The Poynting theorem for harmonic EM plane waves is a fundamental law in electromagnetism that relates the flow of energy in an EM field to its sources and sinks. It states that the time-averaged power per unit area carried by an EM wave is equal to the negative of the time rate of change of the energy density of the wave.
The Poynting vector, denoted by S, is a mathematical representation of the Poynting theorem. It is a vector quantity that describes the direction and magnitude of the flow of energy in an EM wave. The Poynting vector is defined as the cross product of the electric and magnetic field vectors, and its direction is perpendicular to both fields.
In the context of the Poynting theorem, "harmonic" refers to a sinusoidal time variation of the electric and magnetic fields in an EM wave. This means that the fields have a constant amplitude and frequency, and can be described by a simple mathematical function. This simplifies the calculation of the Poynting vector and makes the theorem easier to apply.
The Poynting theorem has numerous practical applications in fields such as telecommunications, radar, and optics. It is used to calculate the power and energy transmitted by EM waves, and to design and optimize devices that utilize EM fields. It is also used to understand the behavior of EM waves in different materials and environments.
The Poynting theorem is limited to only harmonic EM waves, which means it cannot be applied to non-sinusoidal waves. It also assumes that the medium through which the wave is propagating is linear and isotropic, which may not always be the case in practical situations. Additionally, the theorem does not account for losses in the EM wave, which can affect the accuracy of calculations.