Cambridge Encyclopedia :: Cambridge Encyclopedia Vol. 23

electromagnetic radiation - Electromagnetic spectrum, Derivation

Oscillating electric and magnetic fields which propagate together through empty space as a radiated wave; velocity c, the velocity of light. They include radio waves, light, and X-rays. No ether is required for the propagation of electromagnetic waves, which exhibit particle-like properties, more noticeable for higher frequencies, consistent with quantum theory.

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Electromagnetic radiation is generally described as a self-propagating wave in space with electric and magnetic components. Electromagnetic radiation is classified into types according to the frequency of the wave: these types include, in order of increasing frequency, radio waves, microwaves, infrared radiation, visible light, ultraviolet radiation, X-rays and gamma rays.

Electromagnetic waves of much lower frequency than visible light were first predicted by Maxwell's equations and subsequently discovered by Heinrich Hertz. Maxwell derived a wave form of the electric and magnetic equations, revealing the wavelike nature of electric and magnetic fields and their symmetry.

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According to these equations, a time-varying electric field generates a magnetic field and vice versa. Therefore, as an oscillating electric field generates an oscillating magnetic field, the magnetic field in turn generates an oscillating electric field, and so on.

Properties

Electric and magnetic fields obey the properties of superposition, so fields due to particular particles or time-varying electric or magnetic fields contribute to the fields due to other causes. (As these fields are vector fields, all magnetic and electric field vectors add together according to vector addition.) These properties cause various phenomena including refraction and diffraction.

Since light is an oscillation, it is not affected by travelling through static electric or magnetic fields in a linear medium such as a vacuum.

In refraction, a wave crossing from one medium to another of different density alters its speed and direction upon entering the new medium.

EM radiation exhibits both wave properties and particle properties at the same time (see wave-particle duality).

Wave model

An important aspect of the nature of light is frequency.

A wave consists of successive troughs and crests, and the distance between two adjacent crests is called the wavelength. Frequency is inversely proportional to wavelength, according to the equation:

v = fλ

where v is the speed of the wave (c in a vacuum, or less in other media), f is the frequency and λ is the wavelength.

Interference is the superposition of two or more waves resulting in a new wave pattern.

The energy in electromagnetic waves is sometimes called radiant energy.

Particle model

In the particle model of EM radiation, a wave consists of discrete packets of energy, or quanta, called photons.

Speed of propagation

Any electric charge which accelerates, or any changing magnetic field, produces electromagnetic radiation. When considered as particles, they are known as photons, and each has an energy related to the frequency of the wave given by Planck's relation E = hν, where E is the energy of the photon, h = 6.626 × 10-34 J·s is Planck's constant, and ν is the frequency of the wave.

One rule is always obeyed regardless of the circumstances: EM radiation in a vacuum always travels at the speed of light, relative to the observer, regardless of the observer's velocity.

Electromagnetic spectrum

Generally, EM radiation is classified by wavelength into electrical energy, radio, microwave, infrared, the visible region we perceive as light, ultraviolet, X-rays and gamma rays.

Light

EM radiation with a wavelength between approximately 400 nm and 700 nm is detected by the human eye and perceived as visible light.

If radiation having a frequency in the visible region of the EM spectrum reflects off of an object, say, a bowl of fruit, and then strikes our eyes, this results in our visual perception of the scene.

Radio waves

Radio waves carry information by varying a combination of the amplitude, frequency and phase of the wave within a frequency band.

When EM radiation impinges upon a conductor, it couples to the conductor, travels along it, and induces an electric current on the surface of that conductor by exciting the electrons of the conducting material.

Derivation

Electromagnetic waves as a general phenomenon were predicted by the classical laws of electricity and magnetism, known as Maxwell's equations. beginning with Maxwell's equations for a vacuum:

where is a vector differential operator (see Del)

One solution is trivial,

But there is a more interesting one. To see it one can use a useful vector identity which works for any vector:

To see how we can use this take the curl of equation (2):

Evaluating the left hand side:

where we simplified the above by using equation (1).

Evaluate the right hand side:

Equations (6) and (7) are equal, so this results in a differential equation for the electric field:

Applying a similar pattern results in similar differential equation for the magnetic field

These differential equations are equivalent to the wave equation:

where v is the velocity of the wave and f describes a displacement

So notice that in the case of the electric and magenetic fields, the velocity is:

Which, as it turns out, is the speed of light.

But these are only two equations and we started with four, so there is still more information pertaining to these waves hidden within Maxwell's equations. In other words

,

for a generic wave traveling in the direction.

This form will satisfy the wave equation, but will it satisfy all of Maxwell's equations, and with what corresponding magnetic field?

The first of Maxwell's equations implies that electric field is orthogonal to the direction the wave propagates.

The second of Maxwell's equations yields the magnetic field.

Not only are the electric and magnetic field waves traveling at the speed of light, but they have a special restricted orientation and proportional magnitudes, E0 = cB0. The electric field, magnetic field, and direction of wave propagation are all orthogonal and the wave propagates in the same direction as .

From the viewpoint of an electromagnetic wave traveling forward, the electric field might be oscillating up and down, while the magnetic field oscillates right and left;

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