### Magnetic Flux Density

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

| |
[Equation 1] |

In Equation [1], 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:

| |
[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**:

| |
[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].

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