Question 57: Electrostats & Capacitance

Question

A particle ' X ' carrying a charge +Q is moving in a circular path of radius R around another particle ' Y ' having a charge -Q with a frequency ' $v$ '. Then the mass ' $m$ ' of the charged particle is

Accepted Answer

We balance the Coulomb attraction with the required centripetal force:
Coulomb force
$$F_C = \frac{1}{4\pi\varepsilon_0}\,\frac{Q^2}{R^2}.$$
Centripetal force (with $\omega=2\pi v$)
$$F_{\rm cent} = m\,\omega^2\,R = m\,(2\pi v)^2\,R.$$
Equate $F_C=F_{\rm cent}$ and solve for $m$:
$$    m\,(2\pi v)^2\,R \;=\;\frac{Q^2}{4\pi\varepsilon_0\,R^2}    \quad\Longrightarrow\quad    m = \frac{Q^2}{4\pi\varepsilon_0\,R^2\,(2\pi v)^2\,R}      = \frac{Q^2}{16\pi^3\,\varepsilon_0\,R^3\,v^2}.    $$
That matches Option A.

Answer

$M=\frac{Q^2}{\left[16 \pi^3 \varepsilon_0 R^3 v^2\right]}$

Answer

$M=\frac{Q^2}{\left[16 \pi^2 \varepsilon_0 R v^2\right]}$

Answer

$M=\frac{Q^2}{\left[16 \pi^2 \varepsilon_0 R^3 v^2\right]}$

Answer

$M=\frac{Q^2}{\left[16 \pi^3 \varepsilon_0 R^2 v^2\right]}$

Electrostats & Capacitance

A particle ' X ' carrying a charge +Q is moving in a circular path of radius R around another particle ' Y ' having a charge -Q with a frequency ' v '. Then the mass ' m ' of the charged particle is

Choose the correct answer: