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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 2026-10-20

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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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