Question

Three identical small balls, each of mass 0.1g, are suspended at one point on silk thread having a length of I = 20cm. What charges should be imparted to the balls for each thread to form an angle of $\alpha ={30}^{\circ }$with the vertical?

Answer 1

$tan{30}^{\circ }=\frac{F_e}{F_g}$
$F_e=2\frac{1}{4\pi ϵ}\frac{q^2}{a^2}cos{30}^{\circ }=\sqrt{3}\frac{1}{4\pi ϵ}\frac{q^2}{a^2}$
$F_g=mg$
Therefore,
$tan30=\frac{1}{\sqrt{3}}=\sqrt{3}\frac{1}{4\pi ϵ}\frac{q^2}{a^2}\frac{1}{mg}$
And $lsin30=\frac{a}{\sqrt{3}}\Rightarrow a=\frac{\sqrt{3}l}{2}$
$\Rightarrow q=3.3\times {10}^{-6}C$