Unified all previous electro-magnetism theories into one equation.
Explains the propagation of light as a wave, and matches the previously known relationship between the speed of light and electromagnetic constants.
The equations are a system of partial differential equation.
The system consists of 6 unknown functions that map 4 variables: time t and the x, y and z positions in space, to a real number:
and two known input functions:
- , , : directions of the electric field
- , , : directions of the magnetic field
- : density of charges in space
- : current vector in space. This represents the strength of moving charges in space.
Also consider the following cases:
- if a spherical charge is moving, then this of course means that is changing with time, and at the same time that a current exists
- in an ideal infinite cylindrical wire however, we can have constant in the wire, but there can still be a current because those charges are movingSuch infinite cylindrical wire is of course an ideal case, but one which is a good approximation to the huge number of electrons that travel in a actual wire.
The goal of finding and is that those fields allow us to determine the force that gets applied to a charge via the Equation 10. "Lorentz force", and then to find the force we just need to integrate over the entire body.
Finally, now that we have defined all terms involved in the Maxwell equations, let's see the equations:
- Table of contents | 408, 1k, 27
- 1. Lorentz force | 44
- 2. Explicit scalar form of the Maxwell's equations | 95, 245, 1
- 3. Coulomb's law | 87
- 4. Solutions of Maxwell's equations | 48, 153, 2
- 7. Electric field () | 0, 109, 6
- 8. Magnetic field () | 0, 16, 2
- 8.1. Magnetometer | 16
- 9. Hall effect | 73
- 10. Electromagnetic four-potential | 49, 151, 4
- 10.3. Lorentz gauge condition | 71, 102, 1
- 11. Electromagnetism | 12, 12, 1
- Coulomb's law | 87
- Deriving magnetism from electricity and relativity | 65
- Electric current | 84
- Electromagnetic four-potential | 49, 151, 4
- Electromagnetism | 12, 12, 1
- Important partial differential equation | 43, 793, 24
- Maxwell's equations require special relativity | 120, 440, 6
- Maxwell's equations with pointlike particles | 105
- Particle physics | 137, 32k, 513
- Quantum mechanics experiment | 66, 2k, 22
- System of partial differential equations | 77