Maxwell's Equations
James Clerk Maxwell wrote down a set of four equations that are an extremely good summary of most of what we've done in this course so far. Three and a half of the equations were investigated by others, and Maxwell added the second term in the last equation. Maxwell, however, had some great insight into what the equations implied, and he used the four equations to tie electricity and magnetism together with electromagnetic waves and optics.
The integral form of Maxwell's equations goes like this:
| ò |
E · dA
| = |
| Q
|  |
| eo
|
|
Gauss' Law for electric charge
|
| ò |
B · dA
| = |
0 |
Gauss' Law for magnetism
|
| ò |
E · dl
| = |
| -dFB
| |
| dt
|
|
the general form of Faraday's Law
|
| ò |
B · dl
| = |
mo |
( |
Ienc + eo |
| dFE
| |
| dt
|
|
) |
Ampere's Law with Maxwell's displacement current
|
Let's translate these into a more user-friendly form.
The first equation tells us that electric fields come from charges.
The second equation tells us that magnetic field lines are continuous loops.
The third equation tells us that a changing magnetic flux can produce an electric field.
The fourth states that magnetic fields come from charges, or from changing electric flux (this was the piece that Maxwell added).