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# 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:r=Qq16π2ϵ0mT3r3=Qq16π3ϵ0mT2r2=Qq16π3ϵ0mT3r2=Qq16πϵ0mT3

A
r3=Qq16π3ϵ0mT2
B
r2=Qq16π3ϵ0mT3
C
r2=Qq16πϵ0mT3
D
r=Qq16π2ϵ0mT3
Solution
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#### The centrifugal force acting on charge q is:F=kqQr2⇒mv2r=kqQr2⇒V=√kqQrmNow, V=2πrT⇒2πrT=√qQ4πε0rm⇒4π2r2T2=qQ4πε0rm⇒r3=qQT216π3ε0m

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