3AEX0 - Electromagnetism
A Summary
Fe Fan Li
October 20, 2020
, Contents
Preface 2
1 Electric Charge and Electric Field 4
1.1 Electric Charge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.2 Conductors. insulators, and induced charges . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.3 Coulomb’s law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.4 The electric field and electric forces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.5 Electric-field calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.6 Electric field lines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.7 Electric dipoles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2 Gauss’ Law 8
2.1 Charge and electric flux . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.2 Calculating electric flux . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.3 Applications of Gauss’ law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.4 Charges and conductors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
3 Electric Potential 11
3.1 Electric potential energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
3.2 Electric potential . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
3.3 Calculating electric potential . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
3.4 Equipotential surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
3.5 Potential gradient . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
3.6 Final Exam - 2018-08 - Question 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
4 Capacitance and Dielectrics 17
4.1 Capacitors and capacitance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
4.2 Capacitors in series and parallel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
4.3 Energy storage in capacitors and electric-field energy . . . . . . . . . . . . . . . . . . . . . 18
4.4 Dielectrics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
4.5 Molecular model of induced charge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
4.6 Gauss’ law in dielectrics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
4.7 Final Exam - 2017-06 - Question 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
5 Current, Resistance, and Electromotive Force 23
5.1 Current . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
5.2 Resistivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
5.3 Resistance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
5.4 Electromotive force and circuits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
5.5 Energy and power in electric circuits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
6 Magnetic Fields and Magnetic Forces 25
6.1 Magnetism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
6.2 Magnetic field . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
6.3 Magnetic field lines and magnetic flux . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
6.4 Motion of charged particles in a magnetic field . . . . . . . . . . . . . . . . . . . . . . . . 27
6.5 Applications of motion of charged particles . . . . . . . . . . . . . . . . . . . . . . . . . . 27
6.6 Magnetic force on a current-carrying conductor . . . . . . . . . . . . . . . . . . . . . . . . 27
1
, 6.7 Force and torque on a current loop . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
7 Sources of Magnetic Field 29
7.1 Magnetic field of a moving charge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
7.2 Magnetic field of a current element . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
7.3 Magnetic field of a straight current-carrying conductor . . . . . . . . . . . . . . . . . . . . 29
7.4 Force between parallel conductors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
7.5 Magnetic field of a circular current loop . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
7.6 Final Exam - 2016-06 - Question 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
7.7 Ampere’s law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
7.8 Applications of Ampere’s law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
7.9 Magnetic materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
7.10 Final Exam - 2019-08 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
8 Electromagnetic Induction 38
8.1 Motional electromotive force . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
8.2 Induction experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
8.3 Faraday’s law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
8.4 Lenz’ law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
8.5 Inducced electric fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
8.6 Displacement currents and Maxwell’s equations . . . . . . . . . . . . . . . . . . . . . . . . 39
9 Inductance 40
9.1 Mutual inductance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
9.2 Self-inductance and inductors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
9.3 Magnetic field energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
9.4 Final Exam - 2019-08 - Question 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
10 A Recommendation 44
2
, Preface
This summary is based on the course 3AEX0, its lectures and the book University Physics with Modern
Physics. This text is based on the handwritten notes I made when I took the course during the year
2018-2019.
Use this summary at your own risk; I am not responsible for your exam and sections in this
summary may contain errors, redundant information or absence of important information.
Information may be outdated and not part of the course anymore. My recommendation
is that you also study the book, lecture slides and exercises as well as exam questions
thoroughly.
The chapters and sections will be named after the sections in the book. This document will feature
a summary of the concepts along with some example exam questions. There will be another version
available that is slightly shortened. Typos and mistakes or whatever will not be fixed.
3
A Summary
Fe Fan Li
October 20, 2020
, Contents
Preface 2
1 Electric Charge and Electric Field 4
1.1 Electric Charge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.2 Conductors. insulators, and induced charges . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.3 Coulomb’s law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.4 The electric field and electric forces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.5 Electric-field calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.6 Electric field lines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.7 Electric dipoles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2 Gauss’ Law 8
2.1 Charge and electric flux . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.2 Calculating electric flux . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.3 Applications of Gauss’ law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.4 Charges and conductors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
3 Electric Potential 11
3.1 Electric potential energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
3.2 Electric potential . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
3.3 Calculating electric potential . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
3.4 Equipotential surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
3.5 Potential gradient . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
3.6 Final Exam - 2018-08 - Question 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
4 Capacitance and Dielectrics 17
4.1 Capacitors and capacitance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
4.2 Capacitors in series and parallel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
4.3 Energy storage in capacitors and electric-field energy . . . . . . . . . . . . . . . . . . . . . 18
4.4 Dielectrics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
4.5 Molecular model of induced charge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
4.6 Gauss’ law in dielectrics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
4.7 Final Exam - 2017-06 - Question 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
5 Current, Resistance, and Electromotive Force 23
5.1 Current . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
5.2 Resistivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
5.3 Resistance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
5.4 Electromotive force and circuits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
5.5 Energy and power in electric circuits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
6 Magnetic Fields and Magnetic Forces 25
6.1 Magnetism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
6.2 Magnetic field . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
6.3 Magnetic field lines and magnetic flux . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
6.4 Motion of charged particles in a magnetic field . . . . . . . . . . . . . . . . . . . . . . . . 27
6.5 Applications of motion of charged particles . . . . . . . . . . . . . . . . . . . . . . . . . . 27
6.6 Magnetic force on a current-carrying conductor . . . . . . . . . . . . . . . . . . . . . . . . 27
1
, 6.7 Force and torque on a current loop . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
7 Sources of Magnetic Field 29
7.1 Magnetic field of a moving charge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
7.2 Magnetic field of a current element . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
7.3 Magnetic field of a straight current-carrying conductor . . . . . . . . . . . . . . . . . . . . 29
7.4 Force between parallel conductors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
7.5 Magnetic field of a circular current loop . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
7.6 Final Exam - 2016-06 - Question 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
7.7 Ampere’s law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
7.8 Applications of Ampere’s law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
7.9 Magnetic materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
7.10 Final Exam - 2019-08 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
8 Electromagnetic Induction 38
8.1 Motional electromotive force . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
8.2 Induction experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
8.3 Faraday’s law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
8.4 Lenz’ law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
8.5 Inducced electric fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
8.6 Displacement currents and Maxwell’s equations . . . . . . . . . . . . . . . . . . . . . . . . 39
9 Inductance 40
9.1 Mutual inductance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
9.2 Self-inductance and inductors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
9.3 Magnetic field energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
9.4 Final Exam - 2019-08 - Question 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
10 A Recommendation 44
2
, Preface
This summary is based on the course 3AEX0, its lectures and the book University Physics with Modern
Physics. This text is based on the handwritten notes I made when I took the course during the year
2018-2019.
Use this summary at your own risk; I am not responsible for your exam and sections in this
summary may contain errors, redundant information or absence of important information.
Information may be outdated and not part of the course anymore. My recommendation
is that you also study the book, lecture slides and exercises as well as exam questions
thoroughly.
The chapters and sections will be named after the sections in the book. This document will feature
a summary of the concepts along with some example exam questions. There will be another version
available that is slightly shortened. Typos and mistakes or whatever will not be fixed.
3
