Thomson's Apparatus: Clarifying the Question

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In summary, the conversation is about a confusing question on a physics homework assignment. The question involves using sine instead of tangent, which may be due to the presence of a magnetic field in the problem. The person is also unsure about the diagram referenced in the textbook and is wondering how it relates to the problem.
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ElijahRockers
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Homework Statement



The question at the top of this http://www.wlu.ca/physcomp/pc242/Solutions3.pdf is kinda confusing me... I follow it all the way up until it says

[itex]sin\theta \approx \theta \equiv \frac{l}{r} \Rightarrow r \approx \frac{l}{\theta}[/itex]


The Attempt at a Solution



The book I'm using has an identical question (same values even) as this one, but it refers me to "Figure 4.6" which is supposed to be a diagram of the Thomson apparatus in question, but it's not in the book as far as I can tell. I did find a diagram of the apparatus at the beginning of the chapter with a somewhat similar example, (except the book uses tan(theta), and no magnetic field, only uses the electric field) but I'm wondering why we are using sine in the PDF.
 
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I'm guessing it has something to do with the magnetic field, but I'm not sure why that would change the calculation from tan to sin.
 

What is Thomson's apparatus?

Thomson's apparatus is an experimental setup created by British physicist J.J. Thomson in the late 19th century to study the properties of cathode rays.

How does Thomson's apparatus work?

The apparatus consists of a sealed glass tube with a cathode at one end and an anode at the other. The tube is filled with a gas at low pressure. When a high voltage is applied between the cathode and anode, cathode rays are produced and are deflected by electric and magnetic fields within the tube, allowing for their properties to be studied.

What is the significance of Thomson's apparatus?

Thomson's apparatus was instrumental in the discovery of electrons, as well as their charge-to-mass ratio. This led to the development of the modern model of the atom and furthered our understanding of subatomic particles.

How accurate are the results obtained from Thomson's apparatus?

The results obtained from Thomson's apparatus are quite accurate, considering the limitations of the technology available at the time. However, with advancements in technology, more precise measurements have been made using similar experimental setups.

Can Thomson's apparatus still be used in modern experiments?

While Thomson's original apparatus may not be used in modern experiments, the principles behind it are still relevant and similar setups are used to study the properties of particles such as electrons and protons. These setups have been continuously improved upon to provide more accurate and detailed results.

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