James Clerk Maxwell

Physicist and mathematician — James Clerk Maxwell (Edinburgh 1831 – Cambridge 1879) was a Scottish physicist and mathematician, among the greatest theorists in the history of science. He studied at Edinburgh and Cambridge, and taught at Aberdeen, London and finally Cambridge, where he directed the new Cavendish Laboratory. His central contribution was the unification of electricity, magnetism and optics into a single theory: he showed that electric and magnetic fields propagate as waves at the speed of light, concluding that light itself is an electromagnetic wave. He also gave decisive foundations to the kinetic theory of gases, deriving the statistical distribution of molecular speeds, and studied the stability of Saturn’s rings. His work paved the way for Einstein’s relativity and for all of modern field physics.

Trivia

In 1861 he produced the first colour photograph in history, obtained by combining three shots taken with red, green and blue filters.

Theories and contributions

• Maxwell’s equations — Four equations that fully describe the electric and magnetic fields and their sources: $\nabla\cdot\mathbf{E}=\rho/\varepsilon_0$, $\nabla\cdot\mathbf{B}=0$, $\nabla\times\mathbf{E}=-\partial_t\mathbf{B}$, $\nabla\times\mathbf{B}=\mu_0\mathbf{J}+\mu_0\varepsilon_0\partial_t\mathbf{E}$.
• Electromagnetic nature of light — Light is an electromagnetic wave travelling at speed $c=1/\sqrt{\mu_0\varepsilon_0}$.
• Maxwell–Boltzmann distribution — Statistical law for molecular speeds in a gas: $f(v)\propto v^2 e^{-mv^2/2kT}$.

Featured in chapters

09 11 14 17 18 19 20 21 Z

Linked atoms

33 linked atoms.

09 Teoria cinetica dei gas

• History: from the philosophical atom to the physical atom
• The speed distribution
• The three characteristic speeds
• Atoms: from philosophical hypothesis to experimental evidence
• The P-V diagram and the critical point

11 Entropia

• The arrow of time
• The arrow of time: why the past is different from the future

14 Campo elettrico e potenziale

• Is the field a thing or a calculation?
• Why invent the field?
• What is the electric field?

17 Il campo magnetico

• The magnetic field and the tesla
• Absence of magnetic monopoles
• Ampère’s theorem

18 Induzione elettromagnetica

• The phasor method

19 Le equazioni di Maxwell e le onde elettromagnetiche

• The four equations (first, incomplete version)
• The displacement current
• The magnetic field inside a charging capacitor
• The four Maxwell equations
• The equations in vacuum and the birth of waves
• Maxwell in differential form
• Speed of electromagnetic waves
• Sources of EM waves and Hertz’s experiment
• The electromagnetic spectrum
• The transformer
• Maxwell’s equations as poetry
• Maxwell and unification: when c emerges from the equations

20 Relatività ristretta

• The paradox of light
• The three hypotheses
• Einstein’s postulates

21 Introduzione alla meccanica quantistica

• The photon

Z Appendice — Maturità

• Ministerial syllabus and book map
• Tips for the oral exam
• Key formulae: Electromagnetism