PHYC 405: Electricity and Magnetism I

Prof. Alejandro Manjavacas
Office: P&A 21

Teaching assistant
Mr. Vahid Karimi
Office: P&A 31

Description of the class

The goal of this class is to introduce the subject of classical electromagnetism at the advanced undergraduate level. This class correspond to the first part of a two-semester sequence of classes intended to cover the standard topics of classical electrodynamics in a mathematically sophisticated and conceptually rigorous manner. Much of this first part will be concerned with electrostatics and magnetostatics, but some discussion of electromagnetic induction ("Faraday's law") will be also presented, leaving most of the dynamics, including relativistic interactions with the electromagnetic field to be covered in the second part, Physics 406.

Classical electromagnetism (EM) is fundamentally a local theory of vector fields and its proper treatment requires methods of vector analysis and differential equations. Maxwell's equations that constitute the laws of EM are first-order partial differential equations (PDEs) with respect to spatial and time variables and involve vector fields, thus requiring sophisticated vector-analysis methods.  For static fields interacting with charges at rest or in steady motion, the electric and magnetic fields decouple from one another so they can be treated independently. Such independent treatment of electrostatics and magnetostatics is the central content of this class.


Tuesday and Thursday, 11:00-12:15, P&A Room 184.


Textbook for the class
Introduction to Electrodynamics (4th Edition) by D. Griffiths. The course will cover Chapters 1-7.

Additional resources
Berkley Physics Course on "Electricity and Magnetism" by E. Purcell and D. Morin.
Lectures on physics - vol II by R. P Feynman.
Foundations of Electromagnetic Theory by J. R. Reitz, F. J. Mildford and R. W. Christy.

Office hours

Tuesday 12:15-13:15 and Thursday 12:15-14:00 in Room 21. These are nominal office hours, you are welcome to come into my office at other times too if your questions cannot wait, although I would appreciate if you could send an email announcing your visit. Sometimes, this drop-in approach may not work if I am very busy or your question requires more than just a few minutes, but in that case I will ask you to come back at a later time.

Teaching assistant
The teaching assistant is Mr. Vahid Karimi ( He will be available on Mondays from 11:00 to 12:00 and Wednesdays from 2:00 to 4:00 in office P&A 31 for you to drop in and discuss any homework grading issues you may have. If you need to schedule an appointment outside of the TA's office hours please send him an email.


The grading in the course will be based on your performance in homework assignments, two midterm exams, and a final exam. The contribution to the final grade is as follows:

  1. Homework: the best (n-1) scores of the n assignments will represent the 20% of the final grade.
  2. Midterm exams: each of them will represent the 25% of the final grade.
  3. Final: will represent the remaining 30% of the final grade.

The MT exams are tentatively scheduled for February 13 and April 3, during (extended) class time, and the final exam will be held during the week of May 7-13.

Homework assignments

There will be 11 assignments during the semester. The assignments will be posted in the tentative schedule about 7-10 before they are due. Late homework policy: homework returned in the next 24 hours after the due date will be accepted but with 50% penalization. After these 24 hours the corresponding solutions will be posted here.

Problems class

Listed officially as Phyc 415.001 (Thursdays: 14:00 - 14:50 pm, Room 184).  This is a very important adjunct to the main lecture class. It will provide you additional practice with solving problems beyond the homework assignments and self study. We will also cover some examples of numerical approaches to solve problems in electrostatics and magnetostatics. Furthermore, the class will also give you a valuable opportunity to bring to my attention your difficulties with any concepts covered in the lecture class so I can address them in a group setting. The problem sheets would be posted here the Monday before the problem class. The corresponding solutions will be posted after the class. You will receive credit for the problems class as long as you register and show up for more than 10 sessions.

Syllabus topics

You can find the calendar for the course in the tentative schedule.

  1. Review of mathematical tools
    - Vector algebra
    - Vector differential and integral calculus
    - Curvilinear coordinates
    - Dirac delta function
  2. Electrostatics
    - Electric field
    - Electric potential
    - Electrostatic boundary conditions
    - Electrostatic energy
    - Conductors
  3. Special Techniques of Electrostatics
    - Laplace's equation
    - The method of images
    - Separation of variables
    - Multipole expansions
  4. Electric field in matter
    - Bound charges and electric polarization
    - Electric displacement field
    - Linear dielectrics
    - Energy in dielectrics
  5. Magnetostatics
    - Lorentz force
    - Biot-Savart and Ampere laws
    - Correspondences between electrostatics and magnetostatics
    - Magnetic vector potential
  6. Magnetic fields in Matter
    - Magnetic dipoles and magnetization
    - Magnetic field of a magnetized object
    - Magnetic media

Tentative schedule

Date Subject Griffiths Reading Homework HW Due Solutions
Week 1
Introduction - Vector algebra
Vector differential calculus
Vector integral calculus
Ch 1
Ch 1
Ch 1
Week 2
Curvilinear coordinates
Dirac Delta function
Electric field I
Ch 1
Ch 1
Ch 2

Week 3
Electric field II
Electric field III
Electric potential
Ch 2
Ch 2
Ch 2
Week 4
Electrostatic boundary conditions
Electrostatic energy
Ch 2
Ch 2
Ch 2
HW3 02/20  HW3_sol
Week 5
Solutions of Laplace´s equation I
Midterm exam I
Midterm exam I solutions
Ch 3

Week 6
Solutions of Laplace´s equation II
The method of images I

The method of images II
Ch 3
Ch 3
Ch 3
Week 7
Separation of variables I
Separation of variables II

Separation of variables III
Ch 3
Ch 3
Ch 3

Week 8
Separation of variables IV
Separation of variables V

Multipole Expansion
Ch 3
Ch 3
Ch 3
Week 9
Spring Break

Week 10
Electric dipole
Polarization I
Polarization II
Ch 3
Ch 4
Ch 4
Week 11
No class on Tuesday
The field of a polarized object I

The field of a polarized object II
Ch 4
Ch 4

Week 12
Boundary value problems
Midterm exam II

Midterm exam II solutions
Week 13
Energy in dielectrics
No class on Thursday
Ch 4

Week 14
Extra class on Friday 2-3.15 pm in room 184
Forces in dielectrics
Lorentz force

Biot-Savart law I

Biot-Savart law II

Ch 4
Ch 5
Ch 5
Ch 5

Week 15
Extra class on Friday 2-3.15 pm in room 184
Laws of magnetostatics I
Laws of magnetostatics II

Multipole expansion of the vector potential

Magnetic materials
Ch 5
Ch 5
Ch 6
Ch 6
Week 16
Magnetized objects and magnetization
Problems involving magnetized objects

Boundary value problems
Ch 6
Ch 6
Ch 6

Problems class

Date Problems Solutions
01/16 (T) PC1
01/25 (R) PC2 PC2_sol
02/01 (R) PC3 PC3_sol
02/08 (R) PC4 PC4_sol
02/15 (R) PC5 PC5_sol
02/22 (R) PC6 PC6_sol
03/01 (R) PC7 PC7_sol
03/08 (R) PC8 PC8_sol
03/15 (R) Spring break

03/22 (R) PC9 PC9_sol
03/29 (R) PC10 PC10_sol
04/05 (R) PC11 PC11_sol
04/12 (R) Class is rescheduled

04/19 (R) PC12 PC12_sol
04/26 (R) PC13 PC13_sol
05/01 (T) Extra class on Tuesday at 2.00-2.50 pm room 5
05/03 (R) PC15 PC15_sol

In accordance with University Policy 2310 and the Americans with Disabilities Act (ADA), academic accommodations may be made for any student who notifies the instructor of the need for an accommodation. It is imperative that you take the initiative to bring such needs to the instructor’s attention, as I am not legally permitted to inquire. Students who may require assistance in emergency evacuations should contact the instructor as to the most appropriate procedures to follow. Contact Accessibility Resource Center at 277-3506 for additional information.

If you need an accommodation based on how course requirement interact with the impact of a disability, you should contact me to arrange an appointment as soon as possible. At the appointment we can discuss the course format and requirements, anticipate the need for adjustments and explore potential accommodations. I rely on the Disability Services Office for assistance in developing strategies and verifying accommodation needs. If you have not previously contacted them I encourage you to do so.