∙The plates of a parallel-plate capacitor are 3.28 mm apart, and each has an area of 12.2 cm^2 .

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∙The plates of a parallel-plate capacitor are 3.28 mm apart,...

$\bullet$ 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

Parallel-Plate Capacitor

A parallel-plate capacitor consists of two conductive plates separated by a fixed distance with a dielectric (often vacuum) between them. It is a fundamental component in circuits, used to store electrical energy through the separation of positive and negative charges on its plates. The geometry of the plates, specifically their area and the distance between them, directly influences the capacitor's ability to store charge.

Capacitance

Capacitance is the measure of a capacitor's ability to store charge per unit potential difference. For a parallel-plate capacitor, it is given by the formula C = ??A/d, where ?? is the electric constant (permittivity of free space), A is the area of one plate, and d is the distance between the plates. This relationship shows that capacitance increases with larger plate area and decreases with greater separation between the plates.

Potential Difference

The potential difference (voltage) across a capacitor is the energy per unit charge required to move charge from one plate to the other. It can be calculated using the relationship V = Q/C, where Q is the magnitude of the charge on one plate and C is the capacitance. This concept is key for understanding how energy is stored and how capacitors are utilized in electronic circuits.

Electric Field

The electric field between the plates of a parallel-plate capacitor is the force per unit charge experienced by a test charge in the field. It is uniform in an ideal parallel-plate configuration and can be calculated either by dividing the potential difference by the distance between the plates (E = V/d) or via the surface charge density using E = ?/??, where ? = Q/A. This field is responsible for the energy stored in the capacitor and the force experienced by charges.

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