SATHEE: General Physics Question 4

General Physics Question 4

Question 4

Taking the electronic charge as $e$ and the permittivity as $ε_{0}$ , use dimensional analysis to determine the correct expression for $ω_{p}$ . (a) $\sqrt{\frac{N e}{m ε_{0}}}$ (b) $\sqrt{\frac{m ε_{0}}{N e}}$ (c) $\sqrt{\frac{N e^{2}}{m ε_{0}}}$ (d) $\sqrt{\frac{m ε_{0}}{N e^{2}}}$

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Answer:

Correct Answer: 5. (c)

Solution:

$N =$ Number of electrons per unit volume

$\begin{aligned} ∴ [N] & = [L^{- 3}], [e] = [q] = [It] = [AT] [ε_{0}] & = [M^{- 1} L^{- 3} T^{4} A^{2}] \end{aligned}$

Substituting the dimensions, we can see that

$ω_{p} = \sqrt{\frac{{Ne}^{2}}{m ε_{0}}} = [T^{- 1}]$

Angular frequency has also the dimension $[T^{- 1}]$ .

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General Physics Question 4

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