Both the electric field and magnetic field can be defined from the Lorentz force law:

The electric force is straigtforward, being in the direction of the electric field if the charge q is positive, but the direction of the magnetic part of the force is given by the right hand rule.

The standard SI unit for magnetic field is the Tesla, which can be seen from the magnetic part of the Lorentz force law F_magnetic = qvB to be composed of (Newton x second)/(Coulomb x meter). A smaller magnetic field unit is the Gauss (1 Tesla = 10,000 Gauss).

The magnetic quantity B which is being called "magnetic field" here is sometimes called "magnetic flux density". An older unit name for the Tesla is Webers per meter squared, with the Weber being the unit of magnetic flux.

The magnetic fields generated by currents and calculated from Ampere's law or the Biot Savarat's Law are characterized by the magnetic fiels B measured in Tesla. But when the generated fields pass through magnetic materials which themselves contribute internal magnetic fields, ambiguities can arise about what part of the field comes from the external currents and what comes from the material itself. It has been common practice to define another magnetic field quantity, usually called the "magnetic field strength" designated by H. It can be defined by the relationship

and has the value of unambiguously designating the driving magnetic influence from external currents in a material, independent of the material's magnetic response. The relationship for B can be written in the equivalent form

H and M will have the same units, amperes/meter. To further distinguish B from H, B is sometimes called the magnetic flux density or the magnetic induction. The quantity M in these relationships is called the magnetisation of the material.

Another commonly used form for the relationship between B and H is

where

?₀ being the magnetic permeability of space and K_m the relative permeability of the material. If the material does not respond to the external magnetic field by producing any magnetization, then K_m = 1. Another commonly used magnetic quantity is the magnetic susceptibility which specifies how much the relative permeability differs from one.

For paramagnetic and diamagnetic materials the relative permeability is very close to 1 and the magnetic susceptibility very close to zero. For ferromagnetic materials, these quantities may be very large.

The unit for the magnetic field strength H can be derived from its relationship to the magnetic field B, B=?H. Since the unit of magnetic permeability ? is N/A², then the unit for the magnetic field strength is:

An older unit for magnetic field strength is the oersted: 1 A/m = 0.01257 oersted

Now lets look them closely :-

The orbital motion of electrons creates tiny atomic current loops, which produce magnetic fields. When an external magnetic field is applied to a material, these current loops will tend to align in such a way as to oppose the applied field. This may be viewed as an atomic version of Lenz's Law: induced magnetic fields tend to oppose the change which created them. Materials in which this effect is the only magnetic response are called diamagnetic. All materials are inherently diamagnetic, but if the atoms have some net magnetic moment as in paramagnetic materials materials, or if there is long range ordering of atomic magnetic moments as in ferromagnetic materials, these stronger effects are always dominant. Diamagnetism is the residual magnetic behavior when materials are neither paramagnetic nor ferromagnetic.

Any conductor will show a strong diamagnetic effect in the presence of changing magnetic fields because circulating currents will be generated in the conductor to oppose the magnetic field changes. A superconductor will be a perfect diamagnet since there is no resistance to the forming of the current loops.

Some materials exhibit a magnetization which is proportional to the applied magnetic field in which the material is placed. These materials are said to be paramagnetic and follow Curie's law: