We know that force acting on any charge of magnitude q moving with velocity v inside the magnetic field B is given by F=q(v X B)
and this is the magnetic force on charge q due to its motion inside magnetic field.
If both electric field E and magnetic field B are present i.e., when a charged particle moves through a region of space where both electric field and magnetic field are present both field exert a force on the particle and the total force on the particle is equal to the vector sum of the electric field and magnetic field force.
F=qE+q(v X B) (4)
This force in equation(4) is known as Lorentz Force.
Where important point to note is that magnetic field is not doing any work on the charged particle as it always act in perpendicular direction to the motion of the charge.
