Give the definition of magnetic field and provide its unit.

(A) The magnitude of the force $F$ on an electric charge $q$ moving with velocity $v$ in a magnetic field $B$ is given by the Lorentz force formula:
$F = B q v \sin \theta$
Rearranging for $B$:
$B = \frac{F}{q v \sin \theta}$
Definition: The magnitude of the magnetic field $B$ is defined as $1$ unit in the $SI$ system when a force of $1 \ N$ acts on a unit charge $(1 \ C)$ moving perpendicular to the magnetic field with a speed of $1 \ m/s$.
$SI$ unit derivation:
Unit of $B = \frac{\text{Unit of } F}{\text{Unit of } q \times \text{Unit of } v}$
$= \frac{1 \ N}{1 \ C \times 1 \ m/s} = 1 \ N \cdot C^{-1} \cdot s \cdot m^{-1}$
Since $1 \ C/s = 1 \ A$,the unit becomes:
$= 1 \ N \cdot A^{-1} \cdot m^{-1}$
This unit is also known as the Tesla $(T)$.