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Q)

What is Lorentz force? Write an expression for it.

$\begin{array}{1 1} (a)\;\overrightarrow{F}=q(\overrightarrow{B}+\overrightarrow{v} \times \overrightarrow{E})\\ (b)\;\overrightarrow{F}=q(\overrightarrow{E}+\overrightarrow{v} \times \overrightarrow{B}) \\ (c)\;\overrightarrow{F}=q(\overrightarrow{E}-\overrightarrow{B} \\\ (d)\;\overrightarrow{F}=q(\overrightarrow{E}+\overrightarrow{B})\end{array} $

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A)
The total force experienced by a changed particle moving in a region where both electric and magnetic fields are present,is called Lorentz force.

 A charge $q$ in an electric field $\overrightarrow{E}$ experiences the electric force, 

                  $\overrightarrow{F_e} =$ $ q \overrightarrow{E}$

This force acts in the direction of field $\overrightarrow{E}$ and is independent of the velocity of the charge.

The magnetic force experienced by the charge $q$ moving with velocity $\overrightarrow{v}$ in the magnetic field $\overrightarrow{B}$ is given by

                  $\overrightarrow{F_m} = $ $q(\overrightarrow{v} \times \overrightarrow{B})$
 
This force acts perpendicular to the plane of $\overrightarrow{B}$ and depends on the velocity $\overrightarrow{v}$ of the charge.

The total force, or the $Lorentz force$, experienced by the charge $q$ due to both electric and magnetic field is given by

$\overrightarrow{F} = \overrightarrow{F_e} + \overrightarrow{F_m}$
              or
$\overrightarrow{F} = $ $q(\overrightarrow{E}+\overrightarrow{v} \times \overrightarrow{B})$
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