Magnetic field

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Magnetic fields surround magnetic materials and electric currents and are detected by the force they exert on other magnetic materials and moving electric charges. The magnetic field at any given point is specified by both a direction and a magnitude (or strength); as such it is a vector field.[1]

For the physics of magnetic materials, see magnetism and magnet, more specifically ferromagnetism, paramagnetism, and diamagnetism. For constant magnetic fields, such as are generated by magnetic materials and steady currents, see magnetostatics. A changing magnetic field generates an electric field and a changing electric field results in a magnetic field. (See electromagnetism.)

In view of special relativity, the electric and magnetic fields are two interrelated aspects of a single object, called the electromagnetic field. A pure electric field in one reference frame is observed as a combination of both an electric field and a magnetic field in a moving reference frame.

In modern physics, the magnetic (and electric) fields are understood to be due to a photon field; in the language of the Standard Model the electromagnetic force is mediated by photons. Most often this microscopic description is not needed because the simpler classical theory covered in this article is sufficient; the difference is negligible under most circumstances.

B and H

Alternative names for B name used by
magnetic flux density electrical engineers
magnetic induction applied mathematicians
electrical engineers
magnetic field physicists
Alternative names for H name used by
magnetic field intensity electrical engineers
magnetic field strength electrical engineers
auxiliary magnetic field physicists
magnetizing field physicists

The term magnetic field is used for two different vector fields, denoted B and H.[2] There are many alternative names for both, though. (See sidebar.) To avoid confusion, this article uses B-field and H-field for these fields, and uses magnetic field where either or both fields apply.

The B-field can be defined in many equivalent ways based on the effects it has on its environment. For instance, a particle having an electric charge, q, and moving in a B-field with a velocity, v, experiences a force, F, called the Lorentz force (see below). In SI units, the Lorentz force equation is

where × is the vector cross product. The B-field is measured in teslas in SI units and in gauss in cgs units.

An alternate working definition of the B-field can be given in terms of the torque on a magnetic dipole placed in a B-field:

for a magnetic dipole moment m (in ampere-square meters).

Although views have shifted over the years, B is now understood as being the fundamental quantity, while H is a derived field. H is defined as a modification of B due to magnetic fields produced by material media, such that (in SI):

where M is the magnetization of the material and μ₀ is the permeability of free space (or magnetic constant).[3] The H-field is measured in amperes per meter (A/m) in SI units, and in oersteds (Oe) in cgs units.[4]

In materials for which M is proportional to B the relationship between B and H can be cast into the simpler form: H = B/μ, where μ is a material dependent parameter called the permeability. In free space, there is no magnetization, M, so that H = B/μ₀. For many materials, though, there is no simple relationship between B and M. For example, ferromagnetic materials and superconductors have a magnetization that is a multiple-valued function of B due to hysteresis.[5]

See History below for further discussion.

The magnetic field and permanent magnets

Permanent magnets are objects that produce their own persistent magnetic fields. All permanent magnets have both a north and a south pole. They are made of ferromagnetic materials such as iron and nickel that have been magnetized. The strength of a magnet is represented by its magnetic moment, m; for simple magnets, m points in the direction of a line drawn from the south to the north pole of the magnet. For more details about magnets see magnetization below and the article ferromagnetism.

Force on a magnet due to a non-uniform B

Like magnetic poles brought near each other repel while opposite poles attract. This is a specific example of a general rule that magnets are attracted (or repulsed depending on the orientation of the magnet) to regions of higher magnetic field. For example, opposite poles attract because each magnet is pulled into the larger magnetic field near the pole of the other; the force is attractive because for each magnet m is in the same direction as the magnetic field B of the other.

Reversing the direction of m reverses the resultant force. Magnets with m opposite to B are pushed into regions of lower magnetic field, provided that the magnet, and therefore, m does not flip due to magnetic torque. This corresponds to the like poles of two magnets being brought together. The ability of a nonuniform magnetic field to sort differently oriented dipoles is the basis of the Stern–Gerlach experiment, which established the quantum mechanical nature of the magnetic dipoles associated with atoms and electrons.[6][7]