# Cathode Ray Tube Question

1. Dec 22, 2015

### Andrew Wang

1. The problem statement, all variables and given/known data
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 [Broken]
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 [Broken]

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.
2. Relevant Equations

$F = qv x B$
$\frac{mv^2}{R} = F$
$U = qV$

3. 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: May 7, 2017
2. Dec 22, 2015

### TSny

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?