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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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