A moving magnet is known to produce an electric field: this is the principle of the dynamo. It is also known that a moving electric charge produces a magnetic field: this is the principle behind an electromagnet. An oscillating electric charge (in a transmitting aerial, for example) has an associated oscillating electric field which induces a magnetic field. The magnetic field will, in turn, create a new electric field which will then induce a new magnetic field and so on, giving rise to self-supporting electromagnetic oscillations known as electromagnetic waves, which may propagate through empty space.

The laws governing the mutual induction of electric and magnetic fields were established by *James Clerk Maxwell* [see, for example, Ohanian (1989)]. From his equations, Maxwell predicted that electromagnetic waves would propagate with a speed c = 1/ , where μ^{0} and ε^{0} are, respectively, the *permeability* and *permittivity* of vacuum. Inserting numerical values of these constants leads to c = 3.00 × 10^{8} m/s, which Maxwell recognized as the measured Speed of Light in vacuum. He, therefore, deduced that light waves are electromagnetic waves.

In common with other wave phenomena, electromagnetic waves have characteristic frequency (f) and wavelength (λ) whose product equals speed (c): c = λf . *Radio waves* may be generated by an oscillating electric charge on an aerial. A typical frequency for FM radio waves would be 100 MHz which, from the above relationship, corresponds to a wavelength of 3 meters. A long-wave radio frequency of, say, 200 kHz corresponds to a wavelength of 1.5 km. *Visible light* covers the wavelength region 4 to 7 × 10^{–7} m. The complete electromagnetic spectrum is described in the entry Electromagnetic Spectrum. In a propagating electromagnetic wave, the electric and magnetic field directions lie in the plane perpendicular to the direction of motion and are themselves at right angles to each other. If the electromagnetic wave is generated by oscillating electric charges in a vertical aerial, then the electric field will remain in the vertical direction and the magnetic field will be in a horizontal direction perpendicular to the horizontal direction of propagation. Such a wave would be called a *plane polarized wave*. To receive such a polarized wave at a receiving aerial, that aerial would also have to be vertical.

Electromagnetic waves carry both energy and momentum and can exert pressure on surfaces on which they fall. If, in an electromagnetic wave, the electric and magnetic fields are represented by the vectors **E** and **B** (**E** and **B** are perpendicular to each other and lie in the plane perpendicular to the direction of propagation of the wave) then the energy flux (**S**) in the wave is given by:

The energy flux vector **S** lies in the direction of propagation and will have units of watts per square meter. Whenever an electromagnetic wave strikes a body and is absorbed by it, the wave will exert a force on the body and transfer momentum to it. The force per unit area, or pressure, is given by S/c. Since c is a very large number, the resulting pressure is very small. For example, the average energy flux from sunlight on the Earth is about 1.4 × 10^{3} W/m^{2}; this exerts a pressure on the Earth of 6 × 10^{8} N which is, fortunately, much smaller than the gravitational force between the sun and the earth of about 4 × 10^{22} N. Note that when an electromagnetic wave is totally reflected from a body, the momentum transfer is double that when the wave is totally absorbed.

#### REFERENCES

Ohanian, H. C. (1989) Physics, 2^{nd} edn. W. W. Norton & Company, New Yonk.