In 1831, Gauss began to apply mathematical potential theory to the real world. The 54-year-old mathematician helped the 27-year-old physicist Wilhelm Weber to get a physics chair at Göttingen and then worked with him on electricity and magnetism.

The Magnetic Field and SI Units
In 1832, with Weber’s assistance, Gauss carried out experiments whose results allowed him to define the earth’s magnetic field using units of millimeters, grams, and seconds. In other words he showed the earth’s magnetic field can be defined using purely mechanical dimensions – mass, length, and time.

The work provided strong impetus for the use of SI units.

The Telegraph
In 1833, Gauss and Weber invented one of the world’s first telegraph systems. They also invented a binary alphabet code, enabling communication between Weber’s physics building and Gauss’s astronomical observatory about 1.5 miles (2.5 km) apart. By 1835, their telegraph lines had been installed beside Germany’s first railroad.

Kirchoff’s Circuit Laws
In 1833, Gauss and Weber discovered how voltage and current are distributed in the branches of electric circuits: voltage is governed by the law of conservation of energy, and current by the law of conservation of charge. Gustav Kirchoff rediscovered the laws in 1845, and they now bear his name.

Gauss’s Law & Gauss’s Law for Magnetism
Gauss used his formidable mathematical armory to analyze the behavior of electric and magnetic fields. Using his divergence theorem, which he discovered independently of Joseph-Louis Lagrange, he formulated two laws in 1835:

Gauss’s Law, which relates an electric field to the distribution of electric charges that cause it
Gauss’s Law for Magnetism, which states that magnetic monopoles do not exist.
Gauss’s Law (for electric fields and charges) and Gauss’s Law for Magnetism.

Written mathematically, these laws form two of the four equations needed to combine the electric and magnetic fields into a single, unified electromagnetic field. The unification was achieved by James Clerk Maxwell in 1864.