Question

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

• A. $+q$
• B. $-2q$
• C. $\frac{-\sqrt{2}q}{\sqrt{2}+1}$
• D. $\frac{-\sqrt{3}q}{\sqrt{2}+1}$

Answer 1

The correct option is C $\frac{-\sqrt{2}q}{\sqrt{2}+1}$

Given, the potential energy of the system is zero.

Also, the configuration is right-angled isosceles triangle.


So, net potential energy,

$U=k[\frac{q^2}{a}+\frac{Qq}{a}+\frac{Qq}{\sqrt{2}a}]$

$\Rightarrow 0=\frac{kq}{a}[q+Q+\frac{Q}{\sqrt{2}}]$

$\Rightarrow -q=Q[1+\frac{1}{\sqrt{2}}]$

$\Rightarrow Q=\frac{-\sqrt{2}q}{\sqrt{2}+1}$