Magnetic Field Produced by a Current-Carrying Circular Loop
The magnetic field near a current-carrying loop of wire is shown in this figure. Both the direction and the magnitude of the magnetic field produced by a current-carrying loop are complex. RHR-2 can be used to give the direction of the field near the loop, but mapping with compasses and the rules about field lines given in Magnetic Fields and Magnetic Field Lines are needed for more detail. There is a simple formula for the magnetic field strength at the center of a circular loop. It is
\(B=\cfrac{{\mu }_{0}I}{2R}\phantom{\rule{0.25em}{0ex}}(\text{at center of loop})\text{,}\)
where \(R\) is the radius of the loop. This equation is very similar to that for a straight wire, but it is valid only at the center of a circular loop of wire. The similarity of the equations does indicate that similar field strength can be obtained at the center of a loop. One way to get a larger field is to have \(N\) loops; then, the field is \(B={\mathrm{N\mu }}_{0}I/(2R)\). Note that the larger the loop, the smaller the field at its center, because the current is farther away.
(a) RHR-2 gives the direction of the magnetic field inside and outside a current-carrying loop. (b) More detailed mapping with compasses or with a Hall probe completes the picture. The field is similar to that of a bar magnet.