Question

Three charges $Q,+q,-q$ are placed at the vertices of an isosceles right angled triangle as shown. The net electrostatic potential energy of the system is $0$ if $Q=$

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

Answer 1

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

$V=V_{AB}+V_{AC}+V_{BC}$

$⟹V=\frac{1}{4\pi {ϵ}_o}(\frac{q.q}{a}+\frac{qQ}{a}+\frac{qQ}{a\sqrt{2}})=0$

$⟹\frac{q}{a}(q+Q+\frac{Q}{\sqrt{2}})=0$

$⟹\left(\frac{\sqrt{2}q+\sqrt{2}Q+Q}{\sqrt{2}}\right)=0$

$⟹Q(1+\sqrt{2})=-\sqrt{2}q$

$⟹Q=\frac{-\sqrt{2}q}{1+\sqrt{2}}$

Answer-(D)