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

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

Answer 1

Answer: (B)

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

Answer 2

Net electrostatic energy

$U = \frac{kQq}{a} + \frac{kq^{2}}{a} + \frac{kQq}{a\sqrt{2}} = 0$

$\Rightarrow \frac{kq}{a}\left( Q + q + \frac{Q}{\sqrt{2}} \right) = 0$ ⇒ $Q = - \frac{2q}{2 + \sqrt{2}}$