Lecturer: Jiri Vala (jiri.vala@mu.ie) Tutor: Joe Mc Caffrey (joe.mccaffrey.2018@mumail.ie)

2021 Exam with Solutions

2021 May exam (online timed assessment) + solutions

Problem sets

Important equations of electromagnetism

Here is a list of the main equations and results we encounter in MP204.

Practice Problems

- Problem bank (``problem set 12'')

This is marked as `Problem set 12', but it is really a large collection of problems covering all the module material.

Should be useful for practice and for learning the material more thoroughly. - Many of the textbooks have collections of problems and
worked-out exercises.

In particular, the textbook by Griffiths and that by Purcell & Morin both have large numbers of excellent exercises and problems.

Topics covered in Class

We point below to relevant chapters in
Prof. Nash's Notes and
in
Vol. II of the Feynman lectures (referred to as Feynman II below).

Of course, equivalent material is available in many other textbooks,
or in online material such as those linked to further down on this page.

Maxwell's equations, displacement current
density, wave solutions.

Chapters 18 and 20 in Feynman II.
Nash notes: chapters V and VI.

Electromagnetic Induction; Faraday's law.

Chapters 16 and 17 in Feynman II.
Nash notes: chapter V.

Vector Potential.

Chapter 15 in Feynman II.
Unfortunately, Nash notes do not discuss the vector potential.

Magnetic field.

Chapters 13 and 14 in Feynman II.
Nash notes: chapter IV.

Electric Currents.

Chapter 13 in Feynman II.
Nash notes: chapter 3.

Applications of Gauss' law.

In Feynman II, Chapter 5 is highly recommended reading.
In Nash notes, this is chapter 2.

Electric flux. Gauss' dielectric flux theorem
(a.k.a. Gauss' law).

In Feynman II, the discussion of flux begins in Chapter 4 Section 5,
and continues through Chapter 5. Nash-notes covers this
material in Chapter 2.

Continuous charge distributions.
In class, we worked out how to calculate the potential and the
electric field due to a continuous
distribution of charge by first calculating the contribution due to an
infinitesimal element and then integrating (``adding up''). This is
an important technique which will recur throughout this module; please
make sure you are able to set up integrals like this yourself.

Some common examples are discussed in
this
video,
this video,
this video,
this video.

Coulomb's Law, Electric Fields,
Electric Potentials.
Chapter 1 of Nash-notes. The introduction to the electric potential
in Nash-notes Chapter 1 Section 3 is more detailed than we had time
for in class; you might want to read this carefully.

In Feynman lectures Vol. II, you will find similar material
in the first 4 sections of Chapter 4.

Overview and Background.
In Feynman lectures Vol. II, Chapter 1 gives an overview of what we
will learn this semester.

Chapters 2 and 3 introduces grad-div-curl and vector integration.
You are supposed to know most of this material already. Working
through them will be a great help for MP204.

Textbooks, lecture notes, etc

Scanned lecture notes from Dr. Masud Hague

Scanned lecture notes, part A. (Up to page 7)

Scanned lecture notes, part B. (Pages 8 to 16)

Scanned lecture notes, part C. (Pages 17 to 37)

Scanned lecture notes, part D. (Pages 39 to 59)

Scanned lecture notes, part E. (Pages 61 to 83)

Lecture notes from Prof. Charles Nash

MP204 lecture notes of Prof. Charles Nash --- this is roughly the material to be covered in the module, with some additions. It is recommended that you work through these notes, and in addition spend significant time working through at least one textbook.

Textbooks

There are many, many textbooks on introductory electromagnetism or electrodynamics. You are strongly encouraged to read through one or more textbooks.

For example, you could work through the *Feynman
lectures* (Volume II), which are free to read on this website. The material we
will cover in MP204 is mostly contained within the first 20 chapters
of Volume II. (Specifically: Chapters 1, 4--6, 13--18, 20.) This
will be very close to what we will cover. However, the material is
very standard and you will find the same topics in many other texts.

Other texts:

- Fleisch,
*A Student's Guide to Maxwell's Equations*.

Student-friendly, as the title suggests. - Griffiths,
*Introduction to Electrodynamics*.

Slightly more advanced than the level of this module, but reading through this text and working out exercises is very worthwhile. - Purcell & Morin,
*Electricity and Magnetism*.

Slightly more advanced than the level of this module. - Edminister & Nahvi,
*Schaum's Outline of Electromagnetics*.

Many worked-out examples. - Panofsky & Phillips,
*Classical Electricity and Magnetism*. - Grant & Phillips,
*Electromagnetism*. - Shankar,
*Fundamentals of Physics II: Electromagnetism, Optics, and Quantum Mechanics*.

Material available online:

Lecture notes from various places.

Of course, we didn't check in detail for correctness and/or how
closely these notes are aligned to the matter we cover in MP204, so
please use at your own discretion.

Please let us know if any of the links don't work.

- Notes from DAMTP Cambridge.
- Notes from Duke University.
- Notes from Hong Kong.
- Notes from Oxford, 2009.
- Lecture Notes from Ohio State Univ.
- Notes from Univ. Rochester.

Notation

We use SI (also called MKS or MKSA) units. Note that many equations look quite different when written in Gaussian (or CGS) units. When reading a textbook, be sure to watch out for which units that text is using.

Notations vary. We mostly try using the same notations as in Prof. Nash's notes, but do not always succeed. You anyway need to be able to read and learn from multiple sources using different notations for the same physical quantities.

(Solutions to) previous exams + Sample Exams

Here is a sample exam for practice: Sample exam 1, for 2018-2019

Here is the 2019 May exam and here is the 2019 Repeat (August) exam. (Solutions are not available; sorry.)

Below are solutions to some past exams.

(The length
of exams has changed since 2017.)

Below are old sample exams for practice. They are in the style of previous (2017-2018) exams. Later exams was structured slightly differently (divided into 4 questions instead of 3), but the material covered and the level of difficulty should be similar.

Prerequisite: Vector Calculus

This module requires you to be very familiar with Vector Calculus. You should be comfortable with grad/div/curl, Stokes' theorem and the divergence theorem, and of course vector addition and components.

If you need a review, you can try working through some of the following. We strongly suggest making time to do this at the beginning of semester.

- Some of the problem sheets (or past exams) of MP201.
- Feynman lectures Vol. II: Chapter 2 and Chapter 3.
- This review, especially the exercises.
- This review.
- Some practice problems from the latter sections of this online review of multivariate calculus.

This webpage is based on the webpage originally prepared by Dr. Masud Hague.