 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-2-of-the-natural-sciences-course-of-the-university-of-cambridge/2025/paper-2/3/a/solution

E = - \nabla φ

(\partial_{x}^{2} + \partial_{y}^{2}) φ = - ρ / ϵ_{0}, E = - \nabla φ .

The curl equation is automatic because the curl of a gradient vanishes. Independence of

z

makes

E_{z}

constant, and its required decay forces it to be zero, so a

z

-independent potential suffices.

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