 Solution

ID: past-exam-of-the-symmetry-and-relativity-course-of-the-university-of-oxford/2017/1/e/solution

The electron moves in the direction for which the electric field does positive work. Its kinetic energy gain is the magnitude

e E L = 30 MeV

. Hence

γ = 1 + \frac{30}{0.511} = 59.7084, β = 1 - γ^{- 2} = 0.99985974.

This uses the relativistic energy-momentum relation, rather than the nonrelativistic kinetic-energy formula. Acceleration is opposite the field direction for a negatively charged electron, although the energy gain is positive along its actual displacement.

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