Two fixed point particles, each of charge $+q$, are separated by a distance $2 L$. Another point charge $+q$ of mass $m$ is oscillating about its equilibrium position as indicated in the figure below. The time period of oscillation is given by $T=2 \pi^{3 / 2} \alpha \sqrt{m} / q$. Given that $\epsilon_0$ is the permittivity of free space, which of the following options is the dimensionally correct expression for $\alpha$ in SI units?

• A

  $\epsilon_0^{3 / 2} L^{1 / 2}$
• B

  $\epsilon_0^{3 / 2} L$
• Correct answer
  C

  $\epsilon_0^{1 / 2} L^{3 / 2}$
• D

  $\epsilon_0^{1 / 2} L$

Hence, the correct answer is option: 'C'.