Magnetic Fields Due to Current

In a magnet, all the magnetic dipoles created by the motion of electrons around their nucleus are aligned. The direction of this moment the direction of the magnetic field. In objects that are not magnetized, the moments are randomly oriented. Heating or exerting a very large impulse on the magnet can knock the aligned magnetic dipoles out of alignment.

In a current carrying loop, a magnetic moment is produced perpendicular to the plane of the loop. This magnetic moment (mu) is equal to the current multiplied by the area. When the loop is introduced to an external electric field, the field tends to rotate the loop so that the magnetic moment and the external field are parallel. If there are multiple loops, the total magnetic moment is the product of the current, the area of the loop, and the number of loops. In the equation, theta is the angle between the magnetic moment and the magnetic field.

Here is a basic motor. It is a current carrying loop (rotor) in a magnetic field. One end the rotor is half covered in an insulated finish, and the other end is fully exposed. When plane of the rotor is perpendicular to the magnet, the rotor spins so the that the magnetic moment is parallel to the magnetic field. At this point, current stops running through the rotor (due to the half covered end of the wire), and there is no torque to keep the rotor in this position. The momentum gained from the initial 90 degree rotation allows the rotor to keep spinning. Then, both ends are now fully in contact with the wires, allowing a current to flow through again, reproducing a magnetic torque. This cycle continues.

Placing the compasses around the current carrying rod, we see that the needles all point in a circle around the rod. Wrapping our fingers around the rod with our thumbs pointing in the direction of the current, we determine the direction of the field by the direction in which our fingers curl. The magnetic field created forms circles in a plane perpendicular to the direction of the current. 

A current flowing towards you creates a clockwise magnetic field around it, and a current directed away from you creates a counterclockwise field. Amperes law states that the total current enclosed by a surface is equal to the line integral  around the closed surface. We also derived an expression for the magnetic field produced by a current.