2000-level (second year) modules
This year the following modules are available in the School of Physics and Astronomy:
| Module | Coordinator | Room | |
| PH2011 Physics 2A | Dr Lucy Hadfield | 304 | ljh11 |
| PH2012 Physics 2B | Dr Juan Varela | 342 | jv32 |
| AS2001 Astronomy and Astrophysics 2 | Dr Martin Dominik | 316A | md35 |
| AS2101 Astrophysics 2 | Dr Martin Dominik | 316A | md35 |
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PH2011 Physics 2A and PH2012 Physics 2B are both required for any of the degrees taught within the School. Students taking these modules should acquire:
- The ability to reason through scientific concepts, to relate different concepts to one another and to solve qualitative and quantitative problems in the areas covered in the courses with a toolkit of problem-solving techniques.
- Laboratory skills, including the planning of experimental investigations, the use of modern test equipment, and the construction of electronic circuits.
- An appreciation of the value of learning of physics as a transformative experience in terms of motivated use (using physics beyond the course e.g. in everyday situations) and expansion of perception (seeing the world through the lens of physics).
In addition, students who have taken Physics 2A should be able to:
- Apply fundamental laws of mechanics, using vectors in?Cartesian and polar?coordinate systems to solve problems.
- Calculate properties of rigid bodies including centre of mass and moment of inertia, and apply these in problems of rotational motion.
- Analyse and model oscillatory systems, derive and solve equations of motion, including for?undamped and simple cases of damped, forced and coupled oscillations.
- Explain and apply the postulates of special relativity, including Lorentz transformations, spacetime diagrams, velocity addition, time dilation, and length contraction.
- State and apply the laws of thermodynamics, distinguish reversible/irreversible processes, and solve problems involving heat, work, and energy transfer.
- Solve problems involving thermal expansion, heat capacity and transport.
- Use the ideal gas law, equipartition theorem, and kinetic theory to analyse gas behaviour,?and relate the thermodynamic and statistical definitions of entropy in terms of macrostates, microstates, and multiplicity.
- Integrate prior physics knowledge into broader frameworks and confidently select appropriate methods for problem-solving.
In addition, students who have taken Physics 2B should be able to:
- Represent transverse and longitudinal waves and waves in one, two and three dimensions physically, mathematically and graphically and explain the connections between these representations.
- Explain similarities and differences between different types of mechanical waves, and between mechanical and electromagnetic waves.
- Use the concepts of wave interference, energy transport and the behaviour at boundaries to calculate wave properties.
- Compare and contrast classical and quantum descriptions of light and matter, give examples where one description or the other is valid, and summarise experimental evidence that support the use of either description.
- Solve the Schrödinger equation for simple 1-D systems, and use these wave functions to calculate expectation values and measurement probabilities for observables such as energy, position and momentum.
- State Coulomb's Law and the Biot-Savart Law, Faraday's Law and Lenz's Law, the definitions of electric field, electric potential, capacitance, and inductance.
- Be able to model and solve a range of examples in electrostatics, magnetostatics, and electromagnetic induction as well as justify aspects of DC circuit theory and apply this to solving simple electrical circuit problems.
- Be able to justify Gauss' Law and Ampere's Law, and use these two laws on a range of electrostatic and magnetostatic examples.
- Qualitatively describe how relativity and electrostatics can be brought together to explain electromagnetism.
- State descriptions of paramagnetism, diamagnetism, and ferromagnetism.
- Appreciate how the concepts in the electricity and magnetism course may be applied to particle accelerators, fusion tokamaks, atom traps, optical tweezers, modern electronics, and electrical engineering.
- State concepts of pn-junctions, design circuits using AC circuit theory, build and investigate electronic circuits.
PH2011 Physics 2A (30 Credits)
Syllabus
Mechanics (18 lectures) Dr Lucy Hadfield
Dynamics of a single particle: Newton's laws of motion, inertial reference frames. Momentum, conservation of momentum in absence of external forces. Central force problems: velocity and acceleration of particles in plane polar coordinates. Work, energy and power. Conservative forces, relation between force and potential energy. Friction. Torque. Conservation of angular momentum.
Gravitation: Newton's gravitational force law, potential energy for point source. Kepler's laws for planetary motion.
Dynamics of a system of particles: Centre of mass. Internal and external forces. Translational equation of motion. Torque. Angular momentum and kinetic energy of a rotating system. Rotational equation of motion. Rigid bodies. Moments of inertia. Parallel and perpendicular axis theorems.Oscillations in Physics (7 lectures) Dr Pavlos Manousiadis
Introduction to oscillations. Mathematical description of oscillations. Circular motion and simple harmonic motion (SHM). Energy in SHM. Examples of SHM: spring-mass systems, pendulums, other oscillating systems. Damped oscillations. Types of damping, Q factor. Forced oscillations. Resonance. Examples of resonant systems. Coupled oscillations and normal modes.Thermal Physics (11 lectures) Dr Helen Cammack
Temperature, pressure and translational kinetic energy. The thermodynamic temperature scale. The notion of thermal equilibrium. Degrees of freedom. Reversible and irreversible processes. The zeroth law. Ideal gases. Mean Free Path and Maxwell Speed Distribution. Types of thermometer. Thermal expansion (linear, area and volume), interatomic forces and Lennard Jones Potential, crystal structure, elasticity. Equations of state.
Work, heat and the First law of thermodynamics. Heat capacity and phonons. Heat transport, conduction, convection and radiation. Phase changes and latent heat. Adiabatic processes, free expansion of a gas.
Entropy and the second law of thermodynamics. Direction of time. Heat engines, heat pumps, refrigerators, efficiency. Entropy from a statistical viewpoint.Special Relativity (8 lectures) Prof Steve Lee
Inertial frames. The postulate of special relativity. Clock synchronisation and the relativity of simultaneity. Length contraction, time dilation, and the Lorentz transformations. Proper time, invariants, and space-time diagrams. The twin paradox. Transformation of velocity. Relativistic momentum and energy.Mathematics Revision Dr Irina Leonhardt
Trigonometry, dimensional analysis, complex numbers, vectors, functions, graphs, differentiation and integration, differential equations, and Taylor series.Laboratory work Dr Cameron Rae
Direct entry to second year students initially follow a focused laboratory skills development programme that includes: precision and accuracy, error propagation, data analysis and graphical representation, experimental technique and laboratory notebook keeping. All students explore aspects of physics in a practical manner, broaden competence in various forms of experimental and diagnostic instrumentation and will develop data handling and interpretation skills.
PH2012 Physics 2B (30 Credits)
Syllabus
Electricity and Magnetism (21 lectures) Prof Graham Smith
Basic electrostatics: Coulomb's Law, electric field E, electric field from discrete and continuous distributions. Electric potential V, relation between E and V, examples.
DC circuit theory: Electric current and drift velocity of charge-carriers. Electric potential and Kirchoff's laws. Input and output impedance of circuits, equivalent circuits. Gauss' law and capacitors: Electric flux, Gauss' law, use to solve fields around high-symmetry charge distributions, electrostatic shielding, capacitors, role of dielectric materials in capacitors.
Magnetic effects of currents: Forces on charges moving in a magnetic field, Biot-Savart law and application to long straight wire and coil, force between two current carrying wires and the definition of the units of current, Ampere's law and examples.
Electromagnetic Induction: Faraday's law, Lenz's law, induced electric fields, self and mutual inductance.
Electricity and magnetism unified via relativity (qualitative). Magnetic materials.Classical Waves (12 lectures) Dr Pavlos Manousiadis
Waves on stretched strings, the wave equation, wave velocity, transmission of energy, sound waves and light waves, the Doppler effect in sound, superposition of waves, standing waves, Fourier series, interference, Bragg scattering, beats, phase, dispersion, phase and group velocity, reflection and transmission of waves at an interface or boundary, the e-m spectrum, polarisation.Quantum Physics (18 lectures) Dr Helen Cammack
Photoelectric effect and photodetectors. Optical devices and single-photon experiments. Probabilistic measurements, expectation values. Entanglement and the physical interpretation of quantum mechanics. Wave functions and the Schrödinger equation in one dimension. Operators and eigenvalues. The uncertainty principle. Infinite- and finite-depth square well potential. Quantum tunnelling.Laboratory work Dr Cameron Rae
All students explore aspects of physics in a practical manner, broaden competence in various forms of experimental and diagnostic instrumentation and develop analysis skills. Explore the science behind passive, pn-junction and op-amp devices and their incorporation in circuit designs while developing practical skills in electronics and develop computational skills through work with microcontrollers. Develop scientific writing skills.
Recommended Books for PH2011 and PH2012
The core Physics text is: Halliday and Resnick's Fundamentals of Physics, 12th Edition, Extended Edition, by J Walker.
Hard copies and e-book access is available through the University library.Additional texts (available in the library) are:
- Physics for Scientists and Engineers: A Strategic Approach with Modern Physics by R D Knight, Pearson, 2014 e-book.
- Understanding Physics, 1st Edition by K Cummings, PW Laws, E F Redish, P J Cooney, Wiley, 2004.
- Sears and Zemansky's University Physics by H D Young and R A Freedman (12th edition, Addison-Wesley 2008 or other edition).
- Physics for Scientists and Engineers by P A Tipler and G P Mosca (6th edition, Freeman 2008).
These all provide wide coverage of the lecture courses, examples of how physics is applied in realistic situations, and many problems together with hints for solving them. However, neither these nor Halliday, Resnick and Walker go as deep into the topics as do some of the courses within our modules. We recommend the following additional books, but do not expect students to purchase them. There are multiple copies in the library.
Physics 2A
Mechanics – An Introduction to Mechanics, D Kleppner and R Kolenkow, CUP.
Special Relativity – Basic Concepts in Relativity and Early Quantum Theory, R Resnick and D Halliday, (Macmillan, 1992); Nonclassical Physics: Beyond Newton's View, Randy Harris (Addison Wesley Longman, CA, 1999); Relativity Visualised, Lewis Carroll Epstein (Insight Press, CA, 1985).
Thermal Physics – An Introduction to Thermal Physics, D V Schroeder (Pearson, 2004)Physics 2B
Quantum Mechanics – Basic Concepts in Relativity and Early Quantum Theory, R Resnick and D Halliday, (Macmillan, 1992); Quantum Mechanics: A Paradigms Approach, D H McIntyre et al (Oregon State University, 2012); Quantum Mechanics, A.I.M. Rae (fifth edition, 2007, Chapman and Hall) - also available as an e-book; The meaning of quantum theory: a guide for students of chemistry and physics, J E Baggott (2004).Physics 2A and 2B
Useful reading for the labs is Measurements and their Uncertainties: A Practical Guide to Modern Error Analysis by I G Hughes and T P A Hase, Oxford (2010); available as an e-book via the library. -
AS2001 Astronomy and Astrophysics 2
The AS2001 module is designed to complement and extend the knowledge gained in the first level module in Astronomy and Astrophysics, and to prepare the way for the more advanced topics encountered in a study of the subject at honours level. Lectures are based on the principles of physics together with mathematical techniques acquired earlier. It is intended that students should gain:
- a strengthening of the skills learned in AS1001/AS1101 and 1000-level physics and mathematics modules,
- a deeper understanding of the structure and evolution of stars, the design of telescopes and instruments for astronomical observations over the entire electromagnetic spectrum, the dynamical interactions of stars in the Galaxy, and exoplanetary science.
- a greater ability to analyse astronomical data, using the Python language and other computer packages.
AS2101 Astrophysics 2
This is as AS2001, but without the observational techniques lectures and the labs. This is normally taken only by accelerated entry students who are aiming for an astronomy degree. It can also be taken by a continuing student who is more interested in theoretical aspects of astronomy and who, having already taken AS1001, is keen to take an additional 2000-level 15-credit astronomy module in S2.
AS2001 Astronomy and Astrophysics 2 (30 credits)
Syllabus
Stellar Structure and Evolution (11 lectures) Prof Kenny Wood
The determination and distribution of stellar masses, radii and luminosities; the Hertzsprung-Russell diagram, mass-luminosity law and Vogt-Russell theorem. Sources of stellar energy, nucleosynthesis of hydrogen, helium and carbon. Star formation and evolution; the ages of star clusters; supernova events and the synthesis of heavy elements. Final states – white dwarfs, neutron stars (pulsars) and black holes. The evolution of binary stars – Roche lobe overflow, accretion discs and novae.Exoplanetary Science (11 lectures) Dr Rowan Smith
Building on earlier work in the module, this course looks at the formation of planets in circumstellar accretion discs and the implication for internal structures of gas-giant and terrestrial-like planets. Theoretical models and observational techniques are discussed.Galactic Astronomy (10 lectures) Dr Anne-Marie Weijmans
This course will investigate the distribution and motions of stars, gas and dust within our own galaxy in order to determine its dimensions and overall properties. Properties of other galaxies will be discussed. Topics include: galactic coordinate systems; the solar motion and distribution of stellar velocities; differential galactic rotation, the rotation velocity at the Sun and the distance to the Galactic Centre; rotation curves of the Milky Way and other galaxies; galaxy masses and "dark" matter.Observational Techniques (11 lectures) Dr Alexander Scholz
This course provides an introduction to topics relevant to planning and interpreting astronomical observations, including: modern telescopes and telescope design; instruments and detectors for multiwavelength astronomy, including CCDs; atmospheric seeing and extinction; active and adaptive optics; photometry; spectroscopy; aperture synthesis imaging; essential coordinate systems.Laboratory Work
AS2101 Astrophysics 2 (15 credits)
As AS2001, but without the laboratory work and the Observational Techniques lectures.
Recommended books for AS2001 and AS2101:
Recommended books for Astronomy and Astrophysics 2 are:
Astronomy, a Physical Perspective by M L Kutner (available as an e-book) and
An Introduction to Modern Astrophysics (second edition) by B W Carroll and D A Ostlie.Additional reading accessible from e-books includes:
For the exoplanets course: Methods of Detecting Exoplanets by V Bozza, L Mancini, and A Sozzetti (eds), Springer (2016)
For the observational techniques course: To Measure the Sky: An introduction to Observational Astronomy, by F R Chromey, CUP.
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For entry to either of the second-level modules in Physics, it is normally necessary to have one of the following sets of qualifications:
- Passes in the first level modules: PH1011, PH1012 and MT1002.
- Passes in Advanced Higher/A-Level (or equivalent) Physics and Mathematics, both normally at grade A.
For entry to the 2000-level modules in Astrophysics, the entry requirements are as for 2000-level physics, plus the requirement to have passed one of the 1000-level astrophysics modules AS1001 or AS1111.
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Tutorials and Workshops
Workshops and tutorials allow you to develop your problem-solving skills working with the lecture content. Some workshops and tutorials are run with a primary focus of developing specified relevant academic skills.
For Physics 2A/2B and AS2001 each student will typically attend one small group tutorial per week. These sessions are hosted by a designated tutor and allow students to work through tutorial problems and ask specific questions about the lecture material.
Students enrolled on Physics 2A and 2B will attend one workshop (problem solving class) each week.
Practical Work
For the Physics 2A and 2B modules students attend one afternoon session of 2½ hours (15:00 – 17:30) per week of practical work.
The aims of the second level practical work in physics are to build on previously acquired experimental skills while at the same time provide the opportunity for students to:
- work toward desired experimental outcomes but with greater freedom to explore the relevant topic;
- broaden competences in the use of various forms of experimental and diagnostic instrumentation;
- explore subject matter covered in lectures and, particularly in electronics, new material;
- develop skills in scientific writing.
Prior to the start of a practical you should familiarise yourself with the upcoming work and complete any pre-lab questions. Between lab afternoons you should complete any assignments, keep your data analysis and interpretation up-to-date, and prepare for upcoming work. We expect students to typically spend 7.5 hours per week on laboratory work.
At the start of 1st Semester (Physics 2A), the programme is slightly different for returning students and direct entry students, as direct entry students cover some of the lab skills development that has already been explored by our returning students, to gain a similar skill set and understanding of our expectations. In 2nd Semester (Physics 2B) all students will attempt the same programme of work. There is a choice of a physics experiments, followed by work in electronics and lab-related Python programming, and a scientific writing exercise. The module also includes an opportunity to see some of our research laboratories and relate the skills being developed in the teaching laboratory to those practiced by the experimental physics researcher.
For AS2001 Astronomy and Astrophysics 2 students also attend one astronomy laboratory sessions (15:00 – 17:.30) per week.
The aims of practical work in Astronomy and Astrophysics 2 are:
- to develop confidence in working with and interpreting astronomical data,
- to build programming skills and apply them to the analysis of astronomical data.
In all second level modules where practical assignments are to be handed in for marking according to a specified timetable, penalties will be applied for lateness up to and including the loss of all marks in particularly serious cases. Please see later in this handbook under Late penalties.
Mathematics revision
A good grasp of mathematics and its application to physics is essential for all students of physics and astrophysics.
During both the Physics 2A and Physics 2B modules, students will have the opportunity to complete online maths revision quizzes that encourage revision and practice of mathematical techniques which they have learned previously. These quizzes are supported by pre-recorded revision lectures.
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A class medal is awarded in PH2011, PH2012, and AS2001/2101 to the student who gains the highest grade.
The J F Allen Prize is awarded to the most outstanding student (the highest mean module grade) in PH2011 and PH2012 taken together.