PX2131: The Physics of Fields and Flows

School Cardiff School of Physics & Astronomy
Department Code PHYSX
Module Code PX2131
External Subject Code 100425
Number of Credits 20
Level L5
Language of Delivery English
Module Leader Dr Egor Muljarov
Semester Autumn Semester
Academic Year 2014/5

Outline Description of Module

  • To provide greater understanding of Maxwell’s equations, how they unify electric and magnetic forces, and how they predict the existence of electromagnetic waves.
  • To understand the basic physics of fluids.
  • To demonstrate how electromagnetic fields, fluid flows, diffusion, and similar phenomena in physics can be described using vector calculus.
  • To learn and practice standard mathematical techniques to solve physical problems.

On completion of the module a student should be able to

  • Apply vector calculus to scalar and vector fields, including multi-dimensional integrals.
  • Show familiarity with common scalar and vector fields of physics and their associated partial differential equations.
  • Set up and solve various second-order partial differential equations for physical systems using separation of variables, power series, and Fourier transforms.
  • Describe the basic physics of fluid flow.
  • Describe the formation and propagation of an electromagnetic wave in vacuum.
  • Apply Maxwell’s equations to solve problems involving electric and magnetic fields with boundary conditions in simple geometries, and involving particle motion.

How the module will be delivered

Lectures 33 x 1 hr, examples classes 11 x 1hr, marked exercises.

Skills that will be practised and developed

Mathematics.  Problem solving.  Investigative skills.  Analytical skills.

How the module will be assessed

Examination 80%.  Coursework 20%.  [Examination duration: 3 hours].

Assessment Breakdown

Type % Title Duration(hrs)
Exam - Autumn Semester 80 The Physics Of Fields And Flows 3
Written Assessment 20 The Physics Of Fields And Flows N/A

Syllabus content

Vector calculus:  Review of vectors and partial derivatives. Coordinate systems and symmetry. Directional derivatives, gradient; physical interpretation.  Divergence, curl, Laplacian; examples in physics.  Line, surface, and volume integrals. Divergence theorem, Stokes’s theorem, Green’s theorem, Gauss’s law.

Partial differential equations of physics:  Continuity and diffusion equation.  Laplace, Poisson and wave equations. Separation of variables and power-series solutions.

Electrostatics:  Gauss’ law in integral and differential form. Applications to electrostatics and gravity.

Moving charges:  Equation of continuity, Ohm’s Law in vector form.

Fluid Mechanics:  Basic principles.  Viscosity, inviscid fluids, irrotational motion.  Steady flow. The Navier-Stokes equation and analogy to electromagnetism.  Dynamical similarity and  turbulence.  Diffusion, heat flow, stretched membranes.

Magnetic fields:  Magnetic forces and fields, Biot-Savart law.  Ampere’s law in integral and differential form.  Magnetic dipoles, magnetisation of matter.

Electromagnetic induction:  Induced currents and Faraday’s Law in integral and differential form.  Induced electric fields, inductance and magnetic energy. Fluid vorticity as an analogy to magnetism.

Maxwell’s equations: Displacement current, electromagnetic wave equation. Energy and momentum in EM waves; Poynting vector.  Solving Maxwell’s equations in simple physical situations with boundary conditions. Generating EM radiation; relationship to relativity and quantum mechanics.

Fourier series and transforms: Fourier series solutions for periodic systems. Fourier theorem, convolutions, delta functions, Parseval’s theorem.  Solving PDEs by Fourier methods.  Fourier transforms in time and frequency and in position and momentum, relation to the uncertainty principle.  Applications of Fourier series and transforms to physics.

Essential Reading and Resource List

Please see Background Reading List for an indicative list.

Background Reading and Resource List

Principles of Physics (Extended Version), Halliday, Resnick and Walker (Wiley).

Mathematical Methods for Physicists, G.B. Arfken, H.Y. Weber, 5th ed (2001)

Mathematical Methods for Physics and Engineering, 2nd Edition, K F Riley, M P Hobson and S J Bence (CUP).

Theory and Problems of Vector Analysis, M R Spiegel (Schaum Publishing).

Electromagnetism, I S Grant and W R Phillips (Wiley).

Electricity and Magnetism, W J Duffin (McGraw Hill).

Elementary Fluid Dynamics, Acheson (Oxford University Press)

Physical Fluid Dynamics, Tritton (Oxford University Press)

Lectures on Physics, Feynman


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