Multipole moments are a mathematical description of electric and magnetic fields outside of sources. The mathematics of multipoles is introduced in a text chapter written especially for this course. To give a very solid reality to the meaning of these mathematical ideas, multipole moments in PHYCS 3910 are taught in the context of the magnetic multipoles of coils used for magnetic resonance imaging (MRI).
For good image quality MRI requires a very uniform magnetic field. This is usually achieved with a pair of identical coils ("Helmholtz coils") with a separation equal to the radius of the coils. A difficulty of this configuration is that there will be strong magnetic fields well outside the internal region in which the imaging is done.
To "cut off" the external fields one pair of Helmholtz coils is placed inside another, larger pair. By an adjustment of the relative current in the two coils, many of the low order multipoles of the configuration can be set to zero, with the result that the external, unwanted, fields can be made very small.
Students will analyze the coils mathematically (using the symbolic manipulation tool Maple), and will discover the conditions necessary to confine the fields. They will also explore the adequacy of the description of the magnetic field given by keeping only a few of the multipoles. They will then turn to an experimental apparatus in which they are given two different size pairs of Helmholtz coils and must compare magnetic fields they measure (with a magnetometer) to their mathematical modeling.