# Solved… riddle of the formula drawn in the snow on a car in Cambridge

Scribbled snow scribbles on a car windshield aren’t an unfamiliar sight when the temperature plummets, but, in truth, they’re rarely worth a second look.

That is, unless you’re in Cambridge, where occasionally, instead of smearing an anatomically dubious male appendage in the frost, some clever idiot creates something that actually exercises the brain.

This image was seen on the windscreen of a car by Dr. Flavio Toxvaerd, an economist at the University of Cambridge and a fellow at Clare College who focuses on the industrial organization and economics of infectious diseases.

Writing on Twitter, he said: “Where I grew up, kids wrote obscenities in the snow. But this is Cambridge. Does anyone know what formula it is?

His tweet generated over 5,000 likes and over 400 retweets and more than a few suggestions and solutions (some of them correct), while others responded with images of more, well, basic snow prints they’d seen…

We sought the help of the Cavendish Laboratory of the University of Cambridge, home of its Physics Department, to confirm the answer to Flavio’s question.

And sure enough, the Cavendish – 30 members of whom have won Nobel prizes since their inception in 1895 – came up with the merchandise.

“It’s the Lagrangian of electromagnetism,” a department scientist told us. “This means that it is the elegant way to capture the four Maxwell equations that describe the electric and magnetic field. Among other things, this is the equation that predicts light!”

The discoveries of James Clerk Maxwell, a 19th-century Scottish mathematician and scientist who studied and worked at Cambridge for two terms, helped usher in a new era in physics. Considered a genius in terms of theory and experiment, his work provided an essential link between Newton’s physics and Einstein’s.

He developed the classical theory of electromagnetic radiation, describing electricity, magnetism, and light as manifestations of the same phenomenon.

His seminal 1865 work, A Dynamic Theory of the Electromagnetic Field, showed that electric and magnetic fields travel through space as waves, moving at the speed of light. He wrote that “light and magnetism are affections of the same substance,” and the combination of light and electrical phenomena led him to predict the existence of radio waves.

Maxwell arrived at Cambridge University in October 1850, having already studied at Edinburgh University. He attended Peterhouse briefly, but transferred before the end of his first term to Trinity, as he thought it would be easier to obtain a scholarship there. At Trinity, he joined an elite secret debating society known as the Cambridge Apostles.

Having graduated in mathematics with the second highest score on his final examination in 1854, behind Edward Routh, he received an early scholarship in October 1855, but left in November 1856 to take up the post of chair of natural philosophy. at Marischal College. , Aberdeen, at just 25 years old.

After narrowly surviving smallpox, he had a productive period at King’s College London, from 1860 to 1865, before returning to Glenlair in Scotland. But he was at Cambridge in 1871, becoming Cavendish’s first professor of physics and in charge of the development of the now world-famous Cavendish Laboratory. He designed the original laboratory in Free School Lane and was responsible for the regeneration of physical research at Cambridge.

He died of abdominal cancer on November 5, 1879 at the age of 48.

Today, the Maxwell Center, which opened on the university’s West Campus on April 7, 2016, bears his name. It is the focal point for industrial engagement with physical scientists and engineers on site.

Maxwell’s four equations each describe a phenomenon, but he didn’t actually create them. Instead, he combined four equations made by Gauss, Faraday, and Ampere. He added the displacement current to Ampere’s law, the fourth equation, to complete the equation.

The equations are:

- Gauss’s law for static electric fields
- Gauss’s law for static magnetic fields
- Faraday’s law, which says that a magnetic field that changes over time produces an electric field
- The Ampere-Maxwell law, which says that an electric field that changes over time produces a magnetic field.

The combination of the third and fourth equations explains an electromagnetic wave, like light, that can propagate on its own.

And the combination describes that a changing magnetic field produces a changing electric field, and this changing electric field produces another changing magnetic field. The cycle continues, forming an electromagnetic wave that propagates through space.

The equations can be expressed in the form of integral equations and in the form of differential equations.

So the Lagrangian, defined as a function describing the state of a dynamical system, which was written in the snow in a car in Cambridge, is one way of putting these equations together. And it’s certainly more appropriate for a learning city than the usual efforts.