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Q.

A particle of charge -q and mass m moves in a circular orbit of radius r about a fixed charge +Q. The relation between the radius of the orbit r and the time period T is

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a

$r = \frac{Qq}{16 π^{2} ϵ_{0} m} T^{3}$

b

$r^{3} = \frac{Qq}{16 π^{3} \in_{0} m} T^{2}$

c

$r^{2} = \frac{Qq}{16 π \in_{0} m} T^{3}$

d

$r^{2} = \frac{Qq}{16 π^{3} \in_{0} m} T^{3}$

answer is B.

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Detailed Solution

$F = \frac{1}{4 {πε}_{0}} \frac{Qq}{r^{2}} = {mrω}^{2}; ω = \frac{2 π}{T}$

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