Question

Two balls of same mass and carrying equal charge are hung from a fixed support of length $l$. At electrostatic equilibrium, assuming that angles made by each thread is small, the separation, $x$ between the balls is proportional to :

• A. $l$
• B. $l^2$
• C. $l^{2/3}$
• D. $l^{1/3}$

Answer 1

Answer: (D)

In equilibrium, $F_e=Tsin\theta$
$mg=Tcos\theta$
$tan\theta =\frac{F_e}{mg}=\frac{q^2}{4\pi {\in }_0{x}^2\times mg}$
also $tan\theta \approx sin=\frac{x/2}{\ell }$
Hence, $\frac{x}{2\ell }=\frac{q^2}{4\pi {\in }_0{x}^2\times mg}$
$\Rightarrow x^3=\frac{2q^2\ell }{4\pi {\in }_0\times mg}$
$\therefore x={\left(\frac{q^2\ell }{2\pi {\in }_0\times mg}\right)}^{1/3}$
Therefore $x\propto {\ell }^{1/3}$