Question

Taking the electronic charge as ${}^{\prime }{e}^{\prime }$ and the permittivity as ${}^{\prime }{\epsilon }_0^{\prime }$, use dimenstional analysis to determine the correct expression for ${\omega }_p$

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

Answer 1

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

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

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