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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 the time period will be $(k = \frac{1}{4 π ε_{0}})$

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$T^{} = \frac{1}{2 π r} \sqrt{\frac{m}{2 k λ q}}$

$T^{2} = \frac{4 π^{2} m}{2 k λ q} r^{3}$

$T = 2 π r \sqrt{\frac{m}{2 k λ q}}$

$T^{} = \frac{1}{2 π r} \sqrt{\frac{2 k λ q}{m}}$

answer is A.

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Detailed Solution

$E q = \frac{m v^{2}}{r} - (1) E = \frac{λ}{2 π E_{0} r} - (2) v = \sqrt{\frac{2 k q λ}{m}}$

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