Electrostatics Question 725
Question: A particle of charge - q and mass m moves in a circle of radius r around an infinitely long line charge of linear charge density $ +\lambda . $ Then time period will be
Options:
A) $ T=2\pi r\sqrt{\frac{m}{2k\lambda q}} $
B) $ T^{2}=\frac{4{{\pi }^{2}}m}{2k\lambda q}r^{3} $
C) $ T=\frac{1}{2\pi r}\sqrt{\frac{2k\lambda q}{m}} $
D) $ T=\frac{1}{2\pi r}\sqrt{\frac{m}{2k\lambda q}} $
Show Answer
Answer:
Correct Answer: A
Solution:
[a] We have centripetal force equation
$ q( \frac{2k\lambda }{r} )=\frac{mv^{2}}{r}\text{ so }v=\sqrt{\frac{2kq\lambda }{m}} $
$ \text{Now, }T=\frac{2\pi r}{v}=2\pi r\sqrt{\frac{m}{2kq\lambda }}\text{ where }k=\frac{1}{4\pi {\varepsilon _{0}}} $
