Question

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

Answer 1

The correct option is A $6.6\times {10}^{-8}C$

Given : $d=2$ mm $E=3.0\times {10}^4$ $V/cm=3.0\times {10}^6$ $V/m$ $l=5.0cm=0.05$ m

Area of each plate $A=l^2=(0.05{)}^2=25\times {10}^{-4}$ $m^2$

Capacitance of the capacitor $C=\frac{A{ϵ}_o}{d}$

Potential difference between the plates $V=Ed$

$\therefore$ Charge on each plate $Q=CV=A{ϵ}_{o}E$

$⟹$ $Q=25\times {10}^{-4}\times 8.85\times {10}^{-12}\times 3.0\times {10}^6=6.6\times {10}^{-8}$ C