B×H

B×H denotes the cross product of the magnetic flux density B and the magnetic field strength H, two vector fields used in electromagnetism. B represents the magnetic flux density, while H is the magnetic field strength. The cross product B×H is a vector perpendicular to both B and H, following the right-hand rule.

The magnitude of B×H is |B||H|sinθ, where θ is the angle between B and H. In terms of units, B has units of tesla (T) and H has units of amperes per meter (A/m), so B×H has units of T·A/m. In many common materials, B and H are parallel (B = μH with μ a scalar in linear isotropic media), which makes B×H equal to zero. Nonzero B×H can occur in anisotropic or nonlinear magnetic materials where B and H are not aligned.

Physically, B×H is not a standard observable like the Poynting vector E×H or the energy density; it is primarily a mathematical construct used in vector calculus and problem solving. It can appear in theoretical manipulations or in specific magnetostatic or magnetohydrodynamic problems where the relative orientation of B and H matters. However, it is not generally treated as a primary quantity with a widely recognized measured meaning.

In summary, B×H is the cross product of magnetic flux density and magnetic field strength. Its value is context-dependent: it is zero in many common media due to alignment of B and H, and nonzero only when B and H are not parallel. See also cross product, magnetic field, and magnetic flux density.