Magnetics: The Basics
Wherever you go. Whatever you do. Make sure you don't try to build something that doesn't agree with these little gems. 
Maxwell's Equations 

I 
Gauss's Law for Electricity. The surface integral of electric field over any closed surface is proportional to the enclosed charge. The k factor is the dielectric constant, equal to 1 in free space. 

II 
Gauss's Law for Magnetism. The integral of magnetic flux density over any closed surface is zero. This is the mathematical expression of the fact that no magnetic monopoles have ever been discovered. 

III 
Faraday's Law of Induction. The line integral of electric field over any closed path is proportional to the rate of change of magnetic flux in the enclosed region. 

IV 
Ampere's Law (as extended by Maxwell). The line integral of magnetic flux density over any closed path is proportional to the rate of change of electric field and electric current in the enclosed region. The k_{m} factor is the relative permeability, equal to 1 in free space. 
Those Little Constants 

All of the preceding equations work with units of meters, seconds, teslas (units of induced magnetic flux density, commonly referred to as "magnetic field" or "field"), webers (units of induced magnetic flux), amperes, volts and coulombs. The constants have the following values: 

8.85 x 10^{12} F/m 
Permittivity constant 

1.26 x 10^{6} H/m (exactly 4pi x 10^{7}) 
Permeability constant 
This handy little law is the foundation upon which most of the air core coil formulas in this site are based: 

The current element dl on a current filament contributes a magnetic field, dB, in a direction normal to the plane formed by dl and the vector r. The good news is that by solving this integral for an arbitrary configuration of current filaments (like a coil, or set of coils) you can compute the magnetic field vector at any point in space. The bad news is that there is no closed solution to this integral for most interesting configurations of current filaments and vectors r. Oh well. 

