Magnetic induction and magnetic units

There is often confusion regarding units in magnetics. This arises because relations can be derived from either of two fundamental principles, and the results yield different units. In the cgs and emu system of units, is derived from the concept of magnetic force due to magnetic poles. The magnetizing field (or magnetic field strength), , is defined as a force on a unit pole, so it has units of dynes per unit pole, which are called oersteds. In the SI system of units, magnetic field is defined in terms of the consequence of current flowing in a loop. Then, has units of amperes per meters (which = 4 × 10^-3 oersted).

Now, what if there is a magnetizable body in the presence of ? The body becomes magnetized due to the reorientation of atoms and molecules so that their spins line up. The amount of magnetization, m, is quantified as magnetic polarization, also known as magnetization intensity or dipole moment per unit volume. The lineup of internal dipoles produces a field, m, which, within the body, is added to the magnetizing field. m has units of ampere-meter² per meter³, which is amperes per metre, the same as .

In low magnetic fields, m is proportional to ; in fact, m = k, where k is magnetic susceptibility, a physical property. k in the two systems of units is related according to k_SI=4k_emu.

The magnetic induction (or magnetic flux density), , is the total field within the magnetic material, including the effect of magnetization. can be written as:

= µ_o( + m) = (1 + k)µ_o = µ_rµ_o .

The SI unit for is the tesla, which is 1 newton/ampere-meter. The cgs-emu unit for is the gauss, which equals 10^-4 tesla. The magnetic permeability of free space (considered a universal constant) is µ_o = 4 × 10^-7 H/m (the units are Henries/meter). The parameter µ_r is the relative magnetic permeability, and its value is essentially 1 in air or free space. The permeability, µ, is sometimes used, and it is the quantity (1 + k)µ_o = µ_rµ_o = µ.

The above relation shows how a material's magnetic permeability relates to its magnetic susceptibility, k , and how the magnetic flux density within a material depends upon both the ambient field and the induced magnetic moment. There can be some confusion as to whether permeability, µ, or the relative permeability, µ_r, is being used, but you should be able to tell by the value. However, it is best to check, if possible. Susceptibility is becoming the most commonly used physical property for geophysical work, but use of permeability can still be found in older work, or in some countries.

The tesla is a large unit compared to the magnetic fluxes that we ordinarily deal with in applied geophysics, so we generally use a subunit nanotesla (nT) where 1 nT=10^-9 T. There is also another unit, the gamma, which is numerically equivalent to the nT. That is, 1 nT = 1 gamma. The strength of the earth's magnetic field varies between approximately 25,000 and 70,000 nT, depending upon latitude.

So, in the end, are we measuring or during geophysical surveys? This confusion stems partly from the fact that the two are linearly related, so that a map of one looks exactly like a map of the other, except for the units. Most geophysical magnetic surveys involve measuring and maps are shown in units of nanoteslas. If the maps and interpretations are discussed in terms of , the conclusions will not change, so the distinction is not usually worried about.

See also the sidebar on magnetic units, which discusses units in the context of the UBC-GIF dipole JAVA applet., which in turn, is discussed more fully in the section which discusses the response to buried dipoles .