 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/s12/2/4/solution

In a sufficiently uniform flow the Stokes force is

F = γ v

toward trap 2. Its work over separation

d

lowers the second effective well by

F d

. Equal effective free energies require

γ v d = k_{B} T lo g 2

. Hence

v = \frac{k _{B} T lo g 2}{6 π η a d} ≃ 3.0 \times 1 0^{- 7} m s^{- 1}

at 298 K. The temperature was not specified, so the numerical result scales as

T /298 K

. This approximation treats a weak uniform drag as a constant tilt and neglects changes in barrier shape and hydrodynamic interactions with boundaries.

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