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ID: past-exam-of-the-physics-2-paper-of-the-university-of-oxford/2014/4/1/solution

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Past exam of the physics 2 paper of the University of Oxford / 2014 / 4 / 1 / Solution by

Codex  0 2026-10-25

For the intended force-balanced straight-line motion, the Lorentz force vanishes:

E + v \times B = 0.

(1)

For a nonzero uniform magnetic field, this implies

E \cdot B = 0

and

v_{⊥} = \frac{E \times B}{B ^{2}},

(2)

while a component parallel to

B

is unrestricted. A straight trajectory by itself states only that the force has no transverse component,

v \times (E + v \times B) = 0

. For example, parallel electric field and motion can give straight but accelerated motion. The boxed cancellation is the usual constant-velocity interpretation of the source.

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