Electromagnetic (EM) waves are changing electric and magnetic fields, transporting energy and momentum through space. EM waves are solutions of Maxwell"s equations, which are the fundamental equations of electrodynamics. EM waves require no medium, they can travel through empty space. Sinusoidal plane waves are one type of electromagnetic waves. Not all EM waves are sinusoidal plane waves, but all electromagnetic waves can be viewed as a linear superposition of sinusoidal plane waves traveling in arbitrary directions. A plane EM wave traveling in the x-direction is of the form

E(x,t) = Emaxcos(kx - ωt + φ), B(x,t) = Bmaxcos(kx - ωt + φ).

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E is the electric field vector, and B is the magnetic field vector of the EM wave. For electromagnetic waves E and B are always perpendicular to each other and perpendicular to the direction of propagation. The direction of propagation is the direction of E x B.

Let the fingers of your right hand point in the direction of E. Orient the palm of your hand so that, as you curl your fingers, you can sweep them over to point in the direction of B. Your thumb points in the direction of E x B.

Let i denote the x-direction, j the y-direction and k the z-direction. If for a wave traveling in the x-direction E = E j, then B = B k and j x k = i. Electromagnetic waves are transverse waves.

The wave number is k = 2π/λ, where λ is the wavelength of the wave. The frequency f of the wave is f = ω/2π, ω is the angular frequency. The speed of any periodic wave is the product of its wavelength and frequency.

v = λf.

The speed of any electromagnetic waves in free space is the speed of light c = 3*108 m/s. Electromagnetic waves can have any wavelength λ or frequency f as long as λf = c.

When electromagnetic waves travel through a medium, the speed of the waves in the medium is v = c/n, where n is the index of refraction of the medium. When an EM wave travels from one medium with index of refraction n1 into another medium with a different index of refraction n2, then its frequency remains the same, but its speed and wavelength change. For air n is nearly equal to 1.

The electromagnetic spectrum
Electromagnetic waves are categorized according to their frequency f or, equivalently, according to their wavelength λ = c/f. Visible light has a wavelength range from ~400 nm to ~700 nm. Violet light has a wavelength of ~400 nm, and a frequency of ~7.5*1014 Hz. Red light has a wavelength of ~700 nm, and a frequency of ~4.3*1014 Hz.

Visible light makes up just a small part of the full electromagnetic spectrum. Electromagnetic waves with shorter wavelengths and higher frequencies include ultraviolet light, X-rays, and gamma rays. Electromagnetic waves with longer wavelengths and lower frequencies include infrared light, microwaves, and radio and television waves.


Type of Radiation
Frequency Range (Hz)Wavelength Range
gamma-rays1020- 1024-12 m
x-rays1017- 10201 nm - 1 pm
ultraviolet1015- 1017400 nm - 1 nm
visible4 - 7.5*1014750 nm - 400 nm
near-infrared1*1014 - 4*10142.5 μm - 750 nm
infrared1013- 101425 μm - 2.5 μm
microwaves3*1011 - 10131 mm - 25 μm
radio waves11> 1 mm


Polarization is a phenomenon peculiar to transverse waves. Longitudinal waves such as sound cannot be polarized. Light and other electromagnetic waves are transverse waves made up of mutually perpendicular, fluctuating electric and magnetic fields. In the diagram on the right an EM wave is propagating in the x-direction, the electric field oscillates in the xy-plane, and the magnetic field oscillates in the xz-plane. A line traces out the electric field vector as the wave propagates.

For a linearly polarized electromagnetic wave traveling in the x-direction, the angle the electric field makes with the y-axis is unique.

An unpolarized electromagnetic wave traveling in the x-direction is a superposition of many waves. For each of these waves the electric field vector is perpendicular to the x-axis, but the angle it makes with the y-axis is different for different waves. For unpolarized light traveling in the x-direction Ey and Ez are randomly varying on a timescale that is much shorter than that needed for observation. The diagram on the right depicts unpolarized light. Natural light is, in general, unpolarized.
Electromagnetic waves transport energy through space. In free space this energy is transported by the wave with speed c. The magnitude of the energy flux S is the amount of energy that crosses a unit area perpendicular to the direction of propagation of the wave per unit time. It is given by

S = EB/(μ0) = E2/(μ0c),

since for electromagnetic waves B = E/c. The units of S are J/(m2s).μ0 is a constant called the permeability of free space, μ0 = 4π*10-7 N/A2.

Note:The energy transported by an electromagnetic wave is proportional to the square of the amplitude, E2, of the wave.

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Electromagnetic waves transport energy. EM wave also transport momentum. The magnitude of the momentum flux S/c is the amount of momentum that crosses a unit area perpendicular to the direction of propagation of the wave per unit time. If an electromagnetic wave is absorbed, momentum conservation requires that the object acquires momentum. The radiation exerts radiation pressure on the object. If the radiation is reflected instead of absorbed, then its momentum changes direction. The radiation pressure on an object that reflects the radiation is therefore twice the radiation pressure on an object that absorbs the radiation.