Lorentz Force

Class XII - Physics

When a electric charge +q moves with a velocity 'v' through a magnetic field B, then magnetic field exerts a force on the charge. This force is known as Lorentz force. So, Lorentz force can be defined as the force exerted by a magnetic field on the charge when passing through it.

                Let us consider B be the magnetic field in the direction of X-axis and 'v' be the velocity of the charge in the XY plane in any direction such that the angle between B and 'v' is Ѳ. Then, F_m be the force exerted on the charge which is perpendicular to the XY plane. Then, experimentally it was found that,

F_m α  B [Lorentz force is directly proportional to the strength of magnetic field]

F_m α  q [Lorentz force is directly proportional to the magnitude of charge]

F_m α  v [Lorentz force is directly proportional to the velocity of charge]

F_m α   sinѲ [Lorentz force is directly proportional to the sine of the angle between velocity of charge and magnetic field]

Then,

F_m α  BqvSinѲ

F_m = KBqvSinѲ

where K is a proportionality constant and it's value is 1.

So, F_m = BqvSinѲ

In vector form,

F_m =(B×V)q

Here, B and V are the vectors of B and V.