When accelerating particles in a linear accelerator, the machine must get longer to reach higher final particle energies. At high enough energies, the linac becomes awkwardly long. One solution is to take particles exiting an acceleration section and bend them back around to the entrance of the acceleration section so that the accelerator can be used repeatedly.

The magnetic fields of dipole magnets are used to bend particles. Dipole magnets can be used to keep particles moving in a circular trajectory, either to store them (storage ring), or to make them repeatedly pass through an acceleration section inserted into the circular path (circular accelerator). Circular accelerators or storage rings do not always have a perfectly circular shape, other shapes such as a rounded triangle can be used since the beam trajectory still closes on itself. However, a perfect circle has more uniform bending and so may be the easiest example with which to start.

In order for a particle to move in a circle, there must be a centripetal force. To move a positively charged particle in clockwise circular motion as shown below, the magnetic field must be directed out of the plane of the figure. The magnetic force on the particle is given by The direction of the particle velocity at any point in the circular trajectory is tangent to the circle. The force, velocity and magnetic field vectors are mutually orthogonal. Given that the force is directed radially inward, and that the velocity is tangent to the trajectory, the magnetic field must be directed upward, perpendicular to the plane containing the circular particle trajectory.

A typical electromagnetic dipole magnet achieves a uniform magnetic field through the use of a pair of conducting coils wrapped around a steel or iron core. A single current-carrying loop of wire generates a magnetic field that passes through the loop perpendicular to the plane of the loop, as sketched in the figure below. In the figure, the axis of symmetry is the z-axis, the loop lies in the x-y plane, and the current flows in the counter-clockwise direction looking down on it from above (looking down toward more negative z). The direction of the field is given by a right-hand-rule, if you orient the fingers of your right hand to curl around the loop in the direction of current flow, your thumb will point in the direction of the magnetic field along the symmetry axis of the loop.

The strength of the magnetic field generated by a current loop may be enhanced by winding many turns of conductor, instead of a single turn, around the loop. Notice that the magnetic field lines have more curvature as one moves away from the axis of symmetry of the loop. Two coils having the same axis of symmetry, but with their centers separated a distance z along that axis, and having the same direction of current flow, will produce a more uniform (less curved) magnetic field in the region between the coils.

A pair of current loops produces a reasonably uniform magnetic field in the region between the loops. The field can be made stronger in this region if the current loops are wound around blocks of iron or steel, as shown in the sketch below.