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Electromagnetism & Relativity - PHY00030C

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  • Department: Physics
  • Credit value: 20 credits
  • Credit level: C
  • Academic year of delivery: 2023-24
    • See module specification for other years: 2024-25

Module summary

Electromagnetism is one of the four fundamental forces of the Universe, and for many purposes, the most influential. In this module you will develop the theories which describe the interaction of charged particles with electric and magnetic fields, laying the foundation for later studies in topics ranging from atomic physics to fusion energy. You will complete the module by studying one of the most startling conclusions of electromagnetism; the constancy of the speed of light. You will discover how this seemingly minor result rewrites our understanding of the nature of space and time.

Module will run

Occurrence Teaching period
A Semester 2 2023-24

Module aims

The purpose of this module is to build on your existing knowledge of electric, magnetic and electromagnetic phenomena. You will be introduced to the crucial mathematical concepts of fields in physics and how electromagnetic fields are described by Maxwell’s equations. We will show that electromagnetic radiation naturally emerges from these equations and that it travels at the speed of light. In this module you will also be introduced to the ideas and concepts of Einstein’s special theory of relativity

Module learning outcomes

  • Discuss the basic concepts of electromagnetic fields as a vector, forces on charges, scalar potential function in electric fields, and potential energy

  • Calculate the electric field, magnetic field and potential energies due to a distribution of charges or currents

  • Apply Maxwell’s equations in integral and differential form to a range of problems. Understand their practical applications and how they result in electromagnetic waves

  • Understand the postulates of Einstein’s special theory of relativity and how they lead to the Lorentz transformations

  • Solve elementary problems involving objects moving at relativistic velocities such as those concerning the way that time is dilated and length contracted when clocks and objects are seen in uniform motion relative to an observer

  • Solve elementary problems involving the energies and momenta of objects moving at relativistic velocities

Module content

Syllabus: Electromagnetism

  • Electric charge, Coulomb force law. Charge distributions, superposition.

  • Electrostatic force and electric field; electric field as a vector field. Visualising the electric field using field lines

  • Electric flux and integral form of Gauss Law. Application to symmetric charge distributions.

  • Work and energy in the electric field - scalar potential function V. Electric field as negative gradient of V.

  • Potential energy U of a charge distribution.

  • Magnetic force on a moving charge, Lorentz force law.

  • Magnetic field and force, magnetic field as a vector field. Magnetic field lines.

  • Magnetic fields from steady currents, Biot Savart Law.

  • Torque on a current carrying loop

  • Magnetic flux and Gauss Law equivalent for magnetic field

  • Integral form of Ampere’s law applied to symmetric current distributions.

  • Electromagnetic induction. Integral form of Faraday’s Law. Lenz Law

  • Basic electrical circuit concepts: electromotive force, resistance, capacitance and self-inductance.

  • Kirchoff Laws and their application to simple networks of resistors, inductors and capacitors.

  • RC, RL and LC circuits.

  • Motors and generators

  • Maxwell’s equations in differential form, their relation to the integral form and their application to simple problems

  • Laplace’s equation for V

  • Charge conservation and Maxwell's displacement current.

  • Electromagnetic waves from Maxwell’s equations and the resulting constancy of the speed of light.

Syllabus: Relativity

  • Ideas and thoughts that lead to the special theory of relativity

  • Inertial frames of reference

  • Einstein’s postulates of special relativity

  • Spacetime

  • Events; simultaneous events

  • Time dilation; proper time

  • Length contraction; proper length

  • Lorentz transformation; examples and consequences

  • Relativistic addition of velocities

  • Relativistic Doppler shift for electromagnetic radiation

  • Relativistic definitions of linear momentum and energy

  • New units e.g. mass in terms of MeV/c2, linear momentum in terms of MeV/c

  • Relativistic total energy and rest energy (E=mc2)

  • Conservation laws for relativistic (total) energy and momentum

Indicative assessment

Task % of module mark
Closed/in-person Exam (Centrally scheduled) 80
Essay/coursework 20

Special assessment rules

Other

Indicative reassessment

Task % of module mark
Closed/in-person Exam (Centrally scheduled) 80

Module feedback

'Feedback’ at a university level can be understood as any part of the learning process which is designed to guide your progress through your degree programme. We aim to help you reflect on your own learning and help you feel more clear about your progress through clarifying what is expected of you in both formative and summative assessments.

A comprehensive guide to feedback and to forms of feedback is available in the Guide to Assessment Standards, Marking and Feedback. This can be found at:

https://www.york.ac.uk/students/studying/assessment-and-examination/guide-to-assessment/

The School of Physics, Engineering & Technology aims to provide some form of feedback on all formative and summative assessments that are carried out during the degree programme. In general, feedback on any written work/assignments undertaken will be sufficient so as to indicate the nature of the changes needed in order to improve the work. Students are provided with their examination results within 25 working days of the end of any given examination period. The School will also endeavour to return all coursework feedback within 25 working days of the submission deadline. The School would normally expect to adhere to the times given, however, it is possible that exceptional circumstances may delay feedback. The School will endeavour to keep such delays to a minimum. Please note that any marks released are subject to ratification by the Board of Examiners and Senate. Meetings at the start/end of each semester provide you with an opportunity to discuss and reflect with your supervisor on your overall performance to date.

Our policy on how you receive feedback for formative and summative purposes is contained in our Physics at York Taught Student Handbook.

Indicative reading

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) ***

K S Krane: Modern Physics ***

A.P. French: Special Relativity **


The information on this page is indicative of the module that is currently on offer. The University constantly explores ways to enhance and improve its degree programmes and therefore reserves the right to make variations to the content and method of delivery of modules, and to discontinue modules, if such action is reasonably considered to be necessary. In some instances it may be appropriate for the University to notify and consult with affected students about module changes in accordance with the University's policy on the Approval of Modifications to Existing Taught Programmes of Study.