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 +λ. Then its time period is where k=14πε0

A
$T = 2 πr \sqrt{\frac{m}{2 kλq}}$
B
$T^{2} = \frac{4 π^{2} m}{2 kλq}$
C
$T = \frac{1}{2 πr} \sqrt{\frac{2 kλq}{m}}$
D
$T = \frac{1}{2 πr} \sqrt{\frac{m}{2 kλq}}$

Solution:

$\frac{{mv}^{2}}{r} = q \frac{λ}{2 {πε}_{0} r} \Rightarrow v = \sqrt{\frac{qλ}{2 {πε}_{0} m}} = \sqrt{\frac{2 kqλ}{m}} T = \frac{2 πr}{v} = 2 πr \sqrt{\frac{m}{2 kqλ}}$

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 + $λ$ . Then its time period is $(where k = \frac{1}{4 {πε}_{0}})$

Solution:

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