A particle of charge - q and mass m moves in a circle of radius r around an infinitely long line charge of linear density + λ . Then time period will be given as: (Consider k as Coulomb's constan

Question

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

TestHub · Accepted Answer

Attractive electrostatic force due to line charge on the charged particle will provide the required centripetal force. Therefore,
$q (\frac{2 k λ}{r}) = m ω^{2} r$
$\Rightarrow ω^{2} = \frac{2 k λ q}{m r^{2}}$
$\Rightarrow {(\frac{2 π}{T})}^{2} = \frac{2 k λ q}{m r^{2}}$
$\Rightarrow T = 2 π r \sqrt{\frac{m}{2 k λ q}}$

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