Question

Three charges equal to Q is placed at the three corners of an equilateral triangle of side a and a charge Q at its center. If the system is in equilibrium then a 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

The correct option is A $\frac{Q}{\sqrt{3}}$

If we see the forces at corner if the given equilateral triangle. The charge placed at centre should be $-ve$

$|FR|=|F3|\frac{2q2}{4\pi {ϵ}_0{q}^2}\cos 30°=\frac{3qQ}{4\pi {ϵ}_0{q}^2}$

By simplifying will get $Q=\frac{q}{\sqrt{3}}$

$\therefore$ Value of $q=\frac{Q}{\sqrt{3}}$