# `Magnetic Flux Density (B-Field)`

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The Magnetic Flux Density (or B-field) is related to the magnetic field (H) by the permeability (written as of the medium where the fields are observed:

The magnetic flux density has units of magnetic charge/area (Webers/meter-squared or Wb/m^2, also known as a Tesla (T)). The permeability is often frequency-dependent, and is also sometimes anisotropic (which means the permeability is a function of which direction the fields are in):

In the most general case the H-field is related to the the magnetic flux density by a 3x3 matrix, which is also frequency-dependent.

Recall that the electric field can be defined in terms of a "force per unit electric charge". Further, note that magnetic fields are associated with moving electric charges. The magnetic flux density can be defined in terms of a force per unit charge moving at unit velocity. An emperical law relating the speed of an electric charge (u), the magnitude of the charge in Coulombs (q), the magnetic flux density B), and the associated magnetic force (F) can be written as:

In the above equation, the represents the cross product for vectors. This shows that if the charge is moving in the +x-direction, and the magnetic flux density is in the +y-direction, the charge will experience a force in the +z-direction. If the charge is moving in the same direction as the magnetic field, no force will be felt by the charge.