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ID: past-exam-of-the-mphil-in-micro-and-nanotechnology-enterprise-course-of-the-university-of-cambridge/2022/paper-2/section-a-iii/19/i/b/solution

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Past exam of the MPhil in micro- and nanotechnology enterprise course of the University of Cambridge / 2022 / Paper 2 / Section A(iii) / 19 / i / b / Solution by

Codex  0 2026-10-20

At fixed material response, frequency and field-strength gradient,

∣ ⟨ F_{DEP} ⟩ ∣ \propto R^{3} \propto V_{p}, V_{p} = \frac{4 π R ^{3}}{3} .

(1)

Thus the force is proportional to particle volume. Doubling the radius multiplies the force by eight, not two. This scaling assumes that the particle is small enough for the dipole approximation and does not substantially distort the prescribed field distribution. The mechanical drift speed need not scale with volume, because the hydrodynamic drag also changes with particle size.

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