Energy Transport and the Poynting Vector An airplane flying...

Energy Transport and the Poynting Vector An airplane flying at a distance of 10 $\mathrm{km}$ from a radio transmitter receives a signal of intensity 10$\mu \mathrm{W} / \mathrm{m}^{2}$ . What is the amplitude of the (a) electric and (b) magnetic component of the signal at the airplane? (c) If the transmitter radiates uniformly over a hemisphere, what is the transmission power?

Energy Transport and the Poynting Vector
An airplane flying at a distance of 10 $\mathrm{km}$ from a radio transmitter receives a signal of intensity 10$\mu \mathrm{W} / \mathrm{m}^{2}$ . What is the amplitude of the (a) electric and (b) magnetic component of the signal at the airplane? (c) If the transmitter radiates uniformly over a hemisphere, what is the transmission power?

Key Concepts

Poynting Vector

The Poynting vector quantifies the rate of energy transport per unit area in an electromagnetic field. It is defined as the cross product of the electric and magnetic fields and points in the direction of wave propagation. This concept is fundamental for understanding how energy flows in electromagnetic waves and links the field amplitudes to the measurable intensity.

Electromagnetic Wave Intensity

Intensity in the context of electromagnetic waves refers to the power transmitted per unit area, which is directly related to the square of the electric or magnetic field amplitude. It serves as a measure of the energy carried by the wave and is central to assessing how much power an observer or detector receives from a source.

Relationship between Electric and Magnetic Fields

In electromagnetic wave propagation through free space, the electric and magnetic fields are interrelated, with the magnitude of the electric field being proportional to the magnetic field by the speed of light. This relationship, expressed as E = cB, is essential when converting between electric and magnetic field amplitudes and understanding the balance of energy in the wave.

Radiation Pattern and Power Distribution

When a source radiates energy, the spatial distribution of that energy depends on the geometry of the emission pattern, such as spherical or hemispherical dispersion. This concept is important for calculating the total power transmitted by integrating the intensity over the area into which the energy is radiated, linking localized measurements to the overall power output of the source.

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