Prove, for a plane electromagnetic wave that is normally...

Name: Problem 25, Chapter 33: Fundamentals of Physics
Uploaded: 2020-01-13T15:52:35-08:00
Duration: 4 min 40 s
Channel: Carlos Henrique De Lima
Description: Prove, for a plane electromagnetic wave that is normally incident on a flat surface, that the radiation pressure on the surface is equal to the energy density in the incident beam. (This relation between pressure and energy density holds no matter what fraction of the incident energy is reflected.)

Prove, for a plane electromagnetic wave that is normally incident on a flat surface, that the radiation pressure on the surface is equal to the energy density in the incident beam. (This relation between pressure and energy density holds no matter what fraction of the incident energy is reflected.)

Key Concepts

Energy Density of Electromagnetic Waves

In electromagnetism, the energy density quantifies the amount of energy stored in the electric and magnetic fields per unit volume. It is a fundamental concept that determines how much energy is carried by an electromagnetic wave. This energy density is related to the amplitudes of the fields and provides a measure of the intensity of the wave, forming the basis for understanding energy transfer in electromagnetic phenomena.

Momentum Transport in Electromagnetic Waves

Electromagnetic waves carry momentum in addition to energy, and this momentum is directly related to the energy density. The momentum flux, or the rate at which momentum is transported across a unit area, gives rise to a pressure when the wave interacts with matter. This relationship is a consequence of the relativistic formulation of electromagnetism, where energy and momentum are intertwined concepts.

Radiation Pressure

Radiation pressure is the force per unit area exerted by electromagnetic radiation when it impinges upon a surface. This pressure arises from the momentum transfer that occurs during interactions like absorption or reflection. For a plane electromagnetic wave normally incident on a flat surface, it can be shown that the radiation pressure is equal to the energy density of the incident beam, a result that holds regardless of the fraction of energy reflected. This equivalence reflects the fundamental balance between energy and momentum in electromagnetic fields.

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