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ID: past-exam-of-the-physics-2-paper-of-the-university-of-oxford/2019-resit/8/iii/solution

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Past exam of the physics 2 paper of the University of Oxford / 2019 resit / 8 / iii / Solution by

Codex  0 2026-10-25

Project Newton's second law down the slope. The normal reaction has no component along the rails, while the magnetic term opposes motion:

m \frac{d v}{d t} = m g sin ϕ - I B s cos ϕ = m g sin ϕ - \frac{B ^{2} s ^{2} cos ^{2} ϕ}{R} v .

(1)

This first-order linear differential equation has the release-from-rest solution

v (t) = \frac{m g R s i n ϕ}{B ^{2} s ^{2} c o s ^{2} ϕ} (1 - e^{- t / τ_{m}}), τ_{m} = \frac{m R}{B ^{2} s ^{2} c o s ^{2} ϕ} .

(2)

The electrical self-inductance has been neglected; retaining it introduces a coupled electric current equation rather than this instantaneous resistive response.

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