Magnetic Flux Density

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Magnetic Flux Density

The Magnetic Flux Density (B) is related to the Magnetic Field (H) by:

magnetic flux density is equal to permeability times magnetic field
[Equation 1]

In Equation [1], permeability is the permeability of the medium (material) where we are measuring the fields.

The magnetic flux density is measured in Webers per square meter [Wb/m^2], which is equivalent to Teslas [T]. The B field is a vector field, which means it has a magnitude and direction at each point in space.

We know that a particle with a charge q [C] will experience a force when in the presence of an Electric Field E. In addition, it is also known that if the charged particle is moving at velocity v perpendicular to a B field, then it will also experience a force proportional to the B field. This force can be written as:

lorentz force equation for magnetic flux density
[Equation 2]

In Equation [2], x is the cross product. This means that if the charge is travelling parallel to the B field, there will be no force exerted due to the B field. If the charge is travelling perpendicular to the B field, then a force of magnitude q*|v|*|B| is applied in a direction perpendicular to both v and B. As an example, if the particle is travelling in the +x-direction, and a magnetic flux density B is directed in the +y-direction, then the force will push the particle in the +z-direction if q is positive, and in the -z-direction if q is negative.

The Lorentz Force Equation ties the force due to an external electric field E and an external magnetic flux density B on a charged particle moving at velocity v:

lorentz force equation, B and E fields
[Equation 3]

In summary, the Magnetic Flux Density is somewhat analogous to the Electric Field in that it can exert a force on a charged particle, although in a different way. In general, the magnetic field H and the Magnetic Flux Density B can be used somehwat interchangably, and are related by the permeability in Equation [1].

Maxwell's Equations

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