- #1

Andrew Wang

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## 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?

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