 Solution

ID: past-exam-of-the-physics-b-course-of-the-university-of-cambridge/2014/paper-1/section-a/a3/solution

For steady thin beams a distance

d

apart, let

λ_{1}, λ_{2}

be their laboratory charge per length. Their current magnitudes are

∣ λ_{j} ∣ v

f_{E} = \frac{∣ λ _{1} λ _{2} ∣}{2 π ϵ _{0} d}, f_{B} = \frac{μ _{0} ∣ λ _{1} λ _{2} ∣ v ^{2}}{2 π d}, \frac{f _{E}}{f _{B}} = \frac{c ^{2}}{v ^{2}} .

The electric force is repulsive and the magnetic force attractive for the parallel electron velocities. The net force remains repulsive for

v < c

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