24.2. The plates of a parallel-plate capacitor are 3.28 mm apart, and each has an area of 12.2 c

step 1 In the given problem there is a parallel plate capacitor like this. The plate separation D has b

24.2. The plates of a parallel-plate capacitor are 3.28 mm...

24.2. The plates of a parallel-plate capacitor are 3.28 $\mathrm{mm}$ apart, and each has an area of $12.2 \mathrm{cm}^{2} .$ Each plate carries a charge of magnitude $4.35 \times 10^{-8} \mathrm{C}$ . The plates are in vacuum. (a) What is the capacitance? (b) What is the potential difference between the plates? (c) What is the magnitude of the electric field between the plates?

Key Concepts

Permittivity of Free Space

The permittivity of free space (??) is a fundamental constant that characterizes the ability of a vacuum to support electric fields. It is a crucial parameter in the equations governing capacitance, electric field strength, and potential difference in systems where the media between capacitor plates is a vacuum.

Electric Field

The electric field in a capacitor is the region of influence between the plates where a force is exerted on charges. In a parallel-plate capacitor, the field is approximately uniform and can be calculated by either dividing the potential difference by the separation distance (E = V/d) or using the surface charge density and permittivity of free space (E = ?/??).

Potential Difference

The potential difference, or voltage, between the plates of a capacitor is directly related to the amount of stored charge and the capacitance. It is defined as the work done per unit charge to move a charge between the plates and can be calculated using the relationship V = Q/C.

Capacitance

Capacitance is the measure of a capacitor's ability to store charge per unit potential difference. In a parallel-plate capacitor, it is determined by the physical dimensions of the plates and the separation between them, typically expressed by the formula C = ??A/d, where ?? is the permittivity of free space, A is the area, and d is the distance between the plates.

Parallel-Plate Capacitor

A parallel-plate capacitor consists of two conductive plates separated by a small distance, where an electric field is established when the plates are oppositely charged. It is a basic model to study energy storage in an electric field and provides a clear example of how geometry and dielectric properties affect capacitance.

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