magneticfield

A magnetic field is a vector field that describes the magnetic influence of moving electric charges and of magnetic materials. It exerts forces on moving charges and on magnetic dipoles, and it underpins many physical and technological processes.

The field arises from electric currents, changing electric fields, and permanent magnets. In steady situations, currents produce steady magnetic fields; time-varying currents or magnetic materials can produce changing fields that induce electric fields as described by Maxwell’s equations.

In SI units, the magnetic field B is measured in tesla (T). The field strength H is related to B by B = μ0(H + M) in materials, and in simple nonmagnetic media B ≈ μ0 H; the gauss (1 G = 10^-4 T) is an older unit still encountered in some contexts. In vacuum, B = μ0 H with μ0 = 4π×10^-7 N·A^-2.

Fundamental relations include that the divergence of B is zero (no magnetic monopoles) and Faraday’s law relates the curl of E to the negative time rate of change of B. The Biot–Savart law gives B from steady currents. The Lorentz force F = q(v × B) governs the force on a moving charge, and for a current I in a wire, F = I L × B.

Materials respond to magnetic fields through magnetization, described by M. Substances can be diamagnetic, paramagnetic, or ferromagnetic, with ferromagnets showing strong, persistent magnetization. Applications range from compasses and electric motors to MRI and data storage, illustrating the central role of magnetic fields in science and technology.