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PHYS3035 Electrodynamics & Optics
创建日期：2024-05-14 14:23:07
所属分类：物理Physical
标签： PHYS3035
Electrodynamics & Optics
Problem assignment PHYS3035 (Electrodynamics & Optics) 
The unit problem assignment is designed to be different from module-specific assignments. It
is not designed to train you on methods specific to a given lecture module. Instead, you will be
solving a physics problem that covers aspects of different modules within the unit and connect it
to a real-world application. You may choose any method you like to answer questions – analytic,
numerical, experimental, statistical, observational, literature review or any combination thereof -
whatever you think is most appropriate, as long as it is sound science. These need not be methods
you’ve seen explicitly in lectures or tutorials in this unit. When using numerical methods, feel
free to use the programming language you are most comfortable with. Some questions are open
ended – be curious, be creative, and see where your investigation can lead you!
The Unit Problem should take approximately 16 hours, and we expect a report of 2 typewritten
pages in the format described below (3 pages if you must), including figures and references (but
not including numerical code). We strongly encourage you to use the two-column format provided
by the American Physical Society (APS), RevTeX 4.2 Template. To get access to this, please go to
Overleaf  and open an account. Then click New Project and select Academic
Journal, under Templates. Alternatively, if you must, you can use Word. If you do so, then you
need to format it such that it looks like a Physical Review article. Hand-written reports will not be
accepted.
1. Technical content: 40%. The technical details must be presented in a notation consistent
throughout the report.
2. Originality, curiosity and initiative: 20%. How far beyond the specified problem have you
gone? For example, is there evidence of deeper connections to the relevant literature; have
connections to other fields of physics been made; have applications of the research in the
real world been discussed?
3. Well-structured report: 20%. All questions should be addressed in a single cohesive
document, in-line with the format of scientific literature, rather than as a series of dot points
each addressing a question.
4. Link with the material discussed in class: 20%. You need to make a connection between
properties of the waveguides in Table 1 of the url and the material discussed in class. You
also need to add value beyond the discussion in class and the lecture notes.
As a guide, consider the following checklist for scientific formatting:
• Figures clearly showcase results and are labelled appropriately;
• Equations are appropriately included (not every single equation needs to be included);
• Figures and results are discussed in context;
• Typesetting, equations are neat and free of typographical errors;
• Appropriate referencing when needed;
PROBLEM FORMULATION
Consider the problem of transmitting electromagnetic waves, in particular microwaves, through
space in a hollow metal waveguide. A classic way of achieving this is to use a rectangular
waveguide (think of a hollow metal pole, with a rectangular cross-section). How well do these
metal pipes transmit electromagnetic energy? The advantage of these structures is that they don’t
need to be filled with anything. In fact, to simplify our analysis, we can consider that they have
vacuum (or air) inside. In this problem assignment we will explore the electromagnetic waves that
can be transmitted by these structures.
microwave-waveguide-coaxial-cable.htm for common rectangular structures such
as the WR284 design. Your class notes should help you with this assignment, however for further
relevant material please see Chapter 3.3 of David Pozar’s textbook ’Microwave Engineering’,
available on Canvas.
QUESTIONS TO ANSWER
These questions should be answered in a single seamless document, without explicitly numbering
answers. The questions therefore provide a framework for what to include in your text. The
questions are ordered such that answering them in this order would be a natural way to progress
through the problem, and so the order provides a guideline for the structure of your text. You
are expected to answer the first six questions, and you are expected to answer Q10. For Q7 - Q9,
you are expected to answer one out of these three questions. Question 10 is open, and you are
encouraged to take your investigation in your own direction (this will particularly address the
’originality, curiosity, initiative’ element of the marking scheme).
1. Provide the boundary conditions for electromagnetic waves at the interface between vacuum
and the waveguide;
2. Outline how the mode cut-offs are calculated, and provide the general solution in terms of
the side lengths of the waveguide;
3. Calculate the frequency cut-off for the WR284 geometry, does it agree with the result in
Table 1?
4. What happens to the mode cut-offs as the geometry is changed? Plot this cut-off as a function
of a changing side length. Is it possible to recover the results of a planar waveguide?
5. Plot a 2D representation of the fundamental mode. Do the results connect with a plane
wave in vacuum in any way?
6. Comment on the origin of the frequency range shown in Table 1 (and displayed in Fig. 4).
You are not expected to prove anything, some reasonable comment or discussion is fine.
7. Does the material the waveguides are made of have an effect?
8. Comment on the energy flow in the waveguide. Is there a maximum amount of energy that
can be transmitted down the waveguide?
9. What effect will filling the waveguide with a dielectric material have?
10. Inspired by the website, the Pozar textbook, or something else, investigate further something
relevant to this problem.
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