The plates of a parallel-plate capacitor are 2.50 mm apart, and each carries a charge of magnit

step 1 So in this problem we have a capacitor and from the problem we know the parameters the separatio

The plates of a parallel-plate capacitor are 2.50 mm apart,...

The plates of a parallel-plate capacitor are $2.50 \mathrm{~mm}$ apart, and each carries a charge of magnitude $80.0 \mathrm{nC}$. The plates are in vacuum. The electric field between the plates has a magnitude of $4.00 \times 10^{6} \mathrm{~V} / \mathrm{m} .$ What is (a) the potential difference between the plates; (b) the area of each plate; (c) the capacitance?

Key Concepts

Relationship between Electric Field and Potential Difference

In a parallel-plate configuration, the electric field (E) is uniform and directly related to the potential difference (V) between the plates by the equation V = E × d, where d is the separation between the plates. This concept is central to understanding how a constant field produces a voltage difference over a particular distance.

Parallel-Plate Capacitor Capacitance

The capacitance (C) of a parallel-plate capacitor is determined by its geometric factors and the properties of the medium between the plates. The formula C = ??A/d shows that capacitance increases with the plate area (A) and decreases with the separation (d) between the plates, with ?? being the permittivity of free space. This concept highlights how physical dimensions affect a capacitor’s ability to store electrical charge.

Charge-Voltage Relationship in Capacitors

The relationship Q = CV connects the stored charge (Q) to the potential difference (V) across the capacitor and its capacitance (C). This fundamental principle in capacitors explains how the ability to hold charge is influenced by both the voltage applied and the inherent capacitance of the system.

Permittivity of Free Space

The permittivity of free space (??) is a constant that quantifies the ability of a vacuum to permit electric field lines. It is a critical parameter in the equations that describe the behavior of electric fields and capacitance in a vacuum, emphasizing its role in governing electromagnetic interactions.

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