Electromagnetism 1

Contents

1. Introduction
2. Weekly Tutorial Problems
3. Supplemental Material
4. Useful Resources
5. Some Interesting Things

§ 1 Introduction

The aim of this module is to introduce you to electrostatics and magnetostatics. These are the studies of charges at rest and steady currents. The electromagnetic force holds atoms, molecules and materials together and plays a vital role in most day-to-day physics one can observe. For example, TV remote controllers, microwave ovens, any electronic device, mobile phones, glasses and many other things all rely on electromagnetic phenomena to function. Interestingly, electromagnetism is arguably the most complete physical theory we have today, as it describes classical and quantum phenomena with equal effectiveness.

More recent research in electromagnetism has focused on how materials with novel electromagnetic properties can be designed and built. Some famous examples include invisibility cloaks [1] and perfect lenses [2]. Exeter University is a leader in this field, with it's metamaterials centre for doctoral training [3].

These tutorials are not part of the module assessment (problems solved here are not marked). Instead, the aim is to develop problem solving, understanding and intuition. Each week, questions supporting the lectures will be set. These should take approximately 1 hour. The problems will be mostly taken from exam questions, so that students get practice solving these kinds of problems, however some additional `challenge' questions might be included if they illustrate something important or interesting.

§ 2 Weekly Tutorial Problems

• Week 1: Introduction to Fields
• Week 2: Electrostatics
• Week 3: Gauss's Law
• Week 4: Electric Multipoles
• Week 5: Dielectrics, Polarisation and Energy of a Charge Distribution
• Week 6: Poisson and Laplace Equations
• Week 7: Magnetic field, magnetic force and torque
• Week 8: Magnetostatics, Magnetic Potentials
• Week 9: Faraday and Lenz Laws, Magnetic Properties of Matter
• Week 10: Maxwell’s Equations and Electromagnetic Waves
• Week 11: Revision

§ 3 Supplemental Material

Here, I will include any scripts or notes that supplement the tutorial problems. This may include scripts to plot fields, or notes on how to calculate things which you might be given but may wish to know how they can be derived.

• Python script to plot vector fields vector_fields.py
• Notes on how some useful integrals can be calculated (pdf)

§ 4 Useful Resources

• The recommended course textbook is "Introduction to Electrodynamics" by Griffiths [4]. This is an excellent introductory electromagnetism book.
• The wikipedia pages for the gradient, divergence and curl operators in spherical coordinate systems [5] and for vector calculus identities [6] are extremely useful for reference. You should remember these operators in Cartesian coordinates (and you probably will by the end of the module), however if you need them in spherical coordinates for an exam question they will usually be given.
• The Feynman Lectures (vol. 2 covers electromagnetism) [7]. These go far beyond the scope of the course, but do provide a wider context and interesting perspective.
• For mathematics (vector calculus etc.), Arfken and Weber [8] is very clear. It also has many exercises which link very strongly to electromagnetism.
• David Tong's notes of electromagnetism are extensive and very clear. Parts 1-3 are relevant for this course. [9]

§ 5 Some Interesting Things

• What do Voltmeters Measure? Am. J. Phys 50(12) 1982 (pdf)
  A paper by Robert Romer answering this deceptively simple question.
• Struggles with the Continuum (pdf)
  A brief and clear review of the challenges faced by modern physics. This has strong applicability to electromagnetism and quantum electrodynamics in particular.
• Why is Maxwell's Theory so hard to understand? (pdf)
  An essay by Professor Freeman Dyson about some of the history of electromagnetism and why developing an intuition for it can be tricky.
• How far away is infinity? (pdf)
  A simple, intuitive and clear exploration of when some common approximations hold and when they don't.
• Feynman's Proof of Maxwell's Equations. Am. J. Phys. 58 (209) 1990
  An interesting paper written by Dyson about a way of deriving Maxwell's equations from only Newton's second law and the form of the Lorentz force, devised by Feynman.

References

[1] Science 312(5514): 1780–1782 (2006)
[2] Phys. Rev. Lett. 85(18): 3996-3969 (2000)
[3] Exeter Metamaterials CDT (website)
[4] D. J. Griffiths, "Introduction to Electrodynamics" 4th Ed. (Pearson, London, 2013)
[5] Del in cylindrical and spherical coordinates
[6] Vector calculus identities
[7] The Feynman Lectures
[8] G. B. Arfken and H. J. Weber, "Mathematical Methods of Physicists" 6th Ed. (Elsevier Academic Press, London, 2005)
[9] David Tong's Electromagnetism lecture notes (Web page)