Electrostatics Question 675
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:
Options:
A) l
B) $ l^{2} $
C) $ {{l}^{2/3}} $
D) $ {{l}^{1/3}} $
Show Answer
Answer:
Correct Answer: D
Solution:
[d] In equilibrium, $ F _{e}=T\sin \theta $
$ mg=T\cos \theta $
$ \tan \theta =\frac{F _{e}}{mg}=\frac{q^{2}}{4\pi {\in _{0}}x^{2}\times mg} $
$ \text{also }\tan \theta \approx \sin =\frac{x/2}{l} $
$ \text{Hence, }\frac{x}{2l}=\frac{q^{2}}{4\pi {\in _{0}}x^{2}kt} $
$ \Rightarrow x^{3}=\frac{2q^{2}l}{4\pi {\in _{0}}mg}\therefore x={{( \frac{q^{2}l}{2\pi {\in _{0}}mg} )}^{1/3}} $
$ \Rightarrow x\propto {{l}^{1/3}} $
