## PH20014: Electromagnetism 1

[Page last updated: 20 April 2021]

Owning Department/School: Department of Physics
Credits: 6      [equivalent to 12 CATS credits]
Notional Study Hours: 120
Level: Intermediate (FHEQ level 5)
Period:
Semester 2
Assessment Summary: EX 100%
Supplementary Assessment:
Like-for-like reassessment (where allowed by programme regulations)
Requisites: Before or while taking this module you must ( take PH10005 OR take PH10053 ) AND ( take PH10006 OR take PH10051 ) AND ( take PH20107 OR take MA20223 )
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 (Year 2)
• USPH-AAB02 : BSc(Hons) Physics with Study year abroad (Year 2)
• USPH-AKB02 : BSc(Hons) Physics with Year long work placement (Year 2)
• USPH-AFB10 : BSc(Hons) Physics with Astrophysics (Year 2)
• USPH-AAB10 : BSc(Hons) Physics with Astrophysics with Study year abroad (Year 2)
• USPH-AKB10 : BSc(Hons) Physics with Astrophysics with Year long work placement (Year 2)
• USPH-AFM02 : MPhys(Hons) Physics (Year 2)
• USPH-AFM04 : MPhys(Hons) Physics with Research placement (Year 2)
• USPH-AAM03 : MPhys(Hons) Physics with Study year abroad (Year 2)
• USPH-AAM12 : MPhys(Hons) Physics with Study year abroad (Year 2)
• USPH-AKM03 : MPhys(Hons) Physics with Professional Placement (Year 2)
• USPH-AKM04 : MPhys(Hons) Physics with Professional and Research Placements (Year 2)
• USPH-AFM10 : MPhys(Hons) Physics with Astrophysics (Year 2)
• USPH-AFM11 : MPhys(Hons) Physics with Astrophysics with Research placement (Year 2)
• USPH-AAM10 : MPhys(Hons) Physics with Astrophysics with Study year abroad (Year 2)
• USPH-AAM14 : MPhys(Hons) Physics with Astrophysics with Study year abroad (Year 2)
• USPH-AKM10 : MPhys(Hons) Physics with Astrophysics with Professional Placement (Year 2)
• USPH-AKM11 : MPhys(Hons) Physics with Astrophysics with Professional and Research Placements (Year 2)
• USPH-AAM15 : MPhys(Hons) Physics with Astrophysics with Study year abroad and Research Placement (Year 2)
• USPH-AAM13 : MPhys(Hons) Physics with Study year abroad and Research Placement (Year 2)

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

Department of Physics
• USXX-AFB03 : BSc(Hons) Mathematics and Physics (Year 2)
• USXX-AAB04 : BSc(Hons) Mathematics and Physics with Study year abroad (Year 2)
• USXX-AKB04 : BSc(Hons) Mathematics and Physics with Year long work placement (Year 2)
• USXX-AFM01 : MSci(Hons) Mathematics and Physics (Year 2)
• USXX-AAM01 : MSci(Hons) Mathematics and Physics with Study year abroad (Year 2)
• USXX-AKM01 : MSci(Hons) Mathematics and Physics with Year long work placement (Year 2)

 Notes: This unit catalogue is applicable for the 2021/22 academic year only. Students continuing their studies into 2022/23 and beyond should not assume that this unit will be available in future years in the format displayed here for 2021/22. Programmes and units are subject to change 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.Find out more about these and other important University terms and conditions here.