A sinusoidal EM wave has an electric field amplitude Em=32.0 mV / m . What are the intensity and

step 1 The average energy density is given by half, E .M, square, Epsilon, the permittivity of free spa

A sinusoidal EM wave has an electric field amplitude Em=32.0...

A sinusoidal EM wave has an electric field amplitude $E_{\mathrm{m}}=32.0 \mathrm{mV} / \mathrm{m} .$ What are the intensity and average energy density? [Hint: Recall the relationship between amplitude and rms value for a quantity that varies sinusoidally.]

Key Concepts

Intensity of Electromagnetic Waves

The intensity of an electromagnetic wave is defined as the average power transmitted per unit area. It is calculated as the time-average of the Poynting vector, which represents the energy flux in the wave. In free space, the intensity can be expressed in terms of the electric field amplitude and fundamental constants such as the permittivity of free space and the speed of light. Recognizing how to transition from peak field values to average measures using RMS values is essential in these calculations.

Average Energy Density of Electromagnetic Waves

The average energy density describes the energy stored per unit volume in an electromagnetic field. It includes contributions from both the electric and magnetic fields. In free space, the energy density of the electric field is proportional to the square of its effective (RMS) value, with a similar contribution from the magnetic field that is related to the electric field by the speed of light. Understanding this concept allows one to calculate the stored electromagnetic energy within a given volume, which is important for analyzing energy propagation and storage in waves.

Sinusoidal Functions and RMS Values

For any sinusoidally varying quantity, such as the electric field in an electromagnetic wave, the RMS (root-mean-square) value is used to represent its effective magnitude. The RMS value for a sinusoidal wave is obtained by dividing the amplitude by the square root of two. This concept is crucial because many power and energy calculations use RMS values to properly account for time-averaging over one period of oscillation.

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