## MP204: Electricity and Magnetism

### Spring 2021

#### (2nd semester of 2020-2021)

Lecturer:   Masud Haque   (haque@thphys.nuim.ie)     Tutor:   Aonghus Hunter-McCabe   (Aonghus.HunterMccabe@mu.ie)

May Exam with Solutions

Problem sets

Problem set 11.   Was due Monday May 3rd.
(Partial) solutions to problem set 11.

Problem set 10.   Due Monday April 26th.
(Partial) solutions to problem set 10.

Problem set 09.   Was due Monday April 19th.
(Partial) solutions to problem set 09.

Problem set 08.   Was due Monday April 12th.
(Partial) solutions to problem set 08.

Problem set 07.   Was due tuesday March 29th.
(Partial) solutions to problem set 07.

Problem set 06.   Was due Monday March 22nd.
For the Study Break; twice as long as the usual weekly problems.
(Partial) solutions to problem set 06.

Problem set 05.   Was due Monday March 8th.

Problem set 04.   Was due Monday March 1st.

Problem set 03.   Was due Monday February 22nd.

Problem set 02.   Was due Monday February 15th.

Problem set 01.   Was due Monday February 8th.
Problems 3 and 4 in this problem set involve finding the total charge of objects from the linear charge density or from the surface charge density. This will require breaking up the object into infinitesimal pieces and then adding up the contributions of each piece, which amounts to an integration. We will have to do variants of this procedure many times during this module; so please practice until you are fully comfortable.
The relationship between charge density and total charge is the same as that between the usual (mass) density and total mass. For guidance, you could try
this video,   this video,   this discussion,   these notes.

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.

Scanned lecture notes

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)

Topics covered in Class

I 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.

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

Lecture notes from a previous lecturer

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, I 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.

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. I 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. I strongly suggest making time to do this at the beginning of semester.