MAGNETIC POLARIZABILITY

John W. Dooley, Physics Department, Millersville University

Magnetic Polarization INCREASES net B field (for fixed current)

Empty coil and a coil filled with iron oxide,

both with the same current.

Consider the experiment represented in the figure: We compare two coils of wire; one filled with paramagnetic iron oxide, and the other empty. We raise the current in each coil, and measure the magnetic field inside the coils. When the coil is full, this means that we must dig a little hole in the magnetic material and put our measuring probe inside the hole.

Magnetic field versus current in two coils; one empty and one full of paramagnetic

material. Also plotted is difference between the two fields.

The field within paramagnetic material present is larger, as indicated in the figure. This is dramatically different from the corresponding figure for dielectric materials. There, the empty field is stronger. Here the full field is stronger.

At a given current (the same in each coil) we can measure the two magnetic fields and calculate their difference. This difference is the contribution to the magnetic field by the polarized iron oxide:

In an isotropic medium, all three vectors have the same direction. In an anisotropic medium, the polarization B field can be in a direction different from the empty coil field.

The graph represents experimental results. From it we can make several conclusions:

Magnetic field versus current in two coils; one empty and one full of paramagnetic

material. Also plotted is difference between the two fields.

1) The empty coil magnetic field is proportional to the current in the coil.

2) The full coil magnetic field is proportional to the current in the coil.

3) The full coil magnetic field is proportional to the empty coil magnetic field.

4) The difference between the empty coil and the full coil fields is proportional to the empty coil magnetic field.

5) The extra magnetic field due to polarization is proportional to the empty coil magnetic field.

6) If the extra magnetic field is proportional to the magnetic dipole moment per unit volume, then the magnetic dipole moment per unit volume in the iron oxide which fills the coil is proportional to the empty coil magnetic field.

Item 6 is represented mathematically as

This equation is true for isotropic paramagnetic materials. For anisotropic paramagnetic materials, the expression is analogous to the anisotropic dielectric expression. In subscript notation with the Einstein summation convention,

This perfectly good representation of the relation between polarization and magnetic field is not used in practice. See the section on magnetic susceptibility.