Poynting Theorem And Its Meaning.

This article on Poynting Theorem is a guest article by Ariana Vlad, senior at the International Computers High School of Bucharest, Romania, where she focuses on studying Physics and Mathematics.

Meaning of Equation

"The transfer of energy by an electromagnetic wave is at right angles to both electric and magnetic components of the wave vibration and its rate is proportional to the vector product of their amplitudes

The theorem was first formulated by John Henry Poynting while he was a professor at the University of Birmingham and published in late 1884. It links physical quantities like u - the energy density stored in the electromagnetic field -, S - the energy flux through an orthogonal surface (the Poynting vector) -, and J - which measures the rate at which charges go through a closed surface. Poynting introduced another groundbreaking theorem prior to this one: the eponym vector.

The Poynting Theorem is the equivalent of the work-energy balance - first applied in mechanics -used in electromagnetism. It also shows similarities to the continuity equation in hydrodynamics because it relates terms with energy flux dimension.

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Individual Terms In Poynting Theorem

The first term is due to the change in the total energy stored in the given volume.  It comes from the fluctuations in energy due to time variations of electric and magnetic fields and symbolizes the energy carried away by the electromagnetic wave. The minus sign links the value of the derivative to the sign convention: negative energy flows out of the system, while positive energy flows into the system. It should be noted that since this is the local form of the equation, partial derivatives are used. “Local” conservation refers to the idea that a charge can only move from one place to another if some conditions changed between the two places.

The second term is the divergence of the Poynting vector. This physical quantity represents the directional energy flux of an electromagnetic field (the energy transfer per unit area per unit time). For an electromagnetic wave, it points to the direction of propagation, representing the mean to express the radiative pressure. Divergence is a vector operator that gives the scalar measure of a vector field source in a given point.