Question

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-JEE 2000)

• A. $\frac{-q}{1+\sqrt{2}}$
• B. $\frac{-2q}{2+\sqrt{2}}$
• C. -2q
• D. +q

Answer 1

The correct option is B $\frac{-2q}{2+\sqrt{2}}$

The total P.E of the system
$=\frac{K{q}^2}{a}+\frac{KqQ}{a}+\frac{KqQ}{\sqrt{2}a}$

According to question,
$\frac{Kq}{a}\{q+Q+\frac{Q}{\sqrt{2}}\}=0$
$\Rightarrow Q\left\{\frac{\sqrt{2}+1}{\sqrt{2}}\right\}=-q$
$Q=\frac{-\sqrt{2}q}{\sqrt{2}+1}=\frac{-2q}{2+\sqrt{2}}$