Chapter 36, Problem 37A

A magnetic field can deflect a beam of electrons, but it cannot do work on them to speed them up. Why? (Hint: Consider the direction of the force relative to the direction in which the electrons move.)

To determine

To explain: The beam of the electron can be deflected by the magnetic field but it cannot do work on them.

Explanation of Solution

Introduction:

The magnetic field which is produced by the current carrying loop is always perpendicular to the direction of the current flow and the magnetic field is depends upon the velocity of the charged particle. The magnetic force is proportional to the field strength and the particle’s velocity.

As the charged particle enters the magnetic field, it gets deflected by experiences the magnetic force. This force is the Lorentz’s force.

The Lorentz’s force is

$\overrightarrow{L}=q\left(\overrightarrow{V}\times \overrightarrow{B}\right)$

Where, q is the charge of the particle

V is the velocity of the charged particle

B is the magnetic field strength

The velocity of the charged particle always acted in the normal direction to the direction of the magnetic force. Therefore, it cannot do work on them.

Conclusion:

The magnetic force is acted always in the normal direction with the electron’s velocity.