Bfield

The magnetic field B, or B-field, is a vector field that describes the magnetic influence of electric currents and magnetized materials. It is measured in teslas (T) and—together with the electric field—forms the electromagnetic field. A primary relation is the Lorentz force F = q v × B, which governs the motion of charges in magnetic fields.

B sources: moving charges and permanent magnets. The field lines form continuous loops; magnetic monopoles have not been observed; ∇·B = 0 expresses that fact. The field propagates at the speed of light in vacuum.

Maxwell equations state ∇×B = μ0 J + μ0 ε0 ∂E/∂t and ∇·B = 0. In magnetostatics (steady currents, no changing E), ∇×B = μ0 J. The relationship between B and the magnetic intensity H is B = μ0(H + M). In linear, isotropic, non-magnetic media, B ≈ μ0 H.

Examples include the Biot–Savart law for a current distribution: B(r) = μ0 / 4π ∫ I dl × r̂ / r^2. A long straight wire produces B = μ0 I /(2π r).

Measurement and sensing: magnetometers measure B; Hall effect sensors, fluxgate devices, and SQUIDs provide varying sensitivity.

Applications include electric machines (motors, transformers), magnetic data storage, magnetic resonance imaging, and basic research in physics.

In special relativity, B is part of the electromagnetic field tensor; E and B transform into each other under changes of reference frame.