16.1 Maxwell’s equations and electromagnetic waves  (Page 4/8)

The mechanism of electromagnetic wave propagation

To see how the symmetry introduced by Maxwell accounts for the existence of combined electric and magnetic waves that propagate through space, imagine a time-varying magnetic field ${\overrightarrow{B}}_0\left(t\right)$ produced by the high-frequency alternating current seen in [link] . We represent ${\overrightarrow{B}}_0\left(t\right)$ in the diagram by one of its field lines. From Faraday’s law, the changing magnetic field through a surface induces a time-varying electric field ${\overrightarrow{E}}_0\left(t\right)$ at the boundary of that surface. The displacement current source for the electric field, like the Faraday’s law source for the magnetic field, produces only closed loops of field lines, because of the mathematical symmetry involved in the equations for the induced electric and induced magnetic fields. A field line representation of ${\overrightarrow{E}}_0\left(t\right)$ is shown. In turn, the changing electric field ${\overrightarrow{E}}_0\left(t\right)$ creates a magnetic field ${\overrightarrow{B}}_1\left(t\right)$ according to the modified Ampère’s law. This changing field induces ${\overrightarrow{E}}_1\left(t\right),$ which induces ${\overrightarrow{B}}_2\left(t\right),$ and so on. We then have a self-continuing process that leads to the creation of time-varying electric and magnetic fields in regions farther and farther away from O . This process may be visualized as the propagation of an electromagnetic wave through space.

In the next section, we show in more precise mathematical terms how Maxwell’s equations lead to the prediction of electromagnetic waves that can travel through space without a material medium, implying a speed of electromagnetic waves equal to the speed of light.

Prior to Maxwell’s work, experiments had already indicated that light was a wave phenomenon, although the nature of the waves was yet unknown. In 1801, Thomas Young (1773–1829) showed that when a light beam was separated by two narrow slits and then recombined, a pattern made up of bright and dark fringes was formed on a screen. Young explained this behavior by assuming that light was composed of waves that added constructively at some points and destructively at others (see Interference ). Subsequently, Jean Foucault (1819–1868), with measurements of the speed of light in various media, and Augustin Fresnel (1788–1827), with detailed experiments involving interference and diffraction of light, provided further conclusive evidence that light was a wave. So, light was known to be a wave, and Maxwell had predicted the existence of electromagnetic waves that traveled at the speed of light. The conclusion seemed inescapable: Light must be a form of electromagnetic radiation. But Maxwell’s theory showed that other wavelengths and frequencies than those of light were possible for electromagnetic waves. He showed that electromagnetic radiation with the same fundamental properties as visible light should exist at any frequency. It remained for others to test, and confirm, this prediction.