
### Static Magnetic Field

The sources of static magnetic fields are direct currents (DC) and magnets. The direction of the magnetic field from a DC current is determined through the right-hand rule. The magnetic field’s direction from the magnet is outward-oriented from the north pole and inward into the south pole.

It is interesting to see that the magnetic field from a current loop looks very much like a magnetic field of a magnet placed in the center of the loop, perpendicularly to it.

Geographical earth’s south pole is earth’s magnetic north pole.

### Ampere’s Law

Ampere’s law for static magnetic fields states that the magnetic field’s integral $H$ around closed contour is equal to the current enclosed by the contour.

If the contour encloses only part of the current, whose current density is J, then to find the total current, we have to integrate through the cross-section of the conductor carrying current.

The vector $\vec {dS}$ is the surface area enclosed by the contour. The vector of the surface area is determined from the direction of the contour with the right-hand rule. If we orient our fingers in the direction of the contour, the thumb will point in the direction of the surface vector.

We can also re-write the above equations in terms of magnetic flux density $B=\mu H$.