In Fig. 25-40, two parallel-plate capacitors (with air between the plates)are connected to a battery. Capacitor 1 has a plate area of 1.5 cm $^{2}$ and an electric field (between its plates) of magnitude 2000 V/m. Capacitor 2 has a plate area of 0.70 cm $^{2}$ and an electric field of magnitude 1500 V/m.What is the total charge on the two capacitors?

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Solution

Equation 23-14 applies to each of these capacitors. Bearing in mind that $σ = q / A$ , we find the total charge to be
$q_{t o t a l} = q_{1} + q_{2} = σ_{1} A_{1} + σ_{2} A_{2} = ε_{1} E_{1} A_{1} + ε_{2} E_{2} A_{2} = 3.6 p C$
where we have been careful to convert $c m^{2}$ to $m^{2}$ by dividing by $10^{4}$ .

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Equation 23-14 applies to each of these capacitors. Bearing in mind that σ=q/A , we find the total charge to beqtotal=q1+q2=σ1A1+σ2A2=ε1E1A1+ε2E2A2=3.6pCwhere we have been careful to convert cm2 to m2 by dividing by 104.