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Question

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:


A
r=Qq16π2ϵ0mT3
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B
r3=Qq16π3ϵ0mT2
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C
r2=Qq16π3ϵ0mT3
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D
r2=Qq16πϵ0mT3
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Solution

The correct option is B r3=Qq16π3ϵ0mT2
The centrifugal force acting on charge q is:
F=kqQr2
mv2r=kqQr2
V=kqQrm
Now, V=2πrT
2πrT=qQ4πε0rm
4π2r2T2=qQ4πε0rm
r3=qQT216π3ε0m
63721_11146_ans_ba0d285b966045b8942a16cc20f41202.png

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