Question

Three charges (each Q) are placed at the three corners of an equilateral triangle. A fourth charge q is placed at the center of the triangle. The ratio $|q/Q|$ so as to make the system in equilibrium is:

• A. 1 : 3
• B. 1 : $\sqrt{3}$
• C. $\sqrt{3}$ : 1
• D. 2 : $\sqrt{3}$

Answer 1

The correct option is B 1 : $\sqrt{3}$

Net force on q will be zero for any values of q and Q. Net force on each
Q should also be zero. For this q should be negative of Q.
By symmetry,total force on charge q will be zero
Now total force on any on charge Q
$F_2-2F_{1}cos{30}^o=0$
$F_2=2F_{1}cos{30}^o$
or
$\frac{kqQ}{(a/\sqrt{3}{)}^2}=2\frac{k{Q}^2\sqrt{3}}{a^{2}2}$ or $\frac{q}{Q}=\frac{1}{\sqrt{3}}$