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Electric Charges And Fields

Question

A particle of mass m carrying charge + q₁ is revolving around a fixed charge – q₂ in a circular path of radius r. Calculate the period of revolution.

Solution

Since the particle carrying posive charge is revolving around another charge,

Electrostatic force = Centrifugal force

\frac{1}{4 {πε}_{0}} \frac{q_{1} q_{2}}{r^{2}} = {mrω}^{2} = \frac{4 π^{2} mr}{T^{2}}

\Rightarrow

T^{2} = \frac{(4 {πε}_{0}) r^{2} (4 π^{2} mr)}{q_{1} q_{2}}

\Rightarrow

T = 4 πr \sqrt{\frac{{πε}_{0} mr}{q_{1} q_{2}}}

where T is the period of revolution.