Chapter 20, Problem 20P

To determine

To show: The momentum of the particleis

  $P=qBr$

Explanation of Solution

Given:

Charge of particle is q

Radius of circular path is r in which a particle moves in a uniform magnetic field B .

Formula used:

The force is given by,

  $F=qvB$

Calculation:

It is known that force is equal to rate of change of momentum.

So,

  $\frac{dp}{dt}=qvB$

  $\frac{dp}{dt}dt=qBvdt$

  $p=qBvt$

As $r=vt$

  $p=qBr$

Conclusion:

Therefore, it is proved that for a charged particle momentum is $p=qBr$