A charged particle of mass m_{1} and charge q | vedclass

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Question

(C) The necessary centripetal force for circular motion is provided by the electrostatic Coulomb force between the two charges.Equating the centripeta

Vedclass · Accepted Answer

$T=\sqrt{\frac{16 \pi^{3} \varepsilon_{0} m_{1} r^{3}}{q_{1} q_{2}}}$

Vedclass · Answer

(C) The necessary centripetal force for circular motion is provided by the electrostatic Coulomb force between the two charges.Equating the centripetal force to the Coulomb force:$\frac{m_{1} v^{2}}{r} = \frac{1}{4 \pi \varepsilon_{0}} \cdot \frac{|q_{1} q_{2}|}{r^{2}}$Solving for velocity $v$:$v^{2} = \frac{|q_{1} q_{2}|}{4 \pi \varepsilon_{0} m_{1} r}$$v = \sqrt{\frac{|q_{1} q_{2}|}{4 \pi \varepsilon_{0} m_{1} r}}$Now, the time period $T$ is given by $T = \frac{2 \pi r}{v}$.Substituting the expression for $v$:$T = 2 \pi r \sqrt{\frac{4 \pi \varepsilon_{0} m_{1} r}{|q_{1} q_{2}|}}$$T = \sqrt{4 \pi^{2} r^{2} \cdot \frac{4 \pi \varepsilon_{0} m_{1} r}{|q_{1} q_{2}|}}$$T = \sqrt{\frac{16 \pi^{3} \varepsilon_{0} m_{1} r^{3}}{|q_{1} q_{2}|}}$Comparing this with the given options, option $C$ is the correct expression for the time period $T$ (assuming $q_{1}$ and $q_{2}$ have opposite signs for attraction).

$A$ charged particle of mass $m_{1}$ and charge $q_{1}$ is revolving in a circle of radius $r$. Another charged particle of charge $q_{2}$ and mass $m_{2}$ is situated at the centre of the circle. If the velocity and time period of the revolving particle are $v$ and $T$ respectively, then:

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