 Solution

ID: past-exam-of-the-short-options-paper-shared-by-prelims-and-parts-a-and-b-of-the-physics-course-of-the-university-of-oxford/2018/s7/1/a/solution

Only

A_{z}

depends on position. Taking the curl,

B = \nabla \times A = \frac{B _{0} x}{L} \hat{y} .

The field reverses across

x = 0

. Its divergence is zero, as required for a magnetic field; the vanishing field on the midplane is important for the crossing and separatrix trajectories below.

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