CBSE Class 12-science Answered

Let a positive charge particle charge q is moving with velocity  in uniform magnetic field.

Let the angle between  and  is θ.

Due to the interaction between the applied magnetic field and the magnetic field produced by the moving charge, it experiences a force, which is known as magnetic Lorentz force (). The magnitude of this force () is directly proportional to:

 i) The magnitude of charge, F q--------(1)

ii) The component of velocity acting perpendicular to the direction of the magnetic field, F  v sinθ---------(2)

iii) The magnitude of the applied magnetic field, F  B---------(3)

Combining equations (1), (2) and (3)

F α qvB sinθ

F= k qvB sinθ

Where k is the constant of proportionality. Its value is found to be one i.e k=1. Therefore

F= qvB sinθ

In vector form,  = q( ×)

This is an expression for the magnetic Lorentz force.