In physics, the magnetic field is the field produced by a magnet. A field, in this context, is a vector for each point in space, possibly changing in time. Given the symbol B, the magnetic field points in the same direction as would a compass – away from the north pole of a magnet, and towards the north pole of the Earth.
Magnetic fields are produced by charges in motion, and moving charges are deflected by magnetic fields. Spinning particles also produce a magnetic field – this is how a permanent magnet works.
Like the electric field, the magnetic field is generally defined by the force it produces:
where "×" indicates a vector cross product, q is electric charge, and v is velocity. This law is called the Lorentz force law. The simplest mathematical statement describing how magnetic fields are produced makes use of vector calculus:
"File:Del.gif ×" is curl, "File:Del.gif ·" is divergence, μ0 is permeability, J is current, ∂ is the partial derivative, ε0 is the permittivity, E is the electric field and t is time. The first equation is known as Ampère's law with Maxwell's correction. The second term of this equation (Maxwell's correction) can often be ignored. The second equation is a statement of the observed non-existence of magnetic monopoles. These are two of Maxwell's equations.
Maxwell did much to unify static electricity and magnetism, producing a set of four equations relating the two fields. However, under Maxwell's formulation, there were still two distinct fields describing different phenomena. It was Albert Einstein who, using special relativity showed that electricity and magnetism could be fully unified. The existence of magnetism can be predicted from the existence of static electricity, using relativity. The equations given above are valid under relativity – indeed, their validity without relativity is questionable.
See also electromagnetism, magnetism, electromagnetic field, electric field, Maxwell's equations