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# Magnetic flux density

## Magnetic flux density

The magnetic flux density is a physical quantity that indicates the strength of the magnetic field at a particular point in space.

The magnitude of magnetic force on a moving charge is dependent on the magnetic flux density at a point.

The magnetic flux density $B$ is formally defined as the force per unit charge acting on a particle moving with a unit velocity in a direction perpendicular to the direction of a magnetic field.

$$B=\frac{F_{\text{magnetic}}}{qv_{\text{perpendicular}}}$$

$q=$charge of the particle moving with speed $v_{\text{perpendicular}}$ perpendicular to the magnetic field $\vecphy{B}$.

It is equivalent to the force per unit length acting on a straight conductor carrying a unit current placed perpendicular to the direction of a magnetic field (note that current is comprised of moving charges and is hence subject to magnetic forces).

## Magnetic-electric force comparison and units of magnetic flux density

Both magnetic and electric forces are dependent on the respective field strengths at a point.

However, the magnetic force is unique in that it acts in a direction perpendicular to both the direction of the motion of charges as well as the magnetic field.

Magnetic forces also only act on moving charges.

The SI unit of magnetic flux density is the tesla ($\text{T}$). One tesla ($\text{T}$) is equivalent to one newton per ampere per metre ($\text{N A}^{-1}\text{m}^{-1}$).