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The computer's keyboards make use of capacitors at the base of their keys (as shown in the…

Physics20251 markNumerical
The computer's keyboards make use of capacitors at the base of their keys (as shown in the diagram). Each key is connected to a movable plate, which represents one side of the capacitor. The fixed plate on the keyboard's bottom represents the capacitor's other side. External electronic circuits recognize each key by its capacitance when pressed. If the plate area is $2\text{ cm}^2$ and the plate separation is 1 mm, calculate the charge density on the plate, if the potential difference between the plates is 3 V. The plates are separated by a dielectric of $K = 5$.
Figure 81
Figure 81

Answer

Answer

Official answer key
$C = \frac{K\varepsilon_0 A}{d} = \frac{5 \times 8.85 \times 10^{-12} \times 2 \times 10^{-4}}{10^{-3}} = 8.85$ pF $Q = CV = 26.55$ pC Charge density $= \frac{Q}{A} = 13.28 \times 10^{-8}$ C/m$^2$ Alternately: $E = \frac{\sigma}{K\varepsilon_0}$ or $\sigma = EK\varepsilon_0 = (\varepsilon_0 KV/d)$

Final answer: $13.28 \times 10^{-8}$ C/m^2

Electrostatic Potential, Potential Energy and Capacitance

From ISC 2025 Practice Physics, question 81(b).

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