Chapter 16, Problem 24A

When a charged particle moves through a magnetic field, what is the evidence that its momentum is greater than the value mv?

To determine

To Explain: When a charged particle moves through a magnetic field, the evidence that its momentum is greater than the value mv .

Explanation of Solution

Introduction: According to the special theory of relativity,

  $P=\frac{mv}{\sqrt{1-\frac{v^2}{c^2}}}$

In relativistic momentum, electrons has velocity comparable with the speed of light which is the highest known speed of any particle yet. Thus, relativistic momentum is greater than the Newtonian momentum mv with the factor of $\sqrt{1-\frac{v^2}{c^2}}$ .

Conclusion: Thus, a charged particle moving in the magnetic field would approach the speed of light. And, hence, relativistic momentum will be applied on it irrespective of Newtonian momentum, which will be greater than the later.