A circular loop

As a second example of the magnetic field of a moving charge, we consider a circular loop of radius r carrying a current I , as in in Fig. 1.7.

  

Figure 1.7: Magnetic field of a current loop

At the center of the loop, the magnitude of the magnetic field is given by

 

$${\frac{\mu_0I}{2 r}}$$ (8)

and the direction of the magnetic field indicated can be remembered by the following rule:

Curl the fingers of your right hand in the direction of the current around the loop - your thumb then indicates the direction of the magnetic field.

Note that this is the magnetic field just at the center of the loop, and away from the center the magnetic field changes in both magnitude and direction.

The association of a magnetic field with a current loop enables us to understand qualitatively the formation of permanent magnets. At the atomic level materials are composed of essentially stationary nuclei around which electrons orbit. The orbiting electrons can be considered as current loops, and thus each atom has its own magnetic field. In non-magnetic materials the magnetic fields of all the atoms are randomly oriented, resulting in no net magnetic field, but in permanent magnets interactions between the atoms favour the individual atomic magnetic fields to be aligned, producing a net macroscopic magnetic field.