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ID: past-exam-of-the-physics-2-paper-of-the-university-of-oxford/2017/8/d/solution

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Past exam of the physics 2 paper of the University of Oxford / 2017 / 8 / d / Solution by

Codex  0 2026-10-25

With

V = + 20 V

in the outer-minus-inner convention,

η = ln 1.5 = 0.405465

and the radial electric field at the orbit is

E_{r} = - 986.52 V m^{- 1}

. The signed roots are

u_{\pm} = \frac{- e B r \pm e ^{2} B ^{2} r ^{2} + 4 m e V / η}{2 m} .

Using the proton mass and charge gives

u_{+} = 4.88 \times 1 0^{4} m s^{- 1}, u_{-} = - 9.67 \times 1 0^{4} m s^{- 1} .

The speeds are therefore

48.8

and

96.7 km s^{- 1}

, in opposite senses of rotation. Both are nonrelativistic. The slower counterclockwise orbit has an outward magnetic force; the faster clockwise orbit has an inward magnetic force. Reversing

B

interchanges the senses, while reversing the electrode polarity changes the quadratic and may eliminate real orbits; its sign must therefore be specified.

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