Physics 47 (Advanced Electromagnetism) Home Page, Fall 2006

Physics 47: Advanced Electromagnetism


12/16/06 I've added some practice problems from the final three chapters below. I'll add more as I have time to work them.

12/7/06 Problem set 12 is posted below.

12/1/06 Problem set 11 is posted below.

11/19/06 I've set a bunch of solutions to old problem sets outside my office door.

11/17/06 Problem set 10 is posted below.

11/09/06 Problem set 9 is posted below.

11/02/06 Problem set 8 is posted below.

10/26/06 Problem set 7 is posted below.

10/19/06 Problem set 6 is posted below.

10/07/06 Sorry for the delay! Problem set 5 is posted below. Please remind me if I'm late in assigning the problem set...

09/28/06 Problem set 4 is posted below.

09/21/06 Problem set 3 is posted below.

09/14/06 Problem set 2 is posted below.

09/11/06 We'll have the first informal (and optional) Physics 47 problem session tonight in Merrill 114/116 at 10 pm.

09/05/06 I've posted problem set 1 in the syllabus below


Course Information

Course Description (from the course catalog)

A development of Maxwell's electromagnetic field equations and some of their consequences using vector calculus. Topics covered include: electrostatics, steady currents and static magnetic fields, time-dependent electric and magnetic fields, and the complete Maxwell theory, energy in the electromagnetic field, Poynting's theorem, electromagnetic waves, and radiation from time-dependent charge and current distributions.


Times and places:


Physics 24 and 27 or consent of the instructor

Course requirements

Statement of Intellectual Responsibility: particulars for this course

How to get the most from this class:



Required (should be available at the Jeffrey Amherst bookstore): If you are considering physics graduate school, you may also wish to take a look at:
Additional useful references (if the library doesn't have them, I'll try to get them):

  • Introductory books
  • Books at about the level of this course
  • Books at above the level of this course

    Math books:

    Key derivations / chains of logic / results to commit to memory

    Mathematica Tutorials

    We will use Mathematica 5.2 at least occasionally in the homework, to obtain numerical solutions to problems that are not analytically solvable and to simplify plotting of results. If you've never used Mathematica before, or haven't used it much, the tutorials will help you get started. They were written by Professor Hilborn and revised by Rebecca Erwin '02. If you download the file and save it to the desktop with a .nb suffix in the name, your computer will recognize it as a Mathematica notebook and will start up Mathematica automatically when you double-click on the icon, provided you have Mathematica installed. Mathematica is installed on lots of the college's public machines, including on the computers in the Physics Department computer lab. Alternately, you can pay the $140 or so to buy the student version.

    Lecture Schedule
    Week Lectures Hmwk Comments
    1. September 4 Preliminaries: vectors and vector analysis

    Sept 5: Vectors and vector algebra

    Logistics of the course.
    Geometric and algebraic representations of vectors. Vectors in terms of components and basis vectors. Einstein summation convention. Abstract properties of vector spaces and vector operations. Vector products: scalar product, cross product. Kronecker delta, Levi-Civita symbol.

    Sept 7: Vector analysis [special guest lecturer: Prof. Jagannathan]

    Vectors: transformations under rotations
    active vs. passive transformations. rotations in matrix notation. properties of rotation matrices. rotations preserve lengths of vectors. group properties of rotations. scalars are invariant under rotation.

    Vector calculus
    gradient of a scalar field is a vector (transforms properly under rotations). Line integrals. fundamental theorem for gradients. divergence of a vector field is a scalar. flux of a vector field through a surface. fundamental theorem for divergences (gauss's theorem). curl of a vector field. expression in cartesian coordinates. Levi-civita symbol. curl of a vector field is a vector field. curl of gradient is zero. divergence of curl is zero. irrotational vector fields can be expressed as gradient of a scalar field. divergenceless vector fields can be written as a curl of a vector field.

    Read: Griffiths E&M: Chap. 1

    Problems (PS1):
    Griffiths E&M: 1.6, 1.13, 1.14, 1.17, 1.60, 1.61, 1.62

    [Due Tuesday Sept. 12, 11:59 pm]

    2. September 11 vector analysis

    Sept 12: more on vectors and vector analysis

    parity transformation
    euler's thm: right-handed coord systems related by rotation, related to left-handed by rotation + inversion. inversion transformation defined. vectors defined to behave like displacements. momentum is a vector. angular momentum is a pseudovector. electric fields are vectors, magnetic fields are scalars, E.B (a triple product) is pseudoscalar.

    del operator
    recap of geometrical definitions of div, grad and curl. expressions in expressions in cartesian coordinates. [warning: expressions in curvilinear coordinates generally not simple/obvious]. fundamental theorems for each operator. second derivatives formed using del operator.

    Sept 14: vector operators in curvilinear coordinates

    general orthogonal curvilinear coord. systems (u,v,w). coordinate singularity. def. of an orthogonal/orthonormal coord sys., unit vectors in these coord sys. scale factors and the line element. gradient in curvilinear coords. divergence in curviliear coords. special case: spherical coords.

    introduction to the dirac delta function:
    zero everywhere except at a single point, integrates to something nonzero and finite. example: mass density of a point mass (integrates to total mass of particle)

    Read: Griffiths E&M: Chaps 1 and 2, Appendices A and B

    Problems (PS2):
    Griffiths E&M: 1.47, 1.50, 1.51, 1.59, 2.6, 2.7, 2.43

    [Due: Tuesday Sept. 19, 11:59 pm ]

    3. September 18 Electrostatics

    Sept. 19 : More math / Coulomb's law

    dirac delta function
    density of point charge/mass motivates definition of dirac delta fn in physics, but mathematically fraught. can view as limit of functions growing increasingly narrow and high, but with constant area. mathematically, view as linear functional that returns value of function at a point. rules for delta fns with functions as arguments. 3d delta fn. 3d delta fn as divergence of inverse square field.

    helmholtz decomposition theorem
    div, curl and boundary conditions at infinity are enough to uniquely specify a vector field. irrotational fields have zero curl. four equivalent conditions: curl F=0, path independence of line integral, line integral about closed loops vanish, F is gradient of scalar. solenoidal fields have zero divergence. four equivalent conditions: div F=0, flux through open surface with fixed boundary independent of the surface, flux through closed surface is zero, F is curl of a vector.

    electrostatics: coulomb's law
    statement of coulomb force law. obeys strong form of Newton's third law, implying conservation of linear and angular momentum momentum (although that's not static). electrostatic force obeys principle of linear superposition. electric charge is locally conserved (we'll see this follows from maxwell eqns). electric charge is quantized (we don't know why).

    Sept. 21: Electrostatic fields and Gauss's law

    [before lecture, skim the rest of chap. 2]

    Electrostatic field from Coulomb's law and principle of superposition. E-field of physical dipole: on-axis, then off-axis, expanded to 1st order in the d/r << 1 (long-distance) limit. Field lines and the field line picture as a motivation for Gauss's law. Start proof of Gauss's law: (1) for a point particle with spherical gaussian surface, (2) for a point particle with a general surface. Start an aside on solid angle.

    Read: Griffiths E&M: finish Chap 2, start Chap. 3

    Problems (PS3): Griffiths E&M: 2.14, 2.16, 2.26, 2.31, 2.32, 2.48, 2.49

    [Due Tuesday September 26, 11:59 pm]

    4. September 25 Chap. 3

    Sept 26: title

    Sept. 28: title

    Read: Griffiths E&M: Chapter 3

    Problems (PS4): Griffiths E&M:
    2.38, 2.40, 2.52, 3.1, 3.8, 3.9, 3.14
    [Due Tuesday October 3, 11:59 pm]

    5. October 2 Chap. 3

    Oct. 3: title

    Oct. 5: title

    Read: Griffiths E&M:
    Finish Chapter 3, start Chapter 4

    Problems (PS5):
    Griffiths E&M: 3.18, 3.23, 3.24, 3.35, 3.41, 3.42, 3.45

    [Due 11:59 pm, Tuesday October 17]

    6. October 9 Chap. 3

    Oct. 10: Midterm Break

    Oct. 12: title

    Read: Griffiths E&M: Chap. 3

    Problems: wrapped over from last week

    Some suggested study problems for the exam:

    Chap. 1: 1.33, 1.41, 1.53, 1.58
    Chap. 2: 2.1, 2.39, 2.41, 2.45
    Chap. 3: 3.10, 3.15, 3.25, 3.38, 3.48

    7. October 16 Chap. 3/4

    Oct. 17: title

    Oct. 18 (7-10 pm, Merrill 211): Midterm Exam

    Oct. 19: title

    Read: Griffiths E&M: Chap. 4

    Problems (PS6): Griffiths E&M:
    4.2, 4.3, 4.5, 4.8, 4.10, 4.29, 4.33

    [Due 11:59 pm, Tuesday Oct. 24]
    First Midterm Exam: Wednesday, Oct. 18, 7-10 pm
    8. October 23 Chap. 4/5

    Oct. 24: title

    Oct. 26: title

    Read: Griffiths E&M: Chap. 4 & 5

    Problems (PS7):
    Griffiths E&M:
    4.15, 4.16, 4.22, 4.25, 4.38, 5.6, 5.38

    [Due 11:59 pm, Tuesday Oct. 31]

    9. October 30 Chap. 5/6

    Oct. 31: title

    Nov. 2: title

    Read: Griffiths E&M: Chap 5 & 6

    Problems (PS8): Griffiths E&M:
    5.21, 5.36, 5.39, 5.50, 5.51, 5.61, 6.3

    [Due 11:59 pm, Tuesday Nov. 7]

    10. November 6 Chap.

    Nov. 7: title

    Nov. 9: title

    Read: Griffiths E&M: Chap. 6 / 7

    Problems (PS9): Griffiths E&M:
    6.7, 6.16, 6.18, 6.23, 7.4, 7.8, 7.13

    [Due 11:59 pm, Thursday Nov. 16]

    11. November 13 Chap.

    Nov. 14: title

    Nov. 16: title

    Read: Griffiths E&M: Chap. 7 / 8

    Problems (PS10): Griffiths E&M:
    7.16, 7.22, 7.26, 7.35, 7.42, 7.45, 7.60

    [Due 11:59 pm, Friday Dec. 1... but these are also good exam practice problems, so I suggest you look at them earlier.]

    some suggested exam practice problems:

    4.11, 4.13, 4.18, 4.24, 4.28, 4.34

    5.3, 5.9, 5.11, 5.13, 5.15, 5.22, 5.26, 5.46

    6.5, 6.9, 6.10, 6.12, 6.17, 6.21, 6.27

    7.3, 7.7, 7.10, 7.17, 7.20, 7.28, 7.31, 7.39, 7.58

    12. November 27 Chap.

    Nov. 28: title

    Nov. 30: title

    Read: Griffiths E&M: Chap. 8 / 9

    Problems: Griffiths E&M:
    8.2, 8.3, 8.5, 8.12, 9.32

    [Due Tuesday Dec. 5, 11:59 pm]
    Second Midterm Exam: Wednesday, Nov. 28, 7-10 pm
    13. December 4 Chap.

    Dec. 5: title

    Dec. 7: title

    Read: Griffiths E&M: Chap. 9/10

    Problems: Griffiths E&M: 9.6, 9.13, 9.16, 9.30, 9.33, 10.9, 10.21

    [Due Wednesday Dec. 13, 5:00 pm]

    14. December 11 title...

    Dec. 12: title

    Dec. 14: Reading Period

    Practice exam problems:

    Chapter 8: 8.4, 8.7, 8.13, 8.15

    Chapter 9: 9.2, 9.8, 9.19, 9.22, 9.34

    Chapter 10: 10.2, 10.10, 10.13, 10.20

    Finals week Final exam: Tuesday Dec. 19, 2-5 pm, Merrill 211


    I'll keep scheduling information on this site primarily. I may occasionally use Blackboard as well.

    Useful Links

    I'll post interesting or useful links pertinent to the course here as they I come across them. If you come across any others, please let me know.

    Interesting talks in the Five-College area:

    You should start attending the departmental colloquia early and often. They are intended primarily for you, to broaden your exposure to current physics in ways that the department faculty alone cannot. They'll give you an overview of what exciting work is going on in physics and who's doing it. In the beginning you won't always understand all of the talks, but you'll be surprised by how much you can understand even now. In addition, the colloquium food here is better than anywhere else I've ever been. Plus, I organize the colloquia, and it warms my heart to see you there.

    Area Seminars and colloquia

    Interesting and useful papers:

    Interesting and useful websites: