Three charges $Q,\, + q$ and $ + q$ are placed at the vertices of a right-angled isosceles triangle as shown. The net electrostatic energy of the configuration is zero if $Q$ is equal to
IIT 2000, Diffcult
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(b) Net electrostatic energy $U = \frac{{kQq}}{a} + \frac{{k{q^2}}}{a} + \frac{{kQq}}{{a\sqrt 2 }} = 0$
$ \Rightarrow \,\frac{{kq}}{a}\left( {Q + q + \frac{Q}{{\sqrt 2 }}} \right) = 0$ $==>$ $Q = - \frac{{2q}}{{2 + \sqrt 2 }}$
$ \Rightarrow \,\frac{{kq}}{a}\left( {Q + q + \frac{Q}{{\sqrt 2 }}} \right) = 0$ $==>$ $Q = - \frac{{2q}}{{2 + \sqrt 2 }}$
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