ is

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