[latexpage]

### Equation 1

Gausses law – the divergence of the electric vector field foverned by material permittivity parameters (i.e., the electric flux density) is equal to the volume-charge density

- Variables and parameters
- electric flux density
- material permittivity parameter
- electric field
- volume-charge density

- Note: by convention, positive point charges act as sources for electric fields and negative point charge act as sinks for electric fields

### Equation 2

Gausses law of magnetism – the divergence of the magnetic field is zero

- Variables and parameters
- magnetic flux density
- magnetic field
- proportionality constant between the magnetic flux density and the magnetic field

- Note: magnetic monopoles do not exist, magnetic fields always point of of the south pole and towards the north pole of a single magnet. For example consider of a bar magnet with its magnetic fields projecting out of the north pole of the magnet and termining in towards the south pole of the magnet (Figure 1).

### Equation 3

Faraday’s law – the curl of the electric field is equal to the rate of change of the magnetic flux density (and thus, the magnetic field)

### Equation 4

Ampere’s law – the curl of the magnetic field is equal to the change in electrix flux density over time plus the electric/conductive current density

- Variables and parameters
- electric/conductive current
- material conductivity

## Conclusions

- Gausses law implies charges give rise to diverging electric currents
- Diverging electric fields give rise to current
- Current gives rise to rotating magnetic fields
- Changes in magnetic fields (and thus, changes in current) give rise to rotating electric fields
- This is how electromagnetic waves propagate!!!!

Note: I just wanted to say that I did not come up with these conclusions myself. Once I find the source I used for these conclusions I will post it 🙂

## Helpful Diagrams from External Links

Click on the figure label for the source tikz code used to generate this file

#### My own thoughts:

Note: all these thoughts/ideas are based on material presented on the wikipedia page for Coulumb’s constant

- It turns out that the magnetic permeability in a vacuum is
- Does this have anything to do with the fact that is equivalent to two revolutions?

- Electic permittivity in a vacuum is related to as follows:

where the speed of light