James Maxwell

Written by Nick Padula

Living from June 13th, 1831 to November 5th, 1879, James Clerk Maxwell was a Scottish scientist who studied mathematical physics. Maxwell is widely acclaimed as "the father of modern physics"[2]

Personal Life

Life and Education

Maxwell was born in Edinburgh to an affluent family. He was described by his mother as a curious kid, even from the tender age of three. Maxwell attended The Edinburgh Academy. For his tertiary education, Maxwell studied at the University of Edinburgh and the University of Cambridge. At age 25, he became Professor of Physics at Marischal College in Aberdeen. He then moved to King's College in London and subsequently to Cambridge to be the Professor of Experimental Physics in 1871. He was married to Mary Dewar in 1858 [3]

Work

Saturn's Ring

While working at Marischal College, Maxwell studied the rings of Saturn closely. He came to the conclusion that the planet's rings were comprised of small particles orbiting Saturn, as a solid ring would be unstable and break up [4]. This contradicted the accepted idea proposed by Christian Huygens in 1655 (but it did validate the claim in 1660 by poet and friend of Huygens, Jean Chapelain, that Saturn's rings are made of small satellites, a widely denounced claim). A gap in the outer part of Saturn's C ring is named after Maxwell.

Electromagnetism

In the 19th century, the connection between electricity and magnets was studied fervently by European scientists after the work of Hans Christian Oersted, Jean-Baptiste Biot and Félix Savart highlighted this connection. All of these scientists provided support for Maxwell's work, but Michael Faraday provided the most inspiration for Maxwell in his studies. However, Maxwell differed from Faraday in that he looked at the mathematical aspect of his research in addition to the physical aspects.

Maxwell's first step towards his electromagnetic theory was in his paper On Faraday's lines of force (1864), in which he proposed the idea of an incompressible fluid, the flow lines of which could represent the electric or magnetic field or current flow [5]. Here he explained that, in the case of electric fields, sources of the flow lines were positive charges and sinks were negative charges. In his subsequent paper, Maxwell introduced the idea of vortices, small, elastic objects that occupy space and have a small mass. Using this idea, he was able to derive Ampère's circuital law and to provide an explanation of Faraday's law of induction. In his model, these vortices were able to move in a conductor, but not in a dielectric (insulator). However, in a dielectric, the vortices can shift slightly due to an electric field.

Equations

In a paper titled A dynamical theory of the electromagnetic field, Maxwell strove to make his theories more mathematical and less analogical. His four equations that resulted from this are as follows.

1. Gauss' law for electricity: [math]\displaystyle{ \oint \overrightarrow{E} \bullet d \overrightarrow{A} = \frac{q} {\epsilon_0} }[/math]

2. Gauss' law for magnetism: [math]\displaystyle{ \oint \overrightarrow{B} \bullet d \overrightarrow{A} = 0 }[/math]

3. Faraday's law of induction: [math]\displaystyle{ \oint \overrightarrow{E} \bullet \overrightarrow{d s} = -\frac{d \Phi} {dt} }[/math]

4. Ampere's law: [math]\displaystyle{ \oint \overrightarrow{B} \bullet \overrightarrow{d s} = \mu_0i + \frac{1} {c^2} \frac{\partial} {\partial t} \int \overrightarrow{E} \bullet d \overrightarrow{A} }[/math]

Use by Other Scientists

Albert Einstein once said "The special theory of relativity owes its origins to Maxwell's equations of the electromagnetic field."[6] Einstein was said to have a picture of Maxwell on his wall in his study. [7]