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## PH20014: Electromagnetism 1

Owning Department/School: Department of Physics
Credits: 6
Level: Intermediate (FHEQ level 5)
Period: Semester 2
Assessment: EX 100%
Supplementary Assessment: PH20014 - Mandatory Extra Work (where allowed by programme regulations)
Requisites: Before taking this unit you must (take PH10005 or take PH10053) and (take PH10006 or take PH10051) and take PH20019
Description: Aims:
The aims of this unit are to develop a vectorial description of electric, magnetic and electromagnetic fields in infinite materials and at boundaries between materials, to derive some individual solutions and to make use of them in a few important applications. A further aim is to provide an introduction to the operation of lasers.

Learning Outcomes:
After taking this unit the student should be able to:
* derive and interpret Maxwell's equations and their solution in vacuum;
* list the distinguishing features of electromagnetic plane waves and write down a mathematical expression for a linearly or circularly polarised light wave;
* analyse in detail the propogation of vectorial plane waves in vacuum and in various materials;
* describe the origins of polarisation and magnetisation in materials;
* match electric and magnetic fields at boundaries between materials and explain the origins of Brewster's angle and total internal reflection;
* describe how lasting action is obtained and maintained and outline the main properties of laser light.

Skills:
Numeracy T/F A, Problem Solving T/F A.

Content:
Introduction to Maxwell's equations (7 hours): Derivation of integral and differential forms of Maxwell's equations and continuity equation. The wave equation in source-free vacuum. Plane wave solutions.
Electromagnetic plane waves (3 hours): 3D plane waves, vector nature of electromagnetic wavesl relationships between E, B and k. Impedance. Electromagnetic energy and the Poynting vector. Radiation pressure. Polarisation; Law of Malus, circular and elliptical polarisation. Birefringence, wave plates.
Maxwell's equations in infinite materials (6 hours): Concepts of linearity, isotropy and homogeneity. Characterisation of materials in terms of macroscopic parameters. Dipoles, susceptibility and polarisation / magnetisation. The modified wave equation; solution in conductors, dielectrics, lossy media and plasmas.
Boundaries between media (4 hours): The general electromagnetic boundary conditions. Plane waves at a planar boudary, general angle of incidence (Fresnel equations). Total internal reflection and evanescent waves. Coefficients of transmission and reflection. Brewster and critical angles.
Lasers (2 hours): Interaction between light and matter. The Einstein relations. Obtaining and maintaining lasing action. Cavity modes. The properties of laser light.
Programme availability:

#### PH20014 is Compulsory on the following programmes:

Department of Physics
• USPH-AFB01 : BSc (hons) Physics (Full-time) - Year 2
• USPH-AFB05 : BSc (hons) Physics with Computing (Full-time) - Year 2
• USPH-AKB06 : BSc (hons) Physics with Computing (with Placement) (Full-time with Thick Sandwich Placement) - Year 2
• USPH-AAB06 : BSc (hons) Physics with Computing with Year Abroad (Full-time with Study Year Abroad) - Year 2
• USPH-AKB02 : BSc (hons) Physics (with Placement) (Full-time with Thick Sandwich Placement) - Year 2
• USPH-AAB02 : BSc (hons) Physics with Year Abroad (Full-time with Study Year Abroad) - Year 2
• USPH-AFM02 : MPhys Physics (Full-time) - Year 2
• USPH-AFM04 : MPhys Physics with Research Placement (Full-time) - Year 2
• USPH-AAM03 : MPhys Physics with Year Abroad (Full-time with Study Year Abroad) - Year 2

#### PH20014 is Optional on the following programmes:

Programmes in Natural Sciences
• UXXX-AFB01 : BSc (hons) Natural Sciences (Full-time) - Year 2
• UXXX-AKB02 : BSc (hons) Natural Sciences with Industrial Placement (Full-time with Thick Sandwich Placement) - Year 2
• UXXX-AAB02 : BSc (hons) Natural Sciences with Study Year Abroad (Full-time with Study Year Abroad) - Year 2
Department of Mathematical Sciences
• USMA-AFB15 : BSc (hons) Mathematical Sciences (Full-time) - Year 3
• USMA-AKB16 : BSc (hons) Mathematical Sciences (Full-time with Thick Sandwich Placement) - Year 4
• USMA-AAB16 : BSc (hons) Mathematical Sciences with Study Year Abroad (Full-time with Study Year Abroad) - Year 4
• USMA-AFB13 : BSc (hons) Mathematics (Full-time) - Year 3
• USMA-AKB14 : BSc (hons) Mathematics (Full-time with Thick Sandwich Placement) - Year 4
• USMA-AAB14 : BSc (hons) Mathematics with Study Year Abroad (Full-time with Study Year Abroad) - Year 4
• USMA-AFM14 : MMath Mathematics (Full-time) - Year 3
Department of Physics
• USXX-AFB03 : BSc (hons) Mathematics and Physics (Full-time) - Year 2
• USXX-AKB04 : BSc (hons) Mathematics and Physics with Placement (Full-time with Thick Sandwich Placement) - Year 2
• USXX-AAB04 : BSc (hons) Mathematics and Physics with Study Year Abroad (Full-time with Study Year Abroad) - Year 2
• USPH-AFB09 : BSc Physics (Full-time) - Year 3
• USPH-AKB09 : BSc Physics (with Placement) (Full-time with Thick Sandwich Placement) - Year 4
• USXX-AFM01 : MSci (hons) Mathematics and Physics (Full-time) - Year 2

Notes:
* This unit catalogue is applicable for the 2013/4 academic year only. Students continuing their studies into 2014/15 and beyond should not assume that this unit will be available in future years in the format displayed here for 2013/14.
* Programmes and units are subject to change at any time, in accordance with normal University procedures.
* Availability of units will be subject to constraints such as staff availability, minimum and maximum group sizes, and timetabling factors as well as a student's ability to meet any pre-requisite rules.