Deduce an expression for the force experienced by the moving charged particle in a uniform magnetic field?

Asked by Topperlearning User | 19th May, 2015, 10:57: AM

Expert Answer:

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 begin mathsize 11px style proportional to end style q--------(1)

ii) The component of velocity acting perpendicular to the direction of the magnetic field, F begin mathsize 11px style proportional to end style v sinθ---------(2)

iii) The magnitude of the applied magnetic field, F begin mathsize 11px style proportional to end style 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, Syntax error from line 1 column 56 to line 1 column 97. Unexpected 'mathvariant'. = q(begin mathsize 11px style straight v with rightwards arrow on top end style ×begin mathsize 11px style straight B with rightwards arrow on top end style)

This is an expression for the magnetic Lorentz force.

Answered by  | 19th May, 2015, 12:57: PM