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Question:

Taking the electronic charge as 'e' and the permittivity as ε₀, use dimensional analysis to determine the correct expression for ωp.

√Ne²mε₀

√mε₀Ne²

√Nemε₀

√mε₀Ne

Solution:

We have ωp as the angular frequency. Thus its unit would be given as θ/t = [T⁻¹]. We have the units of density N as 1/L³, charge e as IT, mass as M, and ε₀ is evaluated using the force equation F = 1/(4πε₀)q₁q₂/r² as I²T⁴ML³.