Department: PhysicsModule co-ordinator: Prof. Roddy VannCredit value: 15 creditsCredit level: IAcademic year of delivery: 2020-21

## Pre-requisite modules

- None

## Co-requisite modules

- None

## Prohibited combinations

Occurrence | Teaching cycle |
---|---|

A | Spring Term 2020-21 to Summer Term 2020-21 |

The central aim of this module is to understand how Maxwell unified electricity, magnetism and optics into electromagnetic theory. Knowledge of the basic phenomena of electromagnetism, and a good understanding of the mathematics of vector fields, are essential in achieving the central aim. Maxwell’s four equations describe all of electromagnetism, including the propagation of electromagnetic waves. The subsidiary aim of the course is to provide an account of the electrical and magnetic properties of materials.

- Write down Maxwell’s equations in differential form, defining all the variables
- Show a good grasp of the meaning of the div and curl of a vector field
- Understand that the Maxwell equations can be split into two twos for time-independent fields, two for electrostatics, two for magnetostatics
- Use the material in Electromagnetism I (lectures 1-9) to solve problems in electrostatics
- Derive Maxwell’s first equation from Gauss’ Flux Law of Electrostatics, using Gauss’ theorem
- Show a good grasp of the meaning of the gradient of a scalar field, and apply it to obtain electric fields from electric potentials
- Recognise Poisson’s equation and Laplace’s equation of electrostatics
- Use the material in EM I (lectures 10-12) to solve problems in magnetostatics, and calculate the motion of charged particles in magnetic fields
- Define the Ampere
- Relate the differential to the integral form of Ampere’s Law, using Stokes’ theorem
- Use Ampere’s Law to calculate the magnetic field of a current-carrying straight wire and a solenoid
- Define the vector potential
- Use the vector potential to calculate the magnetic field of a current-carrying straight wire
- Use the Biot-Savart Law to calculate the magnetic field on the axis of a current-carrying loop
- Define electro-motive force (emf)
- Write down Faraday’s discovery of the three ways in which an emf can be induced in a wire
- Relate the differential to the integral form of Faraday’s Law, using Stokes’ theorem
- Apply the integral form of Faraday’s Law to calculate the emf induced in a moving circuit, and an AC generator
- Calculate mutual inductance, and apply this to transformers
- Calculate self-inductance, and apply this to the properties of inductors in AC circuits
- Understand that Ampere’s Law contravenes the principle of conservation of electric charge
- Express charge conservation in differential and integral form, and derive the relationship between them, using Gauss’ theorem
- Understand the new term in the Ampere-Maxwell equation
- Show that Maxwell’s equations in free space lead to a wave equation
- Derive the relationship c
^{2}=1/µ_{0}e_{0 }from the electromagnetic wave equation - Describe all the main features of electromagnetic waves, including energy flow
- Define the Poynting vector
- Use expressions for the energy density of electric and magnetic fields and the Poynting vector in various simple circumstances
- Calculate the electrostatic potential and field of a dipole
- Understand the nature of multipole expansions of the electrostatic potential
- Calculate the energy of a dipole in an electric field, and apply understanding of dipoles to the behaviour of dielectric materials in electric fields
- Calculate the capacitance of devices with dielectric materials between the charged conductors
- Define surface and bulk polarization charges, and the electric polarization vector
- Recognise the displacement field
- Calculate electrostatic energy for discrete and continuous charge distributions
- Calculate the energy density of an electric field, and apply this to the energy stored in a capacitor
- Understand the nature of the problem of the infinite energy of a point charge in classical electrodynamics
- Calculate the force on a current-carrying wire in a magnetic field
- Analyse the forces on a current-carrying loop, to prove that it behaves like a magnetic dipole
- Calculate the field of a current-carrying loop, using the vector potential
- Calculate the energy of a magnetic dipole in a magnetic field
- Show an understanding of the properties of magnetic materials in magnetic fields, including an ability to explain qualitatively the behaviour of diamagnetic, paramagnetic and ferromagnetic materials
- Define surface and bulk current densities in magnetic materials, and the magnetization vector
- Define magnetic susceptibility and relative permittivity
- Recognise typical magnetisation and hysteresis curves for soft iron

- Maxwell’s equations
- Review of electrostatics covered in Electromagnetism I
- Poisson’s equation and Laplace’s equation
- Differential and integral forms of Ampere’s Law
- Magnetic fields of wires and solenoids
- Vector potential
- Biot-Savart law
- Induced currents; emfs and generators
- Differential and integral forms of Faraday’s Law
- Induction, generators and transformers
- Mutual inductance and self inductance
- Charge conservation
- Ampere-Maxwell equation
- Electromagnetic waves; the speed of light
- Poynting vector
- Energy density of electric and magnetic fields
- Electric dipoles
- Properties of dielectric materials
- Capacitance of devices with dielectrics
- Polarization charges, polarization vector and displacement field
- Electrostatic energy
- Magnetic energy
- Magnetic dipoles; analysis of forces on a current-carrying loop
- Field of a current-carrying loop; energy of a magnetic dipole in a magnetic field
- Magnetic materials; diamagnetism, paramagnetism and ferromagnetism
- Surface and volume current densities, magnetization vector and magnetic intensity
- Magnetic susceptibility and relative permeability
- Magnetisation and hysteresis curves for soft iron

Students taking this module should have taken PHY00020C or PHY00035I.

Task | Length | % of module mark |
---|---|---|

Essay/courseworkElectromagnetism II Assignment |
N/A | 20 |

Online ExamElectromagnetism II |
N/A | 80 |

None

Task | Length | % of module mark |
---|---|---|

Essay/courseworkElectromagnetism II Assignment |
N/A | 20 |

Online ExamElectromagnetism II |
N/A | 80 |

Our policy on how you receive feedback for formative and summative purposes is contained in our Department Handbook.

Feynman: *Lectures on Physics volume 2* (Addison-Wesley) ****

Griffiths: *Introduction to Electrodynamics* (Prentice-Hall) ***

Grant & Philips: *Electromagnetism* (Wiley) ***

Fleisch: *A student’s guide to Maxwell’s equations* (Cambridge University Press) ***

Hecht: *Optics* (Addison-Wesley) ****

Smith & King: Optics and Photonics (Wiley) ***

The following chapters from the Feynman lectures (vol 2) are particularly useful:

- Ch 1 Electromagnetism
- Ch 3 Vector Integral Calculus
- Ch 8 Electrostatic Energy
- Ch 10 Dielectrics
- Ch 13 Magnetostatics
- Ch 14 The Magnetic Field in Various Circumstances
- Ch 16 Induced Currents
- Ch 17 The Laws of Induction
- Ch 18 The Maxwell Equations
- Ch 20 Solutions of Maxwell’s Equations in Free Space
- Ch 27 Field Energy and Field Momentum
- Ch 33 Reflection from Surfaces
- Ch 34 The Magnetism of Matter
- Ch 36 Ferromagnetism