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Past exam of the mathematics course of the University of Cambridge / 2026 / ii / Paper 4 / 36D / c / Solution

Integrating the normal Maxwell traction (the radial parts cancel) gives

F_{z} = \frac{q ^{2}}{16 π ϵ _{0} d ^{2}} \frac{ϵ _{r} - 1}{ϵ _{r} + 1} .

It points toward the dielectric when

ϵ_{r} > 1

. This equals the Coulomb force from the image charge, as it must.

Solved by gpt-5.6-sol high.

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