0. Charge Q of mass m revolves around a point charge q due
to electrostatic attraction. Show that its period of revolution
is given by T²= (16π³E0 mR3)/Qq
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Charge Q of mass m revolves around a point charge q due to electrostatic attraction. Show that its period of revolution is given by T2=16π3ε0mR3QqT2=16π3ε0mR3Qq
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Hint: As the charge Q of mass m is revolving in a circular motion, it experiences centripetal force. Next, find the electrostatic force between the two particles. As these are the only two forces, they must be equal as energy is always conserved. So, equate and substitute them accordingly.
Formula used:
T=2πrv⇒F=Kq1q2r2T=2πrv⇒F=Kq1q2r2
Complete step by step answer:
The mass m of charge Q is moving in a circular way around the point mass. Therefore, it has some centripetal force acting towards the centre.
Next, the two charged particles experience some electrostatic force of attraction between them. As energy is conserved and these are the two forces acting in the overall system, they must be equal.
The centripetal force acted is
F=mv2RF=mv2R
The electrostatic force of attraction will be,
F=Kq1q2r2F=Kq1q2r2
As these two forces are equal,
mv2r=Kq1q2r2⇒v=Kq1q2mr−−−−−−√mv2r=Kq1q2r2⇒v=Kq1q2mr
Also, the time period formula can be written as,
T=2πv⇒T=2πm×rKq1q2−−−−−−√∴T2=16π3ε0mR3Qq−−−−−−−−−−√T=2πv⇒T=2πm×rKq1q2∴T2=16π3ε0mR3Qq
Therefore, we can derive the time period formula in this way.
hope this answer is helpful for you.
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