# Cathode Ray Tube and magnetic field Question

• Andrew Wang
In summary, the conversation discusses the setup of a cathode ray tube (CRT) in a uniform constant magnetic field and the resulting electron beam trajectory. The goal is to derive an expression for the charge to mass ratio of the electron in terms of the magnetic field, accelerating potential difference, and distance between the anode and screen. The concept of a "focused spot" is introduced, which refers to all electrons hitting the screen within a small area. The shape of the electron's trajectory is also mentioned.
Andrew Wang

## Homework Statement

A cathode ray tube (CRT), consisting of an electron gun and a screen, is placed within a uniform constant magnetic field of magnitude B such that the magnetic field is parallel to the beam axis of the gun, as shown in figure 2.1.http://ipho.phy.ntnu.edu.tw/problems-and-solutions/2000/figure21.png
Figure 2.1

The electron beam emerges from the anode of the electron gun on the axis, but with a divergence of up to 5° from the axis, as illustrated in figure 2.2. In general a diffuse spot is produced on the screen, but for certain values of the magnetic field a sharply focused spot is obtained.

http://ipho.phy.ntnu.edu.tw/problems-and-solutions/2000/Figure22.png

Figure 2.2

By considering the motion of an electron initially moving at an angle b (where 0 £ b £ 5°) to the axis as it leaves the electron gun, and considering the components of its motion parallel and perpendicular to the axis, derive an expression for the charge to mass ratio e/m for the electron in terms of the following quantities:

• the smallest magnetic field for which a focused spot is obtained,
• the accelerating potential difference across the electron gun V (note that V < 2 kV),
• D, the distance between the anode and the screen.

## Homework Equations

[/B]
##F = qv x B##
##\frac{mv^2}{R} = F##
##U = qV##

## The Attempt at a Solution

I guess the electron goes in a "cyclotron" motion. It has initial velocity (out the gun) of ##\sqrt{\frac{2eV}{m}}##. What exactly is meant by a "focused spot", and how do we obtain it?

Last edited by a moderator:
Hello and welcome to PF!

A "focused spot" means that all of the electrons that leave the gun hit the screen within one very small area of the screen.

Can you describe the shape of the trajectory of an electron as it goes from the gun to the screen?

## What is a cathode ray tube and how does it work?

A cathode ray tube is a vacuum tube used to display images in old television sets and computer monitors. It works by accelerating electrons from a negatively charged cathode towards a positively charged anode, creating a narrow beam of electrons. This beam is then directed onto a phosphor-coated screen, producing a visible image.

## What is the role of the magnetic field in a cathode ray tube?

The magnetic field in a cathode ray tube is used to deflect the electron beam and control its movement. This is achieved by applying a varying magnetic field that interacts with the electrons, causing them to move in a curved path towards the phosphor screen.

## Why is the magnetic field necessary in a cathode ray tube?

The magnetic field is necessary in a cathode ray tube to ensure that the electron beam is directed towards the correct location on the screen. Without the magnetic field, the electrons would spread out and produce a distorted image.

## What is the relationship between the strength of the magnetic field and the deflection of the electron beam?

The strength of the magnetic field directly affects the deflection of the electron beam. A stronger magnetic field will cause a greater deflection, while a weaker magnetic field will result in less deflection.

## Can the magnetic field be adjusted in a cathode ray tube?

Yes, the strength and direction of the magnetic field can be adjusted in a cathode ray tube. This allows for precise control of the electron beam and ensures an accurate display of the image on the screen.

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