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Electromagnetic radiation
Electromagnetism 

Electricity · Magnetism 
Lorentz force law • emf • Electromagnetic induction • Faraday’s law • Lenz's law • Displacement current • Maxwell's equations • EM field • Electromagnetic radiation • Liénard–Wiechert potential • Maxwell tensor • Eddy current

Electromagnetic waves are waves that contain an electric field and a magnetic field and carry energy. They travel at the speed of light.^{[1]}
Quantum mechanics developed from the study of electromagnetic waves. This field includes the study of both visible and invisible light. Visible light is the light one can see with normal eyesight in the colours of the rainbow. Invisible light is light one can't see with normal eyesight and includes more energetic and higher frequency waves, such as ultraviolet, xrays and gamma rays. Waves with longer lengths, such as infrared, micro and radio waves, are also explored in the field of Quantum mechanics.
Some types of electromagnetic radiation, such as Xrays, are ionizing radiation and can be harmful to your body. Ultraviolet rays are near the violet end of the light spectrum and infrared are near the red end. Infrared rays are heat rays and ultraviolet rays cause sunburn.
The various parts of the electromagnetic spectrum differ in wavelength, frequency and quantum energy.
Sound waves are not electromagnetic waves but waves of pressure in air, water or any other substance.
Mathematical formulation
In physics, it is well known that the wave equation for a typical wave is
[math]\nabla ^2 f=\frac{1}{c^2}\frac{\partial^2 f}{\partial t^2}[/math]
The problem now is to prove that Maxwell's equations explicitly prove that the electric and magnetic fields create electromagnetic radiation. Recall that two of Maxwell's equations are given by
[math]\nabla \times \mathbf{E}=\frac{\partial \mathbf{B}}{\partial t}[/math]
[math]\nabla \times \mathbf{B}=\mu_o \mathbf{j}+\mu_o \epsilon_o \frac{\partial \mathbf{E}}{\partial t}[/math]
By evaluating the curl of the above equations and vector calculus one can prove the following equations
[math]\nabla ^2 \mathbf{E}=\frac{1}{c^2}\frac{\partial^2 \mathbf{E}}{\partial t}[/math]
[math]\nabla^2 \mathbf {B}=\frac{1}{c^2}\frac{\partial^2 \mathbf{B}}{\partial t}[/math]
Note: the proof involves making the substitution
[math]c=\frac{1}{\sqrt {\mu_o \epsilon}}[/math]
The equations above are analogous to the wave equation, by replacing f with E and B. The above equations mean that propagations through the magnetic (B) and electric (E) fields will produce waves.
Related pages
References
 Hecht, Eugene (2001). Optics (4th ed. ed.). Pearson Education.
.
 Serway, Raymond A.; Jewett, John W. (2004). Physics for Scientists and Engineers (6th ed. ed.). Brooks/Cole.
.
 Tipler, Paul (2004). Physics for Scientists and Engineers: Electricity, Magnetism, Light, and Elementary Modern Physics (5th ed. ed.). W. H. Freeman.
.
 Reitz, John; Milford, Frederick and Christy, Robert (1992). Foundations of Electromagnetic Theory (4th ed. ed.). Addison Wesley.
.
 Jackson, John David (1975). Classical Electrodynamics (2nd ed ed.). John Wiley & Sons.
.
 Allen Taflove and Susan C. Hagness (2005). Computational Electrodynamics: The FiniteDifference TimeDomain Method, 3rd ed.. Artech House Publishers.
. http://www.artechhouse.com/default.asp?Frame=Book.asp&Book=1580538320&Country=US&Continent=NO&State=.
Other websites
 Electromagnetic Waves from Maxwell's Equations on Project PHYSNET.
 Conversion of frequency to wavelength and back  electromagnetic, radio and sound waves
 eBooks on Electromagnetic radiation and RF
 The Science of Spectroscopy  supported by NASA. Spectroscopy education wiki and films  introduction to light, its uses in NASA, space science, astronomy, medicine & health, environmental research, and consumer products.
