Light and electromagnetic spectrum basics (Part 1)
27 Sep 2013  Louis DesmaraisShare this page with your friends
The second equation was obtained from Ampere's law. It was well known at the time that when a current flow occurred in a wire, magnetic effects were produced near it. This was demonstrated by placing a compass near a wire having a current flow. In this case, it was noticed that one point of the compass was attracted to the wire while the other compass point was repelled. Maxwell summarised this result by using the concept of fields:
In this equation, H is the magnetic field strength, E is the electric field strength. The mathematical operations are the same as described in Maxwell's first equation. You will notice that in this second equation, the curl operation is performed on H, and the partial derivative of E with respect to time is called for. The quantity e_{0} is the vacuum permittivity.
This equation basically says that a time varying electric field will produce a magnetic field, H. The third and fourth equations were obtained by using Gauss' laws for electricity and magnetism:
The third equation shows how the electric flux density is related to the electric charge density, pv . This flux density will vary with distance from the electric charge or by the number of electrons in a given space.
The fourth equation basically says that there is no such thing as a magnetic charge in nature. If you cut a magnet in half and in half again several times, you will get a smaller and smaller magnet with north and south poles. Magnetic flux lines always form closed loops. Unlike electric field lines, they do not diverge from a point.
Maxwell's first and second equations show a symmetry in nature between the electric and magnetic fields. A changing magnetic field will produce a changing electric field and visa versa. These fields are not independent of each other in the dynamic case. This fact impressed Maxwell, who believed that nature was truly beautiful and elegant. Thus, an important thing to realise from the first two equations is the symmetry involved with the production of the E and H fields of the electromagnetic wave. When all of the mathematical operations are performed as specified in the equations, time varying E and H fields can be described as illustrated in the figure.
These equations can be used to describe a transverse wave of energy with electric and magnetic field components that are orthogonal to each other as the wave propagates through space at the speed of light. The figure gives a description of this wave. A changing electric field, E, traveling in the z direction induces a changing magnetic field, H.
Figure: The electric and magnetic field distributions for an electromagnetic wave. 
Electric and magnetic field distributions
Both E and H are vector quantities describing the electric and magnetic fields. The length of each vector gives the magnitude of the field at each moment during its propagation in the z direction. The vector k is the wave vector of magnitude k = 2pi/A, where A, is the wavelength of the electromagnetic energy. This wave vector also defines the direction of propagation of the wave. Thus, all three vectors form a mutually orthogonal triad as shown in the figure. When Maxwell calculated the velocity of various electromagnetic waves, he came up with the same number each time. This velocity turned out to be that of light. Thus, he also considered visible light to be an electromagnetic wave.
Maxwell's equations also describe the unification of electricity and magnetism into one fundamental force called the electromagnetic force. This force becomes important when considering the production of photons. In this process, outer electrons of an atom play a very important role. The electromagnetic force is. one of the four fundamental forces in nature. The other three fundamental forces are gravity, the weak force, and the nuclear force. We are all familiar with gravity, the force of attraction that exists between two or more masses. The weak force occurs on the scale of subatomic distances.
This force plays an important role in the processes that make the sun shine. The nuclear force holds the positive protons together in the nucleus of an atom. In this book, we will be primarily interested in the electromagnetic force.
Excerpted with permission from Pearson Publishing, Chapter 3, Light and the Electromagnetic Spectrum from Applied Electro Optics by Louis Desmarais.
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