Physics 24 (Maxwellian Synthesis) Home Page, Spring 2007

Physics 24: Maxwellian Synthesis


04/19/07 I have posted problem set 10 below. It's due on Wednesday, April 25.

04/09/07 Eduardo has kindly provided a copy of the student study guide for Ohanian, which I have placed on reserve in the Science Library.

04/08/07 I have posted problem set 9 below. It's due on Wednesday, April 18.

03/30/07 I have posted problem set 8 below. It's due on Wednesday, April 4.

03/16/07 I have posted problem set 7 below. It's due on Wednesday, March 28.

03/10/07 I have posted problem set 6 below. It's due on Wednesday, March 14.

03/02/07 I have posted problem set 5 below. It's due on Wednesday, March 7. Since you have less than a full week to work on it, I've just made it half the usual length.

02/24/07 I have posted problem set 4 below. It's due on Friday, March 2. Also, the exam on Wednesday will cover to the end of Chap. 26 (which is about where we ended up on Friday) .

02/15/07 I have posted problem set 3 below.

02/08/07 I have posted problem set 2 below.

01/29/07 I have posted problem set 1 below. Also, take note of a few corrections in the course information since the printout I gave you. In particular, note that the lab notebook should be sewn, NOT spiral or looseleaf.

Lecture Instructor

Professor William Loinaz
Office: 223 Merrill Science Center
Phone: (413) 542-7968
Office Hours: W 9-11 am
You're also welcome to drop by my office. If I'm in and free I'm happy to meet with you, but it's not so often during the day that I'm in and I'm free.

Lab Instructor

Professor Paul Bourgeois
Office: 118 Merrill Science Center
Phone: (413) 542-2593
Office Hours: TBA

Lab Teaching Fellow

Ben Heidenreich
Office: 209 Merrill Science Center
Phone: (413) 542-2062
Office Hours: TBA

Grader: Eduardo

Course Information

Course Description (from the course catalog)

In the mid-nineteenth century, completing nearly a century of work by others, Maxwell developed an elegant set of equations describing the dynamical behavior of electromagnetic fields. A remarkable consequence of Maxwells equations is that the wave theory of light is subsumed under electrodynamics. Moreover, we know from subsequent developments that the electromagnetic interaction largely determines the structure and properties of ordinary matter. The course will begin with Coulombs Law but will quickly introduce the concept of the electric field. Moving charges and their connection with the magnetic field will be explored. Currents and electrical circuits will be studied. Faradays introduction of the dynamics of the magnetic field and Maxwell’s generalization of it will be discussed. Laboratory exercises will concentrate on circuits, electronic measuring instruments, and optics.


Times and places:


Physics 16/23 and Math 12, 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): Additional useful references:

Math books: Lab Work: Special topics:

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 Lab
1. January 29
Electric Forces and Fields

Jan 29: A Brief History of Electromagnetism

Importance of electromagnetism in pantheon of physical theories. Organization of the course. Brief timeline of discoveries in electromagnetism.
[Demos: Charge a glass rod by rubbing with newspaper or rabbit fur. It exerts a force on scraps of paper, on pith balls, and it moves leaves of electrometer.]
[Handouts: lab manual, student information survey, course information sheet]

Jan 31: Electric Charge and Coulomb's Law

Electrostatic interaction: similar to gravity as an inverse square force, differs in that it has two charges and is much stronger. Electric charge is conserved, and electric charge comes in units of e (except quarks, which are 2/3e and -1/3e); neither experimental fact has an explanation. Inverse square force law is called Coulomb's law. Electrostatic forces obey principle of linear superposition and strong form of Newton's third law. SI units.
Electric field: Ohanian explains that electric field is a type of matter; for now, it's just a vector field that expresses the force per unit (arising from a fixed configuration of charges) at any point in space.

Feb 1: Electric Fields: visualizing

Aside on the Standard Model of elementary particles, to explain why quarks are never found free. Aside on nonlinear theories.
Virtue of electric fields is that they're local.
Visualizing the electric field: (1) can use arrows to display field vectors on a lattice of points, (2) can use field lines. Field lines are tangent to the field vector at any point; flow from (+) to (-) charges; number of lines is sources is proportional to charge of source; density of field lines is proportional to electric field strength.
Some discussion of electrostatics, sparks, and the breakdown of air, in the context of demos.

[Demos: Wimshurst machine and Van de Graff generator, both of which generate electrostatic charge & fields]

Feb 2: Electric fields: calculating

Visualizing electric fields: field vectors on a grid, field lines. Rules for drawing field lines.
Calculating electric fields algebraically: expressions for point sources and for continuous sources.
Example: electric (physical) dipole--field on the z-axis [exact expression, leading behavior in long-distance approx.]

Read: Ohanian, Chap. 22 & 23

Problem set 1 (PS1):
Chap. 22, problems: 20, 24, 27
Chap. 23, questions: 8, 12, 16; problems: 21, 31, 35, 39

[Due: 11:59 pm, Tuesday February 6]

No lab this week.
2. February 5
Electric Fields: Coulomb's Law and Gauss's Law

Feb 5: Electric Fields: Examples

Electric field of a physical dipole: field on the y-axis [exact expression, leading behavior in long-distance approx.]. Field due to infinite line of charge.

Feb 7: Electric Fields: more examples

Electric field of a ring of charge (on symmetry axis). Electric field of a disk.

Feb 8: Fields and flux

Electric field due to an infinite sheet of charge. Brief discussion of spherical shell.
Flux: Definition and physical significance. Flux for a small surface in a constan field, generalized to arbitrary surface and spatially-varying field. Gauss's law stated.

Feb 9: Proving Gauss's law

(1) Prove Gauss for point charge with spherical Gaussian surface. (2) Prove Gauss for point charge with arbitrary surface.

Read: Ohanian Chap. 24 & 25

PS 2:
from Chap. 24
Questions: 5, 6, 11
Problems: 15, 20, 21, 26, 27, 31
Last problem: Calculate the electric field inside and outside hollow spherical shell of radius R and total charge Q. Assume that the charge is uniformly distributed over the surface of the shell. Proceed by direct evaluation, using Coulomb's law.

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

Lab 1: DC Circuits (Formal)
3. February 12
Gauss's Law / Electrostatic Potential

Feb. 12: Gauss's Law

Some comments on proving Gauss's law with an arbitrary surface (consider both the case in which charge is inside surface and case in which charge is outside surface). Generalize to arbitrary charge distribution using superposition. Examples: Gauss's law to find fields of a uniform shell of charge and an infinite line of charge. .

Feb 14: Using Gauss's law / Conductors

Discussion of Ohanian Problems 24.20 and 24.27, as an application of the principle of superposition. Using Gauss's law to find the electric field of an infinite sheet of charge, and of a pair of sheets with opposite charge. Conductors and insulators. Conductors respond to external electric field by redistributing free charge. Result: electric field within a conductor is zero. By Gauss's law, then, there is no free charge within a conductor; it all resides on the surface.

Feb 15: Electric fields of conductors

Electric field at the surface of a conductor is perpendicular to the conductor. Find the charge distribution on the surfaces of a charged plate and two charged plates. Relate local electric field at the surface of conductor to local surface charge density. Electrostatic shielding.

Feb 16: Electrostatic potential

Reminder of gravitational potential and conservative forces. Proved: the work done by conservative forces (which includes electrostatics) is path-independent. Define potential energy function and potential function. Calculate potential of infinite sheet of charge and of a point charge by integrating the electric field. Can calculate the potential of a configuration of charges by considering it a collection of point charges and using superposition of the point charge potential directly.

Read: Ohanian Chap. 25 & 26

Problems (PS 3):
Ohanian, Chap. 25
Questions: 13, 15
Problems: 20, 21, 23, 27, 30, 32, 33, 40

[Due: Tuesday, February 20, 11:59 pm]

Lab 2: Introduction to the Oscilloscope (EI)
4. February 19
Electrostatic potential and electrostatic energy

Feb 19: More on the electrostatic potential

Potential due to a ring: by integrating the field, and by adding point charge potentials. Interconnections among potentials, charge distributions, and fields. Path independence of line integrals of electrostatic field implies that line integral of electrostatic field about closed loops gives zero. Consequence: electric field lines can never form closed loops. Consequence: empty cavities inside conductors contain no field lines (electrostatic shielding).

Feb 21: From potentials to fields

Going from potential to field by differentiation: partial derivatives, directional derivatives, and gradient defined. Electric field is negative gradient of potential. Equipotential surfaces are surfaces of constant V; they are perpendicular to field lines. No work is done moving charges along equipotential surfaces.

Feb 22: Mean value theorem

Mean value theorem: in a charge-free region, the average value of the potential over the surface of any sphere is equal to the value of the potential at the center of the sphere. Earnshaw's theorem: in an open charge-free region, the potential has no maximum or minimum (for any closed charge-free region, the extrema of the potential are obtained on the boundary). Consequence of Earnshaw: no stable equilibrium of a charged particle in a purely electrostatic field.

Feb 23: Electrostatic energy

Expressions for electrostatic energy of a system of two, three, and many point particles (note that these expressions don't contain the electrostatic self-energy of the point particles, which is infinite). Electrostatic energy of a charged conductor and system of charged conductors obtained.

Read: Ohanian Chap. 26 & 27

Problems (PS 4):
Chap. 26, Problems 5, 10, 15, 25, 29
Chap. 27, Problems 6, 10, 13, 17, 22

[Due: 11:59 pm, Friday March 2]

Lab 3: Capacitors (EI)
5. February 26
Capacitors and Dielectrics

Feb 26: Electrostatic energy and capacitance

Electrostatic energy of a parallel plate capacitor. Electrostatic energy of an isolated conducting sphere. Definition of capacitance. Capacitance of isolated conducting sphere.

Feb 28: Capacitance / Dielectrics

Capacitance of a parallel plate capacitor. Combining capacitors in parallel and in series. Introduction to dielectrics.

Mar 1: Introduction to dielectrics

Dielectrics as composed of tiny electric dipoles. Microscopic dipoles may be induced by external field (as in the case of atoms), or the elementary units may have permanent electric dipole moments which can be macroscopically aligned by external fields (e.g. water molecules). Collection of aligned dipoles equivalent to an appropriate distribution of charge on surface of dielectric. Linear dielectrics: induced dipole proportional to external field. Dielectric constant is ratio of total field to external field (>1). Capacitance in the presence of a dielectric: defined at the ratio of free charge on the capacitor to the voltage across the capacitor (enhanced by 1/dielectric constant for linear dielectrics). Dielectric may also increase the breakdown field of the capacitor over that of air.

Mar 2: Bound charge in dielectrics

Determining bound charges induced on surfaces of dielectrics in arrangements of capacitors filled or partially filled with linear dielectrics (in cases of high symmetry). Case of parallel plate capacitors when dielectric (1) fills and (2) does not fill the space between plates. Gauss's law for systems containing linear dielectrics, recast in terms of free charge. Energy stored by capacitors containing linear dielectrics.

Read: Chap. 28 & 29

Problems (PS 5):
Chap. 28 problems: 29, 37, 43, 47, 48

[Due: Wednesday March 7, 11:59 pm]

Exam #1: Wed 7-10 pm

Covering through the end of Chap. 26

No lab this week
6. March 5
Currents, Resistance, and DC Circuits

Mar 5: Microscopic models of current and Ohm's law

If charges are flowing rather than static, a conductor can support an electrostatic field. Battery drive charges: takes charges from one end of wire, puts them back on the other, so that a current flows but the net charge on the wire doesn't change. Electrostatic field in a long thin wire is approximately uniform througout the wire, points tangent to the wire. Current and current density defined. Ohm's law: V=IR, where R is a constant (i.e. independent of I and V). Microscopic physics of Ohm's law.

Mar 7: Ohm's law / Combining resistors

Microscopic physics of Ohm's law: electrons have large random speed, scatter often. External field imposes a small drift velocity on top of this motion. Resistance in terms of microscopic properties of charge carriers and geometry of conductor. j=E/rho. Adding resistance in series and in parallel.

Mar 8: Analyzing DC circuits

Circuits. Electromotive force (EMF) is the amount of electrical energy per unit charge delivered by a source. Energy balance of a circuit in steady state yields Kirchoff's voltage law. Single-loop circuits using Kirchoff's voltage law. Multiloop circuits using (1) loop method, (2) branch method.

Mar 9: RC circuits

Power and energy in circuits. Power by an EMF on charge. Power dissipated by a resistor. RC circuit: Kirchoff's voltage law and solutions in RC circuits with battery (charging the capacitor). Solutions are simple exponentials with characteristic time RC.

Read: Ohanian Chap. 29 & 30

Problems (PS 6):
Chap. 29, Problems: 13, 15, 17, 31, 37, 43, 54
Chap. 30, Problems: 3, 11, 17

[Due: Wednesday, March 14, 11:59 pm]

Lab 4: Semiconductor diodes (EI)
7. March 12

Mar 12: RC circuits / Magnetic force law

RC circuit: discharging a capacitor in an RC circuit without battery. Magnetism: some history. Empirically-determined force law for the extra (non-Coulomb), velocity-dependent contribution to the force between two charged particles moving parallel to each other (with constant velocities).

Mar 14: Magnetic force law

Mar 15: Title

Mar 16: Title

Read: Chap. 30 & 31

Problems (PS 7):
Chap. 30, Problems: 19, 23, 31, 33, 37, 43
Chap. 31, Problems: 3, 7, 13, 15

[Due: Wednesday March 28, 11:59 pm]

Lab 5: Inductors (EI)
Spring break: March 18-24
no lectures!

Reading: see above

Problems: see above

8. March 26
Ampere's Law

Mar 26: Title

Mar 28: Title

Mar 29: Title

Mar 30: Title

Read: Ohanian Chap. 31 & 32

Problems (PS 8):
Chap. 31, Problems: 25, 29, 39, 40, 47
Chap. 32, Problems: 5, 8, 17, 21, 25

[Due: Wednesday, April 4, 11:59 pm]

Lab 6: RLC Circuits (Formal)
9. April 2
Faraday's Law and Electromagnetic Induction

Apr 2: Title

Apr 4: Title

Apr 5: Title

Apr 6: Title

Read: Ohanian Chap. 32, 33 & 34

Problems (PS 9):
Chap. 32, Problems: 28, 33, 35, 47, 53
Chap. 33, Problems: 7, 9, 15
Chap. 34, Problems: 11, 19, 23, 37

[Due: Wednesday, April 18, 11:59 pm]

Lab 7: Faraday's Law and Induction (EI)
10. April 9
Magnetic Materials / AC Circuits

Apr 9: Title

Apr 11: Title

Apr 12: Title

Apr 13: Title

Read: Ohanian Chap. 34 & 35

continued from last week

Exam 2: Wed. 7-10 pm

No lab this week
11. April 16
AC Circuits / Displacement current / Maxwell's equations

Apr 16: Title

Apr 18: Title

Apr 19: Title

Apr 20: Title

Read: Ohanian Chap. 35 & 36

Problems (PS 10):
Chap. 34: 33, 41
Chap. 35: 9, 11, 17, 25, 27, 29, 31, 33

[Due: Wednesday, April 25, 11:59 pm]

Lab 8: Properties of light
12. April 23
Accelerated charges / Light is electromagnetic waves

Apr 23: Title

Apr 25: Title

Apr 26: Title

Apr 27: Title

Read: Ohanian Chap. 37 & 38

Problems (PS 11):
Chap. 36: 3, 7, 17, 27, 29, 33, 35
Chap. 37: 11, 13, 21

[Due: Wednesday, May 2, 11:59 pm ]

Lab 9: Geometric Optics (Formal)
13. April 30
Geometrical Optics

Apr 30: Title

May 2: Title

May 3: Title

May 4: Title

Read: Ohanian Chap. 39 & 40

Problems (PS 12):
Chap. 37: 31
Chap. 38: 9, 23, 29, 37
Chap. 39: 4, 9, 23, 27
Chap. 40: 7

[Due: Friday May 11, 5 pm]

Lab 10: Interference and Diffraction (EI)
14. May 7
Interference and Diffraction

May 7: Title

May 9: Title

May 10: Title

May 11: Title

Read: Ohanian Chap. 39 & 40

study for the final

No lab this week.
Finals week Final exam: TBA, 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: