50 pJ of energy is stored in a 2.0 cm ×2.0 cm ×2.0 cm region...

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Key Concepts

Electric Field Energy Density

Electric field energy density is the measure of energy stored per unit volume in an electric field, given by the formula u = (1/2)??E², where u is the energy density, ?? is the permittivity of free space, and E is the electric field strength. This concept relates the microscopic field properties to the stored energy.

Permittivity of Free Space

The permittivity of free space (??) is a fundamental constant in electromagnetism that characterizes how electric fields propagate in a vacuum. It directly affects the energy stored in an electric field by influencing the energy density according to the relation u = (1/2)??E².

Volume Integration of Energy Density

In a region with a uniform electric field, the total energy stored is obtained by multiplying the energy density by the volume of the region. This integration over the volume connects the continuous distribution of energy within the field to the overall energy stored in a defined space.

Uniform Electric Field

A uniform electric field is one in which the electric field strength and direction are constant throughout the region of interest. This uniformity simplifies the calculation of stored energy, as the same energy density applies uniformly over the entire volume.

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