Question

Taking the electronic charge as ‘e’ and the permittivity as $‘\epsilon 0^{\prime }$, use dimensional analysis to determine the correct expression for $\omega p$

• A. $\sqrt{\frac{Ne}{m{\epsilon }_0}}$
• B. $\sqrt{\frac{m{\epsilon }_0}{N{e}^2}}$
• C. $\sqrt{\frac{N{e}^2}{m{\epsilon }_0}}$
• D. $\sqrt{\frac{m{\epsilon }_0}{Ne}}$

Answer 1

The correct option is C $\sqrt{\frac{N{e}^2}{m{\epsilon }_0}}$

$\sqrt{\frac{m^{-3}\times C^2\times N{m}^{-2}}{kg\times C^2}}\{N=kgm{s}^{-2}\}$

$=\sqrt{s^{-2}}$