代写PHYS3035、代写C++，Java编程

日期：2022-10-28 09:51

Problem assignment PHYS3035 (Electrodynamics & Optics) 2022

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 (www.overleaf.com) 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.

To provide some additional material we will be making use of the specification details found at the

link: https://www.rfcafe.com/references/electrical/ew-radar-handbook/

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.