Magnetic Field
A magnetic field is created by a moving charge. Practical magnetic fields are created by Electron Current.
But Permanent Magnets are not moving charges, so how is that magnetic field generated??
Through a quantum mechanical property called Electron Spin.
Danger
Magnetic fields are NOT Conservative, because the force on a moving charge depends on the path and velocity, rather than just the initial and final position.
Magnetic interactions are understood in terms of Magnetic Poles: north and south.
Magnetic poles never occur in isolation
All magnets are dipoles, with two poles.
Laws
For a Solenoid, the magnetic field is given by (see solenoid note for details)