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Question 25.42: A parallel-plate air-filled capacitor has a capacitance of 5......

A parallel-plate air-filled capacitor has a capacitance of 50 pF. (a) If each of its plates has an area of 0.35 m², what is the separation? (b) If the region between the plates is now filled with material having \kappa = 5.6, what is the capacitance?

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(a) We use C = ε_0A/d to solve for d:

d=\frac{\varepsilon_0 A}{C}=\frac{\left(8.85 \times 10^{-12}\, C ^2 / N \cdot m ^2\right)\left(0.35\, m ^2\right)}{50 \times 10^{-12} \,F }=6.2 \times 10^{-2} \,m .

(b) We use C ∝ \kappa. The new capacitance is

C^{\prime}=C\left(\kappa / \kappa_{\text {air }}\right)=(50\, pf )(5.6 / 1.0)=2.8 \times 10^2 \,pF .

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