---
tag: 9BWWD4QK8Y
kind: concept
name: Maxwell's equations
msc: [35Q61, 35Q60]
specializes: [GC5BDZ6QBC]
sources:
  - url: https://en.wikipedia.org/wiki/Maxwell's_equations
same_as:
  wikidata: Q51501
  wikipedia: Maxwell's equations
---

## Summary

Maxwell's equations are four partial differential equations that govern the electric field $E$ and the magnetic field $B$.
They relate the fields to their sources, the electric charge density and the current density.
They unify electricity, magnetism and light, since in vacuum each field component solves the [[wave equation|5EHD2XBQDG]] with the speed of light.
They form a linear first-order system and are a basic model for hyperbolic systems in mathematical physics.

## Explanations

### L1 human

Electric charges create electric fields, and there are no magnetic charges.
A magnetic field that changes in time creates a circulating electric field, which is how a generator works.
An electric current, or an electric field that changes in time, creates a circulating magnetic field.
These four rules feed each other, so a disturbance in the fields travels through empty space as a wave: this wave is light.