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ID: past-exam-of-the-physics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2012/paper-1/section-a/6/solution

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Past exam of the physics course of the year 1 of the natural sciences course of the University of Cambridge / 2012 / Paper 1 / Section A / 6 / Solution by

Codex  0 2026-10-20

The breakdown-limited parallel-plate charge follows from the ideal parallel-plate capacitor relation

Q = C V = (ϵ_{0} A / d) (E d) = ϵ_{0} A E

. Dielectric breakdown limits the electric field rather than the voltage independently of separation:

Q_{m a x} = ϵ_{0} (4.0 \times 1 0^{- 6} m^{2}) (3.0 \times 1 0^{6} V m^{- 1}) = 1.06 \times 1 0^{- 10} C ≃ 106 pC .

(1)

This is the magnitude on either plate, not the sum of both magnitudes. Edge enhancement and fringing are neglected, as in the stated parallel-plate model.

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