Electrostatics

JEE Main level, single correct, medium

74 of 311

Question 74 of 311

A particle of charge −q-q and mass mm moves in a circle of radius rr around an infinitely long line charge of linear density +λ+\lambda. Then time period will be given as:
(Consider kk as Coulomb's constant)

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Answer: (B) T=2πrm2kλqT=2\pi r\sqrt{\dfrac{m}{2k\lambda q}}

Attractive electrostatic force due to line charge on the charged particle will provide the required centripetal force. Therefore,
q(2kλr)=mω2rq\left(\dfrac{2k\lambda }{r}\right)=m{\omega }^{2}r
⇒ω2=2kλqmr2\Rightarrow {\omega }^{2}=\dfrac{2k\lambda q}{m{r}^{2}}
⇒(2πT)2=2kλqmr2\Rightarrow {\left(\dfrac{2\pi }{T}\right)}^{2}=\dfrac{2k\lambda q}{m{r}^{2}}
⇒T=2πrm2kλq\Rightarrow T=2\pi r\sqrt{\dfrac{m}{2k\lambda q}}

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