Jacqueline Hochheiser, Corporate Communications

James Clerk Maxwell was best known for his classical equations that proposed electric and magnetic fields propagate at the speed of light in the form of waves (electromagnetic waves). Maxwell’s theory was revolutionary for its time, and it also provided the foundation for radio frequency technology, which has impacted society so greatly that Maxwell is often regarded as one of the most influential physicists of the 19th century, in league with Newton and Einstein.

Early Life and Education

Maxwell was born June 13, 1831 in Edinburgh, Scotland. His father, John Clerk Maxwell, was a lawyer who provided a comfortable middle-class life for his son and wife Frances Cay. Originally, Maxwell’s name was simply James Clerk, but early on his father inherited the Middlebie estate from Maxwell ancestors and so Maxwell was added as a second sir name. It was during this time that the now Clerk Maxwell family moved from Edinburgh to Glenlair, where the 1500-acre Middlebie estate was situated.

As is confirmed in letters sent between Maxwell’s father and his mother’s sister, Jane Cay, he was an inquisitive child from a young age. Recognizing her son’s potential, Frances took on the responsibility of overseeing his education. His early education was conducted by a young tutor, until Maxwell’s mother became ill with abdominal cancer and later perished from it in December, 1839 when he was just 8 years old.

Portrait of James Clerk Maxwell

After his mother’s passing, Maxwell’s father and sister-in-law, Jane Cay, took responsibility for his education and sent him to the Edinburgh Academy, a prestigious boarding school for boys. Maxwell was 10 years old (1841) when he matriculated at the school and instantly demonstrated a knack for math and philosophy. While attending, he also met life-long friends including his future biographer Lewis Campbell and Peter Guthrie Tait, who would later become an early pioneer of thermodynamics.

Maxwell also managed to publish his first scientific paper at the academy when he was just 14 years old titled, “On the Description of Oval Curves and Those Having a Plurality of Foci.” The paper detailed a means for drawing mathematical curves using a piece of twine as a guide to finding the properties of ellipses with multiple foci. It wasn’t a completely original idea, but rather a simplification of Rene Descartes’s properties of multifocal ellipses from the 17th century.

He went on to attend the University of Edinburgh at the age of 16, and published two more papers. In 1850, Maxwell enrolled at the University of Cambridge to further pursue his knack for math and philosophy. It was during his years at the university that his talents began to fully manifest. In 1854, Maxwell earned 2nd wrangler, a wrangler being one who earns first class honors in math examinations at Cambridge. He also won the Smith’s Prize, which was a prestigious award for an essay that incorporates original research by the writer.

Since he was graduating with high honors, Maxwell was elected for a fellowship at Trinity, but his father had taken ill and he opted to return to Glenlair. In 1856, Maxwell was appointed to a professorship of natural philosophy at Marischal College in Aberdeen, but his father passed away before he could announce the new position.

Four years later, Maxwell decided to move to King’s College in London, where he continued to teach natural philosophy. It was during the next five years he spent there, that he would create his four famous classical equations on the laws of electromagnetic waves.

Unpacking Maxwell’s Equations

Maxwell published his finalized equations in a paper titled, “A Dynamical Theory of the Electromagnetic Field” in 1865. His theory consisted of four equations, each used to explain different facets that govern and manifest electromagnetic fields. He predicted that electric and magnetic fields travel through space in the form of moving waves at the speed of light. Therefore, electromagnetic waves and light are all different manifestations of the same medium.

He realized that oscillating charges produce changing electric fields, and that changing electric fields created magnetic fields. His equations unified known concepts from the work of other notable physicists including Carl Friedrich Gauss, Michael Faraday and Andre-Marie Ampere.

The first of Maxwell’s equations was based on Gauss’s law of static electric fields, which states that the electric flux passing through a closed surface is equal to the total electric charge contained within that surface. With this idea, Maxwell put together an equation theoretically demonstrating that an electric field produced from an electric charge moves away from positive charge and toward negative charge (Equation 1).

Equation 1

The second of Maxwell’s equations was inspired by another of Gauss’s laws, the law of magnetism. This law states that static magnetic fields are continuous with no beginning or end, have no known monopoles, and therefore, the total magnetic flux passing through a surface is always zero. Maxwell explains this concept with his equation shown below:

Equation 2

The third of Maxwell’s equations is derived from Faraday’s law of induction, which states that electric currents within a conductor produce magnetic fields and vice versa. Maxwell concluded that a changing magnetic field creates an electromotive force (EMF), and therefore, an electric field, which he describes through the equation shown below:

Equation 3

The fourth and final equation was based on Ampere’s law, which states that a changing electric flux through a closed surface produces a magnetic field around any path that encircles that surface. The changes in the electric currents are proportional to the magnetic fields produced by the electric current. From this, Maxwell devised an equation stating that magnetic fields are generated by moving charges or changing electric fields as represented below:

Equation 4

Of course, these equations proved nothing but a sound theory, and the concept had yet to be physically tested for concrete proof. Unfortunately, Maxwell would not live to see Heinrich Hertz prove his theory in 1887 when he detected the electromagnetic waves Maxwell described. Subsequently, the discovery of electromagnetic waves paved the way for many radio frequency applications and technology including phones, radio broadcasting, radar, navigation and more.

Life After Discovery

After his five years spent at King’s College and accomplishing many significant milestones in his career, Maxwell was elected for the new Cavendish professorship at Cambridge in 1871. Later, he retired to his estate in Glenlair to work on his famous 1873 treatise titled “Treatise on Electricity and Magnetism.” This two-volume treatise provided an even more detailed analysis on the reasoning behind his equations and the existence of electromagnetic radiation. In 1879, Maxwell took ill on several occasions and failed to recover. He died on November 5 that same year at only 48 years old.

Despite his early death, Maxwell managed to make a significant impact on the world in the short time he had. His discoveries laid the framework for future technology involving electromagnetic radiation and would help create navigation and communication technology uniting people all around the world.

Sources

James Clerk Maxwell: Scottish Mathematician and Physicist (Cyril Domb, Encyclopedia Britannica)

James Clerk Maxwell: A Force for Physics (Francis Everitt, Physics World)

Maxwell’s Equations (Maxwells-equations.com)

What is Faraday’s Law of Induction (Jim Lucas, Live Science)

Maxwell’s Equations: Electromagnetic Waves Predicted and Observed (Lumen Candela)

Electric Flux and Gauss’s Law (Lumen Candela)

Gauss’s Law for Magnetic Fields (EM GeoSci)Ampere’s Law (Hyper Physics, Georgia State University)