### PHYS2210 Electromagnetism and Thermal Physics

Students should only enrol into PHYS2050 if they have already completed PHYS2060 Thermal Physics (or vice versa).
All others should enrol into PHYS2210 Electromagnetism and Thermal Physics in 2013.

• Level 2 Physics course
• Units of Credit (UOC): 6
• Offered every year, Session 2

#### Lecturers:

Lecture times:

• Wednesday 11-12pm and Friday 12-1pm in Room G32, Old Main Building (Electromagnetism)
• Monday 3-4pm and Wednesday 1-2pm in Room 112 Old Main Building (Thermal Physics)

Tutorial times: Fri 1-2pm every week commencing week 2 in Room 149, Old Main Building

ELECTROMAGNETISM

Brief Syllabus:

• Vector analysis
• Electrostatic field, electric potential; work and energy in electrostatics
• Electrostatic fields in matter; polarization, displacement, dielectrics
• Current electricity; electric current, current density, continuity equation, Drude's model of a conductor, Ohm's Law, Kirchhoff's Laws
• Magnetostatics; magnetic fields, Lorentz force law, Biot-Savart law, Ampère’s law
• Magnetostatic fields in matter; diamagnetism, paramagnetism, ferromagnetism
• Electrodynamics
• Maxwell’s equations

Assumed Knowledge:
The course assumes familiarity with first year physics, e.g. PHYS1221 or PHYS1231 or PHYS1241 and second year mathematics MATH2011 or MATH2111.

Brush up at Physclips

Course Goals:
Electromagnetism is important from both fundamental and applied viewpoints. This course aims to provide students with an introduction to the principles and behaviour of electric and magnetic systems. The course begins by considering the electric effects of static electric charge distributions. Then, we consider magnetic effects (i.e. what happens when you allow the electric charges to move). Finally, we combine both the electric and magnetic behaviours into a unified topic Electromagnetism and introduce Maxwell’s four equations which provide an elegant summary of this subject. We will also see that there are two, equivalent mathematical descriptions of Electromagnetism i.e differential and integral.

Specific topics include:

• An introduction to the mathematical methods of vector analysis (div, grad and curl) used to describe electromagnetic quantities such as field and potential.
• The effects of static electric charge distributions. Electric fields. Gauss’ law.
• The response of real materials to applied electric fields; dielectrics. Electric polarization and displacement. The fundamental electric vectors E, D and P.
• The magnetic fields due to electric currents. Calculation of magnetic fields, Biot-Savart and Ampère laws.
• The response of real materials to magnetic fields; types of magnetism of real materials, diamagnets, paramagnets, ferromagnets. The fundamental magnetic vectors B, H and M.
• Induced EMF due to changing magnetic flux; Faraday and Lenz laws.
• Maxwell’s equations

Learning Objectives

• Students will gain an appreciation of how the topics of Electricity and Magnetism are related and unified.
• Students will be introduced to Maxwell’s equations which encompass the work of Gauss, Ampère and Faraday.
• Hopefully the student will gain an appreciation of why Maxwell’s equations are often referred to as the crowning glory of 19th century science.

Why is Electromagnetism important?

Electromagnetism underpins the operation of much of today’s technology (e.g. radio, TV, computers, data storage, radar, microwave ovens, motors, MRI, …). From a fundamental perspective, it is one of the four ‘types’ of force found in nature and Maxwell’s ‘discovery’ that light is an electromagnetic wave ranks as one of the greatest breakthroughs in science. Furthermore, Einstein was led to his formulation of the theory of relativity by the in-depth study of Maxwell’s work. To quote J.R. Pierce, “To anyone who is motivated by anything beyond the most narrowly practical, it is worthwhile to understand Maxwell’s equations simply for the good of his soul”.

The course is strongly recommended as groundwork for a number of 3rd year courses such as PHYS3011 Quantum Mechanics and Electrodynamics.

How to succeed - Strategies for Learning

Some students find this subject confusing and, in many cases, this is due to the use of vector analytical techniques involving div, grad and curl. It is important that you gain some familiarity with these techniques of differential calculus by doing problems.

Like most subjects, the key to success is hard work. A number of tutorial sheets covering the entire course will be available on the Web. The student should work through these problems bit by bit, (alone or with a group), to keep pace with the lectures. In this way the student can get the practice and experience necessary to understand the physical phenomena and mathematical techniques presented here. Solutions to specific problems will be discussed during lectures, as appropriate.

The material discussed in lectures will follow the textbook closely and it is very useful, as in any course, for the student to prepare a concise summary of the material presented in lectures. Don’t just memorise all the equations (a formula sheet will be attached to the exam paper) - concentrate on the physics.

Assessment

2 hour written examination 60%
Two assignments 10% each
Mid session test 20%

For rules regarding academic honesty, etc, see the School website here.

Resources:

Textbook

David J. Griffiths, Introduction to Electrodynamics, 3rd edition (Prentice Hall). (You might find copies of the 2nd edition available; this is also a suitable textbook for this course).

It is always a good idea to consult more than one book when studying a course as you may find a book whose particular style is more suited to yours than the prescribed textbook. You will also benefit from studying different approaches to the course material and related problems; here is a short list of books which might be useful:

P. Lorrain and D.R. Corson, Electromagnetic fields and waves.
J.D. Jackson, Classical Electrodynamics (Wiley).
H.M. Schey, Div, Grad, Curl and all that (Norton) – vector analysis.
E.M. Purcell, Electricity and Magnetism (McGraw-Hill)
B. and B.I. Bleaney, Electricity and Magnetism (Oxford) – an old classic.

Information on student support services may be found on the School here.

Detailed Syllabus

 TOPIC TEXT REFERENCE Vectors Scalars, vectors and their products. Div, Grad and Curl. Line, surface and volume integrals. Gradient, Divergence and Stokes’ theorems. Curvilinear coordinates, Dirac delta function, vector fields. 1.1 - 1.6 The Electrostatic Field Coulomb’s law. Electric field (E). Charge distributions, Gauss’ law. Div and Curl of E. Electric potential. Poisson’s equation. Energy stored in a charge distribution. Conductors. 2.1 – 2.5 Special Techniques Multipole expansion 3.4 Dielectrics Polarization (P), dipoles, bound charge density. Electric displacement (D). Electric susceptibility and permittivity. Boundary conditions. Dielectric materials in an E field. 4.1 – 4.4 Current electricity Electric current, current density, continuity equation, Drude's model of a conductor, Ohm's Law, Kirchhoff's Laws 7.1.1 and 8.1.1 Magnetostatics Lorentz force law. The magnetic field (H) and magnetic induction (B). Biot-Savart law. Ampère’s law. Div and Curl of B. Maxwell’s equations for static fields. Magnetic vector potential. 5.1 – 5.4 Magnetization Magnetic torque and force. Hall effect. Magnetic dipoles and Magnetization (M). Bound currents. Magnetic field of a magnetized object. Magnetic materials (diamagnetism, paramagnetism, ferromagnetism, hysteresis, domains, superconductors). 6.1 – 6.4 Magnetic Induction EMF. Faraday’s law. Lenz’s law. Mutual Inductance, Self Inducatance. 7.1 – 7.2 Maxwell’s Equations Ampère’s law revised. Maxwell’s equations inside matter. Electromagnetic waves and the Poynting vector. 7.3; 8.1

Thermal Physics

• Level 2 Physics Course
• UOC 3, HPW 2
• Offered every year, Session 2

Lecturer: Professor Paul Curmi
Lecture Times: Monday 9-10 (Physics Lecture Theatre, OMB), Thursday 2-3   (Rm 112, Old Main Building)
Consultation times: Monday 10-11,  Thursday 3-4 (Rm 130, Old Main Building)

Brief Syllabus: Laws of thermodynamics, kinetic theory, microscopic processes, entropy, solid-state defects, Helmholtz and Gibbs' functions, Maxwell's relations, phase diagrams, chemical and electrochemical potentials.

Prerequisites: PHYS1002 or PHYS1022 or PHYS1111 or PHYS1221 or PHYS1231 or PHYS1241, MATH1021 or MATH1131 or MATH1141 or MATH1031; Excluded: PHYS2011.

Course Goals: Thermodynamics deals with energy, heat and work, and is essential to understanding the principles behind engines, refrigerators, and even life itself. This course aims to provide students with an introduction to thermodynamics. The course begins by considering kinetic theory and exploring how the various thermodynamic quantities, such as pressure, internal energy and temperature, and behaviours such as diffusion emerge from a simple consideration of a gas obeying basic classical physics. We then consider work and heat, looking at topics such as adiabatic processes, phase transitions, Joule-Thompson expansion and heat transfer. Based on these concepts, we will discuss the 1st law of thermodynamics, heat engines and their efficiency, and then Carnot’s work to derive the maximum possibly efficiency of heat engines. We will then look at how this leads to the concept of entropy and the 2nd law of thermodynamics, arguably one of the most debated laws of physics. To conclude, we will look at some of the ramifications of the 2nd law including concepts such as reversibility and the arrow of time, Maxwell’s demon and finally, Boltzmann’s entropy, which then leads directly into the PHYS3020 Statistical Physics course.

Learning Objectives
Students should develop the ability to:

• Explain the key concepts of thermal physics and their consequences, in particular kinetic theory and the 1st and 2nd laws of thermodynamics.
• Apply the key concepts of thermal physics to a variety of thermodynamic systems such as engines, refrigerators and the atmosphere.

Why Thermal Physics is important?
A knowledge of thermal physics –the physics of energy, heat, work and entropy – is essential to understanding the operating principles of a variety of useful technologies ranging from car engines and power stations to fridges and cooling elements. The concepts of entropy and reversibility are important to understanding chemical processes, in particular, which ones occur spontaneously and which ones don’t, how fast reactions proceed, and whether they consume or produce energy. Thermal physics is also important to the working of many biological systems such as molecular motors and cells, and even spreads as far as information technology, where the entropy of information is a key concept.
Thermal physics is also central to our understanding of physics itself. Quantum mechanics evolved from the failure of classical physics to explain the specific heat of gases and the spectra of a hot object (blackbody radiation). The 2nd law of thermodynamics is of great significance to understanding why most processes only go one way (e.g., why humpty dumpty can spontaneously fall off a wall and break, but doesn’t spontaneously reassemble and appear back on the wall), thereby providing us with the so-called ‘arrow of time’.

This course provides an important foundation for PHYS3020 Statistical Physics and PHYS3410 Biophysics 2.

How to Succeed – Strategies for Learning
Thermal physics can be a difficult subject because it has developed from studies in a wide range of fields including physics, chemistry, biology and many branches of engineering, mechanical and chemical in particular. These various influences have lead to a large number of slightly differing variables, definitions, and viewpoints that have evolved to ‘tune’ thermodynamics to specific applications. The key to this subject is to look for the central physical concepts, and how to apply them, rather than focus on the specific mathematical details, which tend to differ from one author’s field/viewpoint to another. This is particularly important to remember as you read amongst the various resources for the course.

Some further tips for successful learning include:

1. Do not hesitate to ask questions during lectures. There is no such thing as a silly or wrong question. While your questions are helpful for you, they are also helpful for other students (you’ll often find other students in your class who have the same question but are too shy to ask), and they are helpful for the lecturer because they allow him/her to gauge whether they are getting the material across effectively or not.
2. Considerable time should be spent ‘thinking’ about the subject, this may seem kind of obvious, but it goes much deeper than simply reviewing notes, reading resources or trying to memorize the various equations. You should try to spend some time after each lecture actively thinking about what you have learned. An ideal way to do this is to ask yourself questions such as “How does this fit into my existing knowledge of physics and my experience of how the world works?”, “Does this make sense?”, “How would I explain this to someone else?”, “Can I find some logical inconsistency or conflict that emerges from how I currently understand what I’ve learned?” (in which case you should aim to figure out and resolve this conflict), “What parts of what I’ve learned do I not fully understand?”, etc. In doing this, you may want to review your notes or books, but you should not see this as normal note-review or study (i.e. you shouldn’t do this by sitting there staring at your notes), to give an analogy, it should be more like being a Zen monk contemplating the sound of one hand clapping.
3. Students should also try to do as many problems as possible – just doing the assignments is usually not enough. A variety of suggested tutorial problems will be given during the course, and some will be discussed during lectures. However, as individual students, you can help yourself by seeking out problems that make you confront aspects of the course that you least understand, just doing the easy questions will not help you very much. Forming small study groups to discuss the course material and work together on tutorial problems is highly encouraged, this approach will help you learn better by teaching each other (n.b. care should be taken that this doesn’t cross over to plagiarism for assignments – make sure you know the rules). Plagiarism guidelines.
4. You should work throughout the course on compiling your own concise set of revision notes. A good way to do this is to write a brief review after each lecture. You should also add lessons learned in doing tutorial questions and from thinking about the lectures to these revision notes.

Finally, remember, don’t focus on just memorising all the equations (a formula sheet will be attached to the exam paper) – concentrate on the understanding physics instead, and the mathematical aspects should then follow naturally.

Assessment

• Two assignments worth 10% each (20% total)
• 1 hour midsession exam 20%
• 2 hour written final examination 60%

Resources

• S.J. Blundell and K.M. Blundell, "Concepts in thermal physics" (Oxford)
• D.V. Schroeder, “An Introduction to Thermal Physics” (Addison-Wesley) – A good, well-explained book on some key topics in thermodynamics and statistical mechanics.
• Sears and Salinger, “Thermodynamics, Kinetic Theory and Statistical Thermodynamics” – Considered a standard text by many, but it is probably the most technical of the books listed here and can sometimes be difficult to follow. A good reference and worthwhile reading for more mathematically inclined students.
(n.b., Please consider these books to be somewhat optional. This course will follow none of the listed books very closely, and none of the books will cover everything in the course in a single volume).

It is always a good idea to consult more than one book when studying a course as you may find a book whose particular style is more suited to yours than the prescribed textbook. You will also benefit from studying different approaches to the course material and related problems; here is a short list of books that may be useful:

Adkins, “An Introduction to Thermal Physics” (Cambridge Univ. Press) – A short but thorough text on thermodynamics with many good problems.

Van Ness, “Understanding Thermodynamics” (McGraw Hill) – A short, old but very well explained book that contains some excellent insight into some of the more difficult concepts of thermodynamics.

Feynman, Leighton and Sands, “The Feynman Lectures on Physics” Vol. 1 (Addison Wesley) – This is an excellent text that contains many insightful explanations of a wide range of undergraduate physics topics, not just thermodynamics.

Zemansky and Dittman, “Heat and Thermodynamics” (McGraw-Hill) – A far more technical thermodynamics text but very comprehensive.

Sonntag, Borgnakke and Van Wylen, “Fundamentals of Thermodynamics” 6th Ed (Wiley) – A very good general textbook with a bit more mathematics than the Feynman lectures or Van Ness, and a lot of very good problems and worked examples.

Information on student support services may be found on the School website here.