PHYC 405: Electricity and Magnetism I

Prof. Alejandro Manjavacas
Office: P&A 1136
Phone: 505 277-1064

Teaching assistant
Mr. Karthik Chinni
Office: P&A 22

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.


Monday, Wednesday and Friday, 10:00-10:50, P&A Room 184.


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

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

Monday 11:00-1:00 and Wednesday 11:00-12:00, and 1:00-2:00 in Room 1136. 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. Karthik Chinni ( He will be available on Tuesdays from 2:00 to 4:00 in office P&A 22 for you to drop in and discuss any homework grading issues you may have.


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 two Fridays, February 19 and April 8, during (extended) class time, and the final exam will be held during the week of May 9-13.

Homework assignments

There will be 9-10 assignments during the semester each with 5-7 problems apiece. The assignments will be given throughout the semester and will be posted in the tentative schedule about 7-10 before they are due. Late homework policy: homework returned in the next five days after the due dat will be accepted but 50% penalization. After five days of the due date the corresponding solutions will be posted here.

Problems class

Listed officially as Phyc 415.001 (Wednesdays: 12:00 - 12:50 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 Friday 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
  7. Electromagnetic Induction
    - Electromotive force
    - Faraday's law

Tentative schedule

Topic Date Subject Griffiths Reading Homework HW Due Solutions
Review of mathematical tools
01/20 (W) Introduction - Vector algebra
Ch 1 HW1  02/01 (M) HW1_sol

01/22 (F) Vector differential calculus Ch 1

  01/25 (M) Vector integral calculus Ch 1  

01/27 (W) Curvilinear coordinates
Ch 1
  01/29 (F) Dirac Delta function
Ch 1

Electrostatics 02/01 (M) Electric field I
Ch 2 HW2  02/10 (W) HW2_sol

02/03 (W) Electric field II
Ch 2

  02/05 (F) Electric field II Ch 2
  02/08 (M) Electric potential Ch 2

02/10 (W) Electrostatic boundary conditions
Ch 2
HW3  02/22 (M)
  02/12 (F) Electrostatic energy
Ch 2
  02/15 (M) Conductors
Ch 2
Special techniques in electrostatics
02/17 (W) Solutions of Laplace´s equation I
Ch 3

02/19 (F) Midterm exam I -- It starts at 9:45 am !!


02/22 (M) Solutions of Laplace´s equation II Ch 3 HW4  03/02 (W)
  02/24 (W) The method of images I Ch 3

  02/26 (F)
Double class
The method of images II
Separation of variables I
Ch 3
  02/29 (M) Separation of variables II
Ch 3

  03/02 (W) Separation of variables III
Ch 3
HW5  03/09 (W) HW5_sol

03/04 (F)
Double class
Separation of variables IV & V
Ch 3

  03/07 (M) Multipole Expansion Ch 3    
  03/09 (W) Electric dipole Ch 3 HW6  03/23 (W) HW6_sol
 Elelctric field in matter 03/11 (F) Polarization I Ch 4    
  03/14 (M) Spring break

03/16 (W) Spring break

03/18 (F) Spring break

03/21 (M) Polarization II Ch 4

03/23 (W) The field of a polarized object I Ch 4 HW7  03/30 (W) HW7_sol

03/25 (F) The field of a polarized object II Ch 4

  03/28 (M) Boundary value problems Ch 4    
  03/30 (W) Energy in dielectrics Ch 4 HW8  04/11 (M) HW8_sol
  04/01 (F) Midterm exam II -- It starts at 9:10 am !!

04/04 (M) Forces in dielectrics
Ch 4

04/06 (W) Solution of midterm exam 2

  Magnetostatics 04/08 (F) Lorentz force Ch 5

04/11 (M) Biot-Savart law I Ch 5 HW9  04/18 (M)
  04/13 (W) Biot-Savart law II Ch 5      

04/15 (F) Laws of magnetostatics I Ch 5

04/18 (M) Laws of magnetostatics II Ch 5
HW10  04/25 (M)

04/20 (W) Multipole expansion of the vector potential Ch 5

  Magnetic field in matter 04/22 (F) Magnetic materials Ch 6
HW11  05/06 (F)

04/25 (M) Magnetized objects and magnetization Ch 6

04/27 (W) Problems involving magnetized objects Ch 6

04/29 (F) No class

05/02 (M) No class

05/04 (W) Boundary value problems Ch 6

05/06 (F) Review class

05/13 (F)
Final exam -- It starts at 7:30 am !!

Problems class

Date Problems Solutions
01/20 (W) PC1 PC1_sol
01/27 (W) PC2 PC2_sol
02/03 (W) PC3 PC3_sol
02/10 (W) PC4 PC4_sol
02/17 (W) PC5 PC5_sol
02/24 (W) PC6 PC6_sol
03/02 (W) PC7 PC7_sol
03/09 (W) PC8 PC8_sol
03/16 (W) Spring break

03/23 (W) PC9 PC9_sol
03/30 (W) PC10 PC10_sol
04/06 (W) PC11 PC11_sol
04/13 (W) PC12 PC12_sol
04/20 (W) PC13 PC13_sol
04/27 (W) PC14 PC14_sol
05/04 (W) PC15 PC15_sol