Three charges Q, + q and + q are placed at the vertices of a… | JEE Main 2019 (11 Jan, Shift 1)

Q50JEE Main 2019 · 11 JAN · SHIFT 1Medium

Electrostatic Potential Energy

Three charges Q, + q and + q are placed at the vertices of a right-angle isosceles triangle as shown below. The net electrostatic energy of the configuration is zero, if the value of Q is:

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Answer: (d)

Let each leg be $a$ , so the hypotenuse is $\sqrt{2}a$ . $Q$ is $a$ from one $+q$ and $\sqrt{2}a$ from the other; the two $+q$ are $a$ apart.
$U = k\left[\frac{qQ}{a} + \frac{qQ}{\sqrt{2}a} + \frac{q^2}{a}\right] = 0$
$Q\left(1 + \frac{1}{\sqrt{2}}\right) = -q \Rightarrow Q = -\frac{\sqrt{2}q}{\sqrt{2}+1}$
So the answer is (d).

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