 Solution

ID: past-exam-of-the-mphil-in-micro-and-nanotechnology-enterprise-course-of-the-university-of-cambridge/2021/paper-2/section-b/20/iv/b/solution

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Past exam of the MPhil in micro- and nanotechnology enterprise course of the University of Cambridge / 2021 / Paper 2 / Section B / 20 / iv / b / Solution by

Codex  0 2026-10-20

Substituting

r_{c} = ℏ k_{F} / (e ∣ B ∣)

into

L = 2 j r_{c}

gives

B_{j} = \frac{2 j ℏ k _{F}}{e L}, L = 1 0^{- 6} m .

(1)

Using the density-derived Fermi wave vector gives the first three peak magnitudes

∣ B_{1} ∣ = 0.1807 T, ∣ B_{2} ∣ = 0.3613 T, ∣ B_{3} ∣ = 0.5420 T .

(2)

The equally spaced sequence follows from the number of reflected half-orbits, not from successive quantum Hall fillings. The field polarity selecting a given injector–collector orientation follows from the Lorentz force direction.

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