And Maxwell (also Faraday) said - 'Let there be Light'
Michael Faraday (1791 – 1867) did not have much of a formal education but became a consummate experimental scientist. He wasn’t a great mathematician but did have a brilliant ability to convey the concepts he uncovered with clarity and precision. As a chemist he discovered Benzene and developed a simple, early form of the Bunsen burner. He also worked on the production of optical glass but it is his contributions to our understanding of electricity and magnetism (the relationship between which was arguably initially ‘discovered’ by the Danish scientist Hans Christian Ørsted) that really marks him out. He produced an early form of electric motor and went on to demonstrate and measure the phenomenon of electromagnetic induction, using this to produce an electric dynamo the precursor to all our modern electrical generation. He went on to demonstrate that the current idea that there were several forms of electricity was wrong and that the various measurable phenomena were just manifestations of the same underlying physical force.
He developed the concept of lines of flux emanating from charged bodies and finally, not long before he died, he proposed that the electromagnetic forces he had measured and described extended away from the conducting media into ‘empty’ space. A truly revolutionary idea that was just not acceptrable at the time.
James Clerk Maxwell (1831 – 1879), unlike Faraday, was a consummate mathematicial scientist and could build on Faradays work to finally produce a beautiful mathematical model of the electromagnetic phenomenon, successfully combining electricity, magnetism and light. He showed that electrical and magnetic effects move through space as waves, traveling at a constant speed – the speed of light. His equations paved the way for much of our modern understanding of the physical world including special relativity and quantum mechanics.
Maxwell’s equations (there were orignally 20 of them) can be reduced and combined to just 4 using modern partial differential forms and here they are:
\[ \begin{align} \nabla & \cdot \vec{E} = \frac{\rho}{\epsilon_0} \\ \nabla & \cdot \overset{\mbox{→}}{B} = 0 \\ \nabla & \times \vec{E} = - \frac{\partial \vec{B}}{\partial t} \\ \nabla & \times \vec{B} = \mu_0 \vec {J} + \frac{1} {c^2 } \frac{\partial \vec{E}}{\partial t} \end{align} \]
Where \(\vec{E}\) is the electric field, \(\vec{B}\) is the magnetic field, \(\vec{J}\) is the total current density, \(\rho\) is the electric charge density. And we have some fundemental properties of space; \(\epsilon_0\) is the permitivity of free space and \(\mu_0\) is the permeability of free space. Finally, of course, \(c\) is the speed of light in a vacuum.
The meaning of each part of this set of equations can roughly be described something like:
(1) The electrical flux leaving a region is proportional to the total charge within it" (Gauss's Law)
(2) The magnetic flux through an enclosing surface is zero" - this precludes magnetic monopoles. (Gauss's Law of magnetism)
(3) If you have a closed loop, the voltage induced in this by a changing magnetic flux is proportional to the rate of change of the magnetic flux enclosed by the loop." (Maxwell-Faraday)
(4) The magnetic field integrated around a closed loop is proportional to the electric current in it plus the rate of change of the electric field that the loop encloses." (Ampere's circuit law)
