A parallel plate capacitor is made of two circular plates...

A parallel plate capacitor is made of two circular plates separated by a distance of $5 \mathrm{~mm}$ and with a dielectric constant of $2.2$ between them. When the electric field in the dielectric is $3 \times 10^{4} \mathrm{~V} / \mathrm{m}$, the charge density of the positive plate will be close to (A) $6 \times 10^{-7} \mathrm{C} / \mathrm{m}^{2}$ (B) $3 \times 10^{-7} \mathrm{C} / \mathrm{m}^{2}$ (C) $3 \times 10^{4} \mathrm{C} / \mathrm{m}^{2}$ (D) $6 \times 10^{4} \mathrm{C} / \mathrm{m}^{2}$

A parallel plate capacitor is made of two circular plates separated by a distance of $5 \mathrm{~mm}$ and with a dielectric constant of $2.2$ between them. When the electric field in the dielectric is $3 \times 10^{4} \mathrm{~V} / \mathrm{m}$, the charge density of the positive plate will be close to
(A) $6 \times 10^{-7} \mathrm{C} / \mathrm{m}^{2}$
(B) $3 \times 10^{-7} \mathrm{C} / \mathrm{m}^{2}$
(C) $3 \times 10^{4} \mathrm{C} / \mathrm{m}^{2}$
(D) $6 \times 10^{4} \mathrm{C} / \mathrm{m}^{2}$

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Key Concepts

Electric Field and Charge Density Relationship

The electric field in a capacitor is directly related to the charge density on the plates through the equation E = ?/?, where ? is the surface charge density and ? is the permittivity of the medium. This relationship allows one to compute the charge on the plates when the electric field and material properties are known.

Permittivity

Permittivity quantifies the ability of a medium to support an electric field. In capacitors with dielectrics, the effective permittivity is the product of the dielectric constant and the permittivity of free space, determining the relationship between the electric field and the charge stored on the plates.

Dielectric Materials

Dielectrics are insulating materials placed between the plates of a capacitor. They affect the capacitor's ability to store charge by increasing the capacitance through a property called the dielectric constant, which multiplies the permittivity of free space.

Parallel Plate Capacitor

A parallel plate capacitor consists of two conductive plates separated by a small distance. The capacitor stores electrical energy in the electric field created between the plates when a voltage is applied, and its basic behavior can be analyzed using the geometry of the plates and the separation distance.

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