Homework: I'll assign weekly problem sets, due Tuesday @ 11:59 pm. You may leave your homework in my mailbox near the physics department office, or of course you may give it to me personally (please do NOT leave it in the box beside my office or stick it under my door). Homework submitted late without prior arrangement will receive a 50% penalty if submitted within three days of the due date (i.e. by Friday @ 11:59 pm), and will not be accepted for a grade after that.
Why do the homework?
I can't emphasize enough the importance of working the problems. In some of your classes homework is primarily evaluative; the point is for you to demonstrate what you've learned from the readings and lectures. In physics the homeworks are primarily instructional; you learn physics primarily by doing working problems. You must work the problems, think about the results, and understand any mistakes you've made if you wish to attain the type of understanding of the subject required of a working physicist. In at nutshell: If you can't work problems you don't know physics. I (or a grader) will grade the problems, and I'll hand out solutions. I encourage you to read the solutions and understand any mistakes immediately. If it doesn't make sense, ask me about it right away---don't wait until right before an exam.
If you've got a compelling reason why you need an extension, come talk to me in advance. I will not grant a homework extension without penalty if you ask for it on the day the homework is due, so don't ask for one. [If you need such a last-minute or post-facto extension due to extenuating circumstances (e.g. death in the family, sudden illness, travel problem), you'll need to have the Dean of Students or your Class Dean formally make such a request to me and suggest a rescheduled due date. You should also take this route if you need an extension but you don't want to tell me why (say, it's for personal or legal reasons). If you explain your reason to a Dean and the Dean tells me it's OK, that's good enough for me.] In general, though, life will be easier for you and for me if you get into the habit of doing your best to finish the problem set on time and handing in as much as you've been able to complete by the deadline.
The College requires that all written work for a course except for a final be submitted by 5 pm on the last day of classes. The physics department takes this deadline seriously. After that day/time no homework will be accepted.
Attendance at all labs is mandatory; if you must miss a lab for some compelling reason, please see Prof. Bourgeois well in advance so that we can schedule an alternative time for you to work the lab. He'll hand out a lab manual at the beginning of the semester. Please read the relevant portions of the lab manual before coming to lab. There will typically be a pre-lab quiz, administered at the beginning of the lab period, that will be based on the text of the lab manual for the day's lab. Some labs will be graded by exit inteviews, others by formal lab writeups (listed respectively as EI or formal in the last column of the lecture/lab schedule below). Please bring to lab a bound lab notebook that can be used solely for Physics 24 (we collect your lab notebooks at some point during the semester). It should be a sewn notebook (not spiral or loose leaf), and we recommend it be quadrille ruled. I also recommend you get into the habit of saving your in your network filespace when you enter data into the lab computers.
The formal lab writeups are due one week from the day the lab was performed, unless otherwise noted. Late labs will be penalized as set by Prof. Bourgeois. In any case, each lab not performed or lab report not submitted will automatically cost at least a full letter grade in the final course grade.
The roles of lectures and textbooks
Lecture will not be a regurgitation of the text, a summary of all you need to know for the course, or a how-to guide for the homework. Rather, I'll try go deeper into selected points. In lecture I'll cover material and do demonstrations related to the readings, but I won't feel obliged to be comprehensive in those places where I feel the text is adequate and I may focus only on a few points that I feel are particularly interesting or subtle. You shouldn't expect to understand what's going on without close study of the readings, and you should come to class with questions you have on the readings. Further, after we settle into the semester a bit, I expect the classes will become less lecture-oriented and more participatory; it will be difficult to reap the maximum benefit from that format if you're not sufficiently prepared to fully participate.
For the problems you can't solve, talk to classmates, attend the problem sessions, or ask me. When you ask me, either try to give you just enough of a hint to get you through, or I'll guide you through the problem with a series of leading questions. I'll never just tell you how to do it. If you run out of time and don't finish the set, start earlier next week. When the solutions come out, look over them right away, before you've forgotten all of the points you were confused about. You think you'll just get clear on it before the next exam, but there's never as much time as you think.
On the other hand, if you find the class too slow for your liking, if you have questions that you aren't getting answers to, if you'd like more detail, if you are frustrated that we aren't digging deeply enough, if you crave more applications, come talk to me. I'm very happy to provide you with additional materials or explanations that will will stimulate you and challenge you at whatever level you can handle.
One word of warning: Amherst College students tend to have lots of extracurriculars of all types. I support this (enthusiastically), and I am occasionally willing to be flexible to facilitate your participation in range of activities, but don't let your extracurriculars overshadow your academics. If you become concerned that your courses are getting in the way of your extracurriculars, you definitely have the wrong mindset. Remember why you're here.
If circumstances in your life beyond the class are the problem, you can come talk to me, but also talk to your class Dean.
Key derivations / chains of logic / results to commit to memory
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.
|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
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||
Reading: see above
Problems: see above
|8. March 26||
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||
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
Area Seminars and colloquia