Carl Friedrich Gauss

Mathematician, physicist and astronomer — Carl Friedrich Gauss (Brunswick, 1777 – Göttingen, 1855) was a German mathematician, physicist and astronomer, often called the “prince of mathematicians” for the depth and breadth of his contributions. A child prodigy from humble origins, he studied thanks to the patronage of the Duke of Brunswick and spent most of his life as director of the astronomical observatory at Göttingen. In physics his name is tied to the flux theorem in electrostatics and magnetism (one of the fundamental equations of electromagnetism later systematised by Maxwell), which relates the flux of a field through a closed surface to the charges or masses it contains. Together with Wilhelm Weber he built one of the first electromagnetic telegraphs at Göttingen and promoted a coherent system of absolute units for magnetic quantities. His work on error theory and on the statistical distribution that bears his name (the “Gaussian”) remains central to experimental physics today.

Fun fact

In 1801 he calculated the orbit of the newly discovered minor planet Ceres, which astronomers had then lost track of, allowing it to be found again exactly where he had predicted: a triumph that made him famous throughout Europe.

Theories and contributions

• Gauss’s theorem (electric flux) — The flux of the electric field through a closed surface is proportional to the enclosed charge: $\Phi_E = \oint \vec{E}\cdot d\vec{A} = \dfrac{Q_{int}}{\varepsilon_0}$.
• Gaussian distribution — Bell-shaped curve describing random measurement errors: $f(x)=\dfrac{1}{\sigma\sqrt{2\pi}}\,e^{-\frac{(x-\mu)^2}{2\sigma^2}}$.
• Magnetism and absolute units — With Weber he introduced the absolute measurement of the Earth’s magnetic field; the gauss is still the unit of magnetic induction in the CGS system.

Featured in chapters

14 17 19

Linked atoms

17 linked atoms.

14 Campo elettrico e potenziale

• Conductors in electrostatic equilibrium
• From potential to field: the gradient
• Circulation theorem
• Flux and Gauss’s lemma
• Gauss for closed surfaces
• Field of a uniformly charged sphere
• Field of a spherical shell
• Field of an infinite plane
• Field of an infinite wire
• Cylindrical and spherical capacitors
• Two ways to calculate the field

17 Il campo magnetico

• Systematic analogy between E and B
• Absence of magnetic monopoles
• Ampère’s theorem

19 Le equazioni di Maxwell e le onde elettromagnetiche

• The four equations (first, incomplete version)
• The displacement current
• Maxwell’s four equations