Magnetic Fields due to Currents
Learning Objectives
Learning Objectives
Force Between Two Parallel Currents
Ampere’s Law
Solenoids and Toroids
A Current-Carrying Coil as a Magnetic Dipole
Summary

Magnetic Field of a Toroid
Figure (a) shows a toroid, which we may describe as a (hollow) solenoid that has been curved until its two ends meet, forming a sort of hollow bracelet. What magnetic field B is set up inside the toroid (inside the hollow of the bracelet)? We can find out from Ampere’s law and the symmetry of the bracelet. From the symmetry, we see that the lines of B form concentric circles inside the toroid, directed as shown in Fig. (b). Let us choose a concentric circle of radius r as an Amperian loop and traverse it in the clockwise direction. Ampere’s law yields
where i is the current in the toroid windings (and is positive for those windings enclosed by the Amperian loop) and N is the total number of turns. This gives