Two parallel plates of area 100 cm^2 are given charges of equal magnitudes 8.9 ×10^-7 C but opp

step 1 Okay, so we apply Gauss -lock with the dialectics to solve. So basically we know that, we know t

Two parallel plates of area 100 cm^2 are given charges of...

Two parallel plates of area $100 \mathrm{~cm}^{2}$ are given charges of equal magnitudes $8.9 \times 10^{-7} \mathrm{C}$ but opposite signs. The electric field within the dielectric material filling the space between the plates is $1.4 \times 10^{6} \mathrm{~V} / \mathrm{m} .$ (a) Calculate the dielectric constant of the material. (b) Determine the magnitude of the charge induced on each dielectric surface.

Key Concepts

Polarization and Induced Surface Charges

Polarization refers to the alignment of bound charges within a dielectric material when exposed to an electric field. This alignment results in induced surface charges on the interfaces between the dielectric and the conductive plates. These induced charges, which arise from the molecular dipoles aligning with the field, play a significant role in reducing the effective field in the dielectric and thereby altering the capacitance.

Electric Field in a Dielectric

In capacitors, the electric field is determined by the surface charge density on the plates and the permittivity of the intervening medium. When a dielectric is inserted between the plates, the field is reduced by a factor equal to the dielectric constant. This reduction is directly related to how the dielectric material influences the overall potential difference and stored energy in the capacitor.

Dielectric Constant

The dielectric constant (or relative permittivity) is a measure of how much a material reduces the electric field relative to a vacuum. It quantifies the ability of a material to be polarized by an external field, thereby diminishing the effective internal electric field. This concept is crucial in determining the behavior of capacitors when a dielectric material is introduced between the plates.

Parallel Plate Capacitor

A parallel plate capacitor is an electrical component consisting of two conductive plates separated by a distance, with an insulating material (dielectric) between them. Its capacitance depends on the plate area, the distance between the plates, and the permittivity of the material filling the space. Understanding this model is essential for analyzing how capacitance and electric fields are affected by different materials.

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