Consider a charged particle or charge =q is moving with velocity v on a magnatic field B can experience magnatic force FM. If the direction of magnatic field is represented by Y-axis, velocity of charged particle is along XY plane making angle θ with direction of magnatic field (B), then the direction of magnetic force is represented by Z-axis.
Experimentally it is found that magnitude of magnetic force is
directly proportional to the magnitude of the charge i.e.
directly proportional to the velocity of the charge i.e.
directly proportional to the strength of magnatic field i.e.
directly proportional to the sine of angle between v and B i.e
Now from above equations, we get
This is the expression for Lorentz magnetic force where FM is perpendicular to the plane of v and B