# Maxwell's Equations Electricity and magnetism are described by four special equations, known as maxwell's equations:  These equations are written in the language of [Divergence](Divergence.md) and [Curl](Curl.md). #### Equation 1 - Gauss's Law Consider the first equation above, Gauss's Law. It states that the divergence of the electric field is proportional to the charge density:  Visually a beautiful way to think about this is:  We can think of positively charged regions acting as *sources* of some imagined fluid, and negatively charged regions as being the *sinks* of that fluid. In parts of space where there is no charge the fluid would be flowing incompressibly, just like water. #### Equation 2 Another important equation is that the divergence of the magnetic field is 0 everywhere.  We can understand that by saying: if the fluid represented a fluid flow, that fluid would be incompressible, with no sources and no sinks.  This also tells us that *magnetic monopoles* (something that acts like the north or south end of a magnet in isolation) don't exist! There is nothing analogous to positive and negative charges in an electric field. #### Equation 3, 4 The last two equations just tell us that the way one these fields changes depends on the curl of the other field! What is very interesting is that the *back and forth* of equations 3 and 4 is [what gives rise to light waves](https://youtu.be/rB83DpBJQsE?t=434). --- Links to: [Divergence](Divergence.md) [Curl](Curl.md) References: * [Divergence and Curl: 3b1b](https://youtu.be/rB83DpBJQsE?t=357)