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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=Qq16π2ϵ0mT3
- r3=Qq16π3ϵ0mT2
- r2=Qq16π3ϵ0mT3
- r2=Qq16πϵ0mT3

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Solution

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F=kqQr2

⇒mv2r=kqQr2

⇒V=√kqQrm

Now, V=2πrT

⇒2πrT=√qQ4πε0rm

⇒4π2r2T2=qQ4πε0rm

⇒r3=qQT216π3ε0m

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