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The electric-field energy density is a way to understand how much energy is stored in the electric field component of an electromagnetic wave. It is denoted by \( u_E \) and is calculated using the formula:

• \( u_E = \frac{1}{2}\varepsilon_0 E^2 \)

where \( \varepsilon_0 \) is the permittivity of free space, and \( E \) is the electric field strength. In simpler terms, it describes how much energy is held in the electric field part of the wave, per unit volume.
For electromagnetic waves in free space, the formula simplifies further because of the known relationship between wave intensity and energy density. The wave intensity \( I \) relates to the electric field energy density through:

• \( u_E = \frac{I}{c} \)

where \( c \) is the speed of light in free space. This expression highlights that a higher wave intensity or a stronger wave increases the energy density in the electric field.
Understanding electric-field energy density helps in comprehending how energy is transferred in space through electromagnetic waves.

Magnetic-field energy density, similar to electric-field energy density, quantifies the energy contained within the magnetic component of an electromagnetic wave. This energy density is represented by \( u_B \) and is determined using the formula:

• \( u_B = \frac{1}{2\mu_0}B^2 \)

where \( \mu_0 \) is the permeability of free space, and \( B \) is the magnetic field strength. Essentially, \( u_B \) tells us how much energy is held in the magnetic field portion per unit volume.
In a situation where electromagnetic waves travel through free space, the energy density in the magnetic field equals that in the electric field due to their intrinsic relationship:

• \( u_B = u_E \)

This equality arises because electromagnetic waves possess an equal partition of energy between their electric and magnetic components. This concept underscores the harmonious and interconnected nature of electromagnetic wave dynamics.
Grasping magnetic-field energy density helps in visualizing the distribution of energy between the components of an electromagnetic field.

Wave intensity is a measure of how much power an electromagnetic wave transmits through a particular area. It is a crucial concept that summarizes the energy conveyance capacity of the wave and is represented by \( I \). The intensity is calculated using the equation:

• \( I = \frac{Power}{Surface Area} \)

For a wave emitting uniformly in all directions, forming a sphere around the source, the intensity further becomes:

• \( I = \frac{Power}{4\pi r^2} \)

where \( r \) is the distance from the wave source. This demonstrates that intensity decreases with the square of the distance from the source, a representation of how the energy spreads over a larger area.
For practical calculations, the power is the energy output, and \( 4\pi r^2 \) is the surface area of the sphere created by the wave's reach. Hence, wave intensity communicates how concentrated the wave's power is at a particular distance.
Understanding wave intensity provides insights into how strong or weak a wave's influence, in terms of energy transfer, can be at different distances from the source.