Chapter 20, Problem 1CQ

If an electron beam in a cathode-ray tube travels in a straight line, can you be sure that no magnetic field is present?

To determine

Whether it be sure that there is no magnetic field inside the cathode-ray tube if an electron travels in a straight line.

Answer to Problem 1CQ

It cannot be sure that there is no magnetic field inside the cathode-ray tube if an electron travels in a straight line.

Explanation of Solution

When a charged particle moves in a magnetic field, it experiences a magnetic force. The magnitude of the force exerted by the field on the charged particle is given by the expression;

$F=\left|q\right|vB\sin \varphi$

Here, $F$ is the force, $\left|q\right|$ is the magnitude of charge, $v$ is the speed of the charged particle, $B$ is the magnetic field, and $\varphi$ is the angle that the velocity of the charged particle makes with the field direction.

The magnetic force tend to deflect the charge from its direction through which it entered the field region. When a charged particle moves along the direction of the magnetic field, the angle $\varphi =0$. Thus, the magnetic force on the charged particle reduces to zero. This leads the charged particle to travel undefiled or in straight line.

Similarly, in the case of the cathode-ray tube and the electron, if the magnetic field is along the direction of motion of electron, electron will travel in straight line without affected by the field. Therefore, it cannot be sure that there is no magnetic field inside the cathode-ray tube if an electron travels in a straight line