What is the dielectric constant of the material that fills...

What is the dielectric constant of the material that fills the gap between a parallel-plate capacitor with plate area of $20.0 \mathrm{~cm}^{2}$ and plate separation of $1.00 \mathrm{~mm}$ if the capacitance is measured to be $0.0142 \mu \mathrm{F}$ ? Example $17-12$

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Key Concepts

Parallel-Plate Capacitor

A parallel-plate capacitor consists of two conductive plates separated by a distance with an insulating material (dielectric) in between. Its capacitance depends on the area of the plates, the distance between them, and the dielectric constant of the insulating material. This basic configuration is commonly used to study the influence of physical dimensions and material properties on capacitance.

Capacitance

Capacitance represents the ability of a capacitor to store electrical charge per unit voltage. For a parallel-plate capacitor, the capacitance is calculated using the formula C = (??kA)/d, where ?? is the permittivity of free space, k is the dielectric constant of the material between the plates, A is the plate area, and d is the separation between the plates. This relationship shows how changes in geometry and material properties affect the storage capability of the capacitor.

Dielectric Constant

The dielectric constant, or relative permittivity, quantifies how much a material can reduce the electric field within it compared to a vacuum. This dimensionless number is a measure of the material’s ability to become polarized in response to an electric field, which directly affects the capacitance of a capacitor when such a material is used as the dielectric.

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