Question

Three charges equal to $-Q$ are placed at the three corners of equilateral triangle of side $a$ and a charge $q$ at its centre. If the system is in equilibrium then value of $q$ is

• A. $\frac{Q}{\sqrt{3}}$
• B. $\frac{Q}{3\sqrt{3}}$
• C. $\sqrt{3}Q$
• D. $\frac{2Q}{\sqrt{3}}$

Answer 1

Answer: (A)

$\frac{Q}{\sqrt{3}}$

$r\cos \theta +r\cos \theta =a$

$2r\cos \theta =a$

$r=\left(\frac{a}{2\cos \theta }\right)=\frac{a}{2}\frac{2}{\sqrt{3}}$

$r=\frac{a}{\sqrt{3}}$

$\left|F_R\right|=\left|F_3\right|$

$\frac{2q^2}{4\pi {\epsilon }_{0}q}\cos 0=\frac{3q\theta }{4\pi {\epsilon }_{0}q}$

$\theta =\frac{q}{\sqrt{3}}$