Give features of force on charge particle inside magnetic field.

Magnetic force acted upon $q$ electric charge moving with $\vec{v}$ velocity in magnetic field $\overrightarrow{\mathrm{B}}$ is given by,

$\overrightarrow{\mathrm{F}_{\mathrm{m}}}=q(\vec{v} \times \overrightarrow{\mathrm{B}})$

$\therefore \mathrm{F}_{\mathrm{m}}=q v \mathrm{~B} \sin \theta$ where $\theta$ is angle between $\vec{v}$ and $\overrightarrow{\mathrm{B}}$.

Features :

$(i)$ It depends on $q, \vec{v}$ and $\overrightarrow{\mathrm{B}}$ (charge of the particle, the velocity and the magnetic field)

Force on a negative charge is opposite to that on a positive charge so we can write it as $\overrightarrow{\mathrm{F}}_{\mathrm{m}}=q(\overrightarrow{\mathrm{B}} \times \vec{v})$

$(ii)$ $\mathrm{F}_{\mathrm{m}}=q v \mathrm{~B} \sin \theta$ or $\overrightarrow{\mathrm{F}_{\mathrm{m}}}=q(\vec{v} \times \overrightarrow{\mathrm{B}})$ or $\left|\overrightarrow{\mathrm{F}_{\mathrm{m}}}\right|=q v \mathrm{~B} \sin \theta$ which is vector product of velocity and magnetic field. So, if $\theta=0^{\circ}$ or $\theta=180^{\circ}$, then $\mathrm{F}_{\mathrm{m}}=q v \mathrm{~B} \sin 0^{\circ}=0$ or $\mathrm{F}_{\mathrm{m}}=q v \mathrm{~B} \sin 180^{\circ}=0$

The force acts in a direction perpendicular to both the velocity and the magnetic field. Its direction is given by the screw rule or right hand rule as illustrated in figure $(a)$ and $(b)$.

Diagram $(a)$ is for positive charge and diagram $(b)$ is for negative charge.

$(iii)$ The magnetic force is zero if charge is not moving as then $v=0$.

$\therefore$ In magnetic force $\mathrm{F}_{\mathrm{m}}=q v \operatorname{Bsin} \theta v=0$, then

$\therefore \mathrm{F}_{\mathrm{m}}=0$

Thus, only a moving charge feels the magnetic force but static charge does not.