Question

Here a particle of mass m and carry charge q¹ is revolving around a fixed charge -q² in a circular path of radius r calculate the period of revolving and it's speed?

Answer 1

The particle $\sf{q_1}$ experiences centripetal force since it is in circular motion, which is provided by the electrostatic force of attraction between the particles.

Thus,

$\longrightarrow\sf{\dfrac{mv^2}{r}=\dfrac{kq_1q_2}{r^2}}$

Hence speed of the particle is,

$\longrightarrow\underline{\underline{\sf{v=\sqrt{\dfrac{kq_1q_2}{rm}}}}}$

The time period of revolution of the particle is given by,

$\longrightarrow\sf{T=\dfrac{2\pi r}{v}}$

$\longrightarrow\sf{\underline{\underline{T=2\pi r\sqrt{\dfrac{rm}{kq_1q_2}}}}}$

$\longrightarrow\sf{\underline{\underline{T=2\pi\sqrt{\dfrac{mr^3}{kq_1q_2}}}}}$