 Solution

ID: past-exam-of-the-short-options-paper-shared-by-prelims-and-parts-a-and-b-of-the-physics-course-of-the-university-of-oxford/2017/s19/3/b/solution

The supplied density is

4 \times 1 0^{24}

^{- 3}

. Therefore

ω_{p} ≃ 1.13 \times 1 0^{14} s^{- 1}, λ_{p} = 2 π c / ω_{p} ≃ 16.7 μ m .

The cold relativistic field scale is

E_{0} = m_{e} c ω_{p} / e ≃ 1.92 \times 1 0^{11}

^{- 1}

, corresponding to an energy gradient

e E_{0} ≃ 192 GeV m^{- 1}

. It is an upper scale for the stipulated large-amplitude wave, not proof that the particular weak driver produces that field.

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