Force on moving charge on a magnetic field (Lorentz Force)



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.

Force on moving charge on a magnetic field

 

Experimentally it is found that magnitude of magnetic force is

directly proportional to the magnitude of the charge i.e.

Force on moving charge on a magnetic field

 

directly proportional to the velocity of the charge i.e.

Force on moving charge on a magnetic field

 

directly proportional to the strength of magnatic field i.e.

Force on moving charge on a magnetic field

 

directly proportional to the sine of angle between v and B i.e

 

 

 

Force on moving charge on a magnetic field

 

Now from above equations, we get

Force on moving charge on a magnetic field

 

This is the expression for Lorentz magnetic force where FM is perpendicular to the plane of v and B