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AP® Physics C: E & M

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Moderate

Dielectric Breakdown: Maximum Charge on Capacitor

APPHEM-JOAFKG

A capacitor contains two square plates with side lengths $5.0$ cm. The plates are separated by $2.0$ mm. Dry air fills the space between the plates. Dry air has a dielectric constant of $1.00$ and experiences dielectric breakdown when the electric field exceeds $3.0 \times 10^4 $ V/cm.

What is the magnitude of charge that can be stored on each plate before the capacitor exceeds its breakdown limit and sends a spark between the plates?

A

$6.6 \times {10}^{-8}$C

B

$6.6 \times {10}^{-5}$C

C

$3.3 \times {10}^{-7}$C

D

$3.3 \times {10}^{-84}$C

E

$8.1 \times {10}^{-2}$C