*Updated: 03 May 2011 Tuesday.*

FINAL EXAM RESULTS: n 10 10 hi 165 200 lo 75 133 ave 135.5 176.3 s.d. 28.76 21.23

Monday 4/25: Office hours.

Tuesday 4/26: FINAL EXAM (2 HOURS) 8-10am. Office hours.

- Missed the Final Exam Tuesday morning? You could come by 1110 Rood at my Wednesday final, or by my office on Friday. Send me e-mail in either event.

Wednesday 4/27: (PHYS-2050 FINAL EXAM (2 HOURS) 2:45-4:45pm). Office hours.

Thursday 4/28: NOTE: No office hours.

Friday 4/29: LATE FINAL EXAM (2 HOURS) 11am-1pm.Office hours.

Monday 5/2: Office hours.

Tuesday 5/3: Grades will be done by Noon.

**Useful Suggestion:**If you can find your textbook and notes from PHYS-2070 or equivalent Introductory Physics E&M course, then your first week of class in PHYS-4400 will go much smoother. Ditto for your Calculus materials on partial derivatives, Del, Grad, Div, Curl and non-rectangular co-ord systems (polar, cylindrical and spherical).

Monday 1/10: Class begins. We begin by locating this course in the overall
study of Physics. Next we recognize that it has been some time for most people
since they had PHYS-2070 (or equivalent) Introductory E&M, so we start this
week by doing a **quick review of basic E&M**: The simple hydrogen atom
-- whatever charge is, the charge on the electron (-e) and the proton (+e)
exactly cancel. The Electric Force between two
point charges, Coulomb's Law looks like Newton's Law of Universal Gravity.
Real Electric Charges. Two charges: like
charges repel, unlike (opposite) charges attract. 1 Coulomb of charge is an
enormous amount of charge. Two 1.00 C charges separated by 1.00 meters have a
force of nine-billion Newtons acting on each other. Four Fundamental Forces in
Nature: Gravity, E & M, Weak Nuclear Force, Strong Nuclear Force. The
Hydrogen Atom: Gravity loses to Electric Force by
a factor of 200 million dectillion (!!!). The Helium Atom:
Putting more than one proton in the nucleus
produces enormous forces on the tiny protons -- Need the Neutron and the Strong
Nuclear Force (!!!).

- Quiz 1 will be in-class on Friday 14 January 2011. It will be for attendance purposes. If you miss class on Friday, you will be able to get some of the points by downloading Quiz 1A from the website and turning it in.

Tuesday 1/11: Finding the net vector electric force F_{E} for a
system of point charges. Remember: In PHYS-2070, Looking at Symmetry and Zeroes
(problems where the answer is zero) as a way of solving problems. How does
q_{1} know that q_{2} is there? -- "Action at a
Distance" -- Gravity and the Electric Force are not contact forces. The
mathematical construct of the Electric Field. E is not an observable quantity.
(Side example: Methods of measuring speed v, do not directly measure speed v.)
Electric Field is a vector. F_{E} = q E. For a point charge, E = k
q_{1} /r^{2}. SI units for E-field: (N/C). E-field lines
radiate *away* from a positive point charge; converge *towards* a
negative point charge. If the universe is charge neutral, can have all E-field
lines from + charges terminating on - charges.Why use E-fields, when you need
the force F = q E anyway? Because it allows us to examine the environment
without needing another charge. Direct integration of Electric Force and
Electric Field are similar, so we'll just go over direct integration of the
E-field. Charge distributions -- lamda (linear charge density, C/m), sigma
(surface charge density, C/m²), rho (volume charge density, C/m³).
Note the similarity to mass distributions from PHYS-2050. Examples: Rod in-line
with line from point P (1-dimensional integration). Rod perpendicular to line from point P. Note that
in all these cases, we can predict the long range behavior (E-field behaves as
a single point net charge), and anticipate the close-in short range
behavior.** Electric Flux: **Electric field times Area. Analogy of a bag or
box around a light, captures all the light rays no matter the size or shape.
Use known E-field of a point charge to evaluate what the Electric Flux must be
equal to. Review of Dot Product.
Gauss' Law for Electricity. Using
Gauss' Law for Point Charge, Conducting Sphere
(case 1: r < R). Note that E-field is zero inside a spherical conducting
sphere (solid or hollow). If the Earth were hollow, there'd be no gravity
inside the Earth either, besides being zero-gee at center of core. Using
Gauss' Law for Point Charge, Conducting Sphere,
Insulating Sphere, Infinite Line of Charge. P.E. is minus the Work.
Potential V is similar, but the integral is done on E-field not Force. More
importantly the Potential V is an observable quantity. Find components of E by
negative of the partial derivative of Electric Potential function V. It will
turn out that charge accumulates on the tips of long pointy things -- applies
in why some things seem to always get hit by lightning (golfers, people
standing in an open field, church steeples). E_{max} = 3,000,000 N/C =
3,000,000 V/m, in dry air. Ben Franklin and lightning rods. Why your hair
stands up warning you that you are getting charged. Handy chart of the four
quantities: F_{E} (vector, 2 charges), E (vector, 1 charge),
U_{E} (scalar, 2 charges), V (scalar, 1 charge) .Simplified equation V
= E d. (But remember that it's really *delta-V = - E d .*) Example:
Lightning.

- NOTE: All these review items come from the lecture notes for PHYS-2070 from Summer-II 2010.
- Review of vectors and vector forces. Review of vector notation for components and Standard Form. Right Triangles and Adding and subtracting vectors: Analytical method. (Check to make sure your calculator is set for Degrees mode. Try cos 45° = sin 45° = 0.7071) Why arctangent is a stupid function on your calculator.
- Sample Solution for Vector Problem of net Force on charge 1.
- Review of 2-D and 3-D Integration. Rectangular (area, volume), Polar (circumference, area), Cylindrical (volume, surface area). Spherical Co-ordinates (volume, surface area, hollow volume).
- Please note there will not be classes on Monday 17 January 2011 as Western observes the commemoration of Dr. Martin Luther King, Jr.-- MLK Day activities start on Friday 14 January 2011.

Thursday 1/13: Distribute Syllabus.
Moving from Field Theory to Applications leading to Devices. Start of
Capacitors and Capacitance. The Capacitor stores charge +Q on one plate and -Q
on second plate, stores energy in the E-field between the plates. This is
different from a battery, which has energy stored in its chemical reaction.
Capacitor Equation. SI unit for Capacitance is
the Farad. 1F is a large capacitor. Usually deal with µF (microfarad =
1/1,000,000th of a Farad) and pF (picofarad = 1/1,000,000,000,000th of a
Farad). Apply Gauss' Law for Electricity to the constant E-field of the
Parallel Plate Capacitor. We now have an
"operational equation", true for all capacitors, and a "by
geometry" equation for the special case of the parallel plate capacitor.
Work to assemble charges on a capacitor = Energy stored in the capacitor = U =
½CV² . Making a real capacitor. What if not filled with air? Filling
with conductor, must have at least one gap, otherwise will short outthe plates.
A conducting slab inside a parallel plate capacitor makes two capacitors in
series. Charge neutral slab stays charge neutral, but +Q of top plate attracts
-Q on top of slab, and -Q of bottom plate attracts +Q on bottom of slab.
Dielectrics -- an insulator where the +/- charge pairs are free to rotate, even
if they do not move. Dielectric constant (kappa) and Dielectric strength
(E-max). (See Table 26-1, p. 736) Dielectic constant increases capacitance over
air gap. Dielectric strength usually bigger than E_{max} in air. Both
allow you to (a) make bigger capacitors (or smaller for the same values) and
(b) make non-hollow, self-supporting components. Electrolytic capacitors --
must be connected into the circuit with correct + and - polarity. Resistance
vs. Conductance. Ohm's Law: V=IR form. (Ohm's
"3 Laws") We usually treat the wires in a circuit as having R=0, but
they usually are not superconductors. Resistance is a function of temperature.
Kammerleigh Onnes 1916 work on extending the R vs. T curve toward T = 0 Kelvin.
Discovered Superconductivity, where R=0 identically. Resistance by geometry. R
= rho (L / A), where rho = resistivity of the material, L = length and A =
cross-sectional area. Magnetic Force on a Moving
Electric Charge - The Cross Product and Right-Hand Rule (R.H.R.). The Cross
Product (or Vector Product) is the exact opposite of the Dot Product (or Scalar
Product). Multiplying two vectors together by a cross product gives us another
vector (instead of a scalar). And the cross product is not commutative,
vector-A × vector-B = - (vector-B × vector-A), so the order is
paramount. Using Right Hand Rule to assign directions to x,y,z coordinates.
Constant speed, perpendicular constant magnetic force --> Uniform Circular
Motion. Cyclotron frequency -- no dependence on
the radius (constant angular velocity). Velocity
Selector - the Magnetic Force is speed dependent, the Electric Force is
not. So we can use an E-field to create an Electric Force to cancel the
Magnetic Force on a moving charged particle, such that at the speed v = E / B,
the particle travels exactly straight with no net force -- any other speed and
the particle is deflected into a barrier. Hence a velocity selector
"selects" velocities... A current carrying wire consists of moving
electric charges, and so therefore would see a magnetic force from a magnetic
field. Discussion of microscopic theory of charges in a conductor. Drift
velocity is the very slow net movement of the electrons moving randomly in the
wire. Magnetic Force on a Current Carrying
Wire. Demo -- hey it works and even in the right direction! Technically
current is not a vector, despite the fact we talk of direction of current. J =
current density = current/cross-sectional area is the vector related to
current. *NOTE: J-vector = sigma × E-vector (current density =
conductivity × E-field) is the vector version of Ohm's Law. *

- Hopefully the door to 3363 Rood will not be locked tomorrow -- otherwise we might have to move to 2202 Everett -- Bradley Commons -- again.

Friday 1/14: Q1 and your PID number. (If you missed Quiz 1 you will be able
to get some of the points by downloading Quiz
1A from the website and turning it in.) The
Biot-Savart Law.
B-field from a infinitely long straight current
carrying wire by direct integration. Gauss' Law for Magnetism. Not as useful as
Gauss' Law for Electricity, because it is always zero (no magnetic monopoles).
However, there is something we can use in a similar way which involves
involving a path integral along a B-field and the current(s) contained inside
-- Ampere's Law. Use in a way similar to the
way we used Gauss' Law for Electricity. Use symmetry and geometry to select
your Amperean Loop to your advantage. 3-D directions and R.H.R. *You can make
a list of axes directions or unit vectors (x y z x y z) and (i j k i j k) and
find the 3rd direction of the cross product by going to the right (+) or to the
left (-) in the list. Example: i-hat × j-hat = +k-hat, since order is
"i j k", but j-hat × i-hat = -k-hat, since "j i k"
goes to the left. *Ampere's Law. Use in a
way similar to the way we used Gauss' Law for Electricity. Use symmetry and
geometry to select your Amperean Loop to your advantage.
Faraday's Law of Induction. A changing
magnetic flux induces a current, induces an e.m.f., in the circuit,
substituting for the battery as the power source. Lenz's Law "of
maintaining the status quo." The coil acts as if it opposes any change of
the magnetic flux inside, by inducing a magnetic field to cancel and increasing
flux or maintain a decreasing flux. To create this induced magnetic field, one
needs an induced current, which is powered by an induced *emf*. It is
Lenz's Law that gives us the minus sign in Faraday's Law of Induction. -- it
doesn't work properly in the gap between the plates of a capacitor while it is
charging. So James Clerk Maxwell fixed it with a "displacement
current" term, involving the time derivitive of the Electric flux in the
gap. Ampere-Maxwell Law. Maxwell's
Equations in integral form. Note that Maxwell didn't invent the four
equations, only half of one, but he figured out what todo with them. E & M
Waves. In vacuum (free space): a traveling set of perpendicular E-fields and
B-fields, as sine waves constantly changing in space and time, moving with wave
speed c (the speed of light in vacuum). **Review of the Del operator.**
Partial derivatives, gradient, divergence, curl, Del-squared.

- Hooray! We have a key to 3363 Rood now.
- Q2 will handed out next week, reviewing the Del operator. HW1 will now be due Thursday 20 January 2011.
- Remember, no classes on Monday due to MLK Day Activities.

- HW Set 1 is now due on Thursday 20 January 2011.
- NOTE: Dr. Phil has an appointment with the new PIO rep at 11:30am-Noon on Tuesday 18 January 2011.

Monday 1/17: MLK Day -- No Classes.

Tuesday 1/18: Working with 3rd and 4th of Maxwell's Equations to generate
partial differential equations of E(x,t) and B(x,t). (see pp. 958-959 in
Serway) Looking at the solution to Traveling E-M
Wave, with v in x-direction, E in y-direction and B in z-direction. Angular
frequency omega, wave number k. c = E_{max} / B_{max}.

Thursday 1/20: **Modern Physics** -- goes to size/time/length scales far
outside our normal experience. Classical Relativity (two observers, two frames
of reference), Special Relativity (speed constant), General Relativity
(accelerations or gravity). Einstein's postulates: (1) All observers see the
same Physics laws. (2) All observers measure the speed of light in vacuum as c.
Beta, gamma, Length Contraction and
Time Dilation. Alpha Centauri is 4.20 LY from Earth (proper length). Those
on a starship see a different distance and experience a different time than the
observer left on the Earth. But both think the other observer is moving at v
< c. No preferred observer in Special Relativity. Two observers cannot agree
on what they see, distance or time. They can only agree that the speed of light
in vacuum is c. One sees the proper length: a length measurement where both
ends are measured at the same time. One sees the improper length: a length
measurement made at two different times. Neither observer is preferred -- that
is one is not "more right" than the other. They are both right. These
differences in time and length measurements have been confirmed by experiment.
Experimental confirmation of Special Relativity: put atomic clocks on aircraft,
spacecraft. Two observers cannot agree on the *order* of events, either.
The concept of "simultaneity" is gone. Another confirmation of
Special Relativity: Muons (a form of heavy electron) are created in the upper
atmosphere -- they're unstable and will decay. Muons measured at mountaintop --
by sea level, nearly all should have already decayed. But you detect almost as
many at sea level as on the mountaintop, because the muon lifetime is measured
in the muon's rest frame *not* while we are watching it moving. The
Correspondence Principle -- at some point our Classical Physics results need to
match the Modern Physics results. So when do we need Special Relativity? For
eyeball measurements, we have trouble distiguishing the size of things that are
only off by 10%. That would correspond to a gamma = 1.10, and a beta = 0.417 c.
Difference in time with identical clocks left on the ground. Quiz 2 Take-Home
handed out Thursday 20 January 2011 on reviewing the Del operator, due Tuesday
25 January 2011.

Friday 1/21: *Apologies for cancelling class -- it normally takes me 1
hour 15 minutes to drive in. Friday it took over 2 hours -- there was no way,
given how fast cars were traveling on the slick roads, that I could get to
Kalamazoo in time. Sorry for anyone inconvenienced.*

Monday 1/24: **Prologue (Chapter 0):** Brau's review of E&M uses more
technical versions of the equations we used in PHYS-2070. For Coulomb's Law and
the Electric Field, it looks like we now have an inverse cube law ( 1/r³ )
instead of inverse square ( 1/r² ). But this is an illusion, brought on
because we are using r-vectors in the top of the fraction and not r-hat unit
vectors. Previously we saw Maxwell's
Equations in integral form. Now we have
Maxwell's Equations
in differential form.

- Exam 1, originally scheduled for Friday 28 January 2011, will be moved to next Thursday 3 February 2011.

Tuesday 1/25: **Chapter 1:** Previous waves involved some sort of medium
-- vibrating strings, vibrating drumheads, sound in air, waves in water, etc. A
disturbance traveled *through* the material, the material itself only
undergoes small displacements. If Maxwell was right and light is an E-M wave,
then what is waving in free space (vacuum)? It was postulated that there had to
be an "aether" -- spreads throughout space, no mass, can't be seen,
but has extremely high tension to account for visible light vibrations.
Fizeau's
experiment for determining speed of light in flowing water. At first it was
thought to confirm the possibility of an aether, but others showed it was
possible to come up with the same terms without an aether.
Michelson-Morley
experiment showed no variation in speed of light due to the background flow
of any aether. The speed of light in vacuum is the same, regardless of
direction or motion. Therefore there cannot be an aether. This leads eventually
to Einstein's postulates for relativity. Previously we looked at 1-dimension
plus time. Now we want to look at 3 spatial dimensions (x, y, z) and 1 temporal
dimension (ct) -- by looking at *ct* and not *t*, this fourth
dimension has the same units as the others. Minkowski space and the world line
of an event. Light cone -- event at origin, information about the event (past
and future) must lie within the line cone.
For Euclidean
geometry in 3-dimensions, the square of the magnitude of the differential
displacement is always going to be positve.
For the Pseudo
Euclidean used for relativistic Minkowski space, we add minus signs to the
spatial part, so that the square of the magnitude of the differential
displacement will be *ds² > 0* for time-like events, *ds² =
0 *for light-like events and *ds² < 0* for space-like events.
The *ds² = 0* result will make sense when we realize that if you are
a photon, a particle of light, there is no time to the universe and the
universe has zero length.

- NOTE: I made an error, which was bugging me, on the board -- misread the
Euclidean differential distance as
*dt*when it should be*dl*. Now it makes sense. Error brought on by a combination of poor lighting and small italic font.

Thursday 1/26:

- Hyberbolic functions.
**HW2 (Part 1):**Exercises 1.2, 1.3 p.41. Due Tuesday 1 February 2011.

Friday 1/27: Q2 Solution handed out. Topic 1 assigned.

- Exam 1, originally scheduled for Friday 28 January 2011, will be moved to next Thursday 3 February 2011.
**HW2 (Part 2):**Exercises 1.4, 1.5 p.44-46. Due Tuesday 1 February 2011.*NOTE: It's okay if you can't complete these two problems.*

- HEADS UP: Weather forecast for Tuesday night / Wednesday is for Serious Snow -- if the storm follows one particular track, we may have more than a foot of snow or more. Even if WMU is open on Wednesday, there is a chance I might not be able to dig out of my driveway in time for Office Hours..

Monday 1/31:

- Exam 1 will have two problems -- (1) on some aspect of our review of E&M, (2) a "relatively" simple relativity problem.

Tuesday 2/1:

- Solution for Q2 (Del operator quiz).

Thursday 2/3:

Friday 2/4: Exam 1. (Re-Rescheduled)

Monday 2/7: Multi-pole moments. Dipoles, quadripoles.

**HW3:**Exercises 3.3, 3.6 p.135-136. Due Friday 11 February 2011.

Tuesday 2/8: Showing that solutions for Phi in boundary values are the same
solution. Work to assemble charges on multiple conductors in a capacitor. NOTE:
If you are wondering why the C_{ij} matrix is the inverse of the
K_{ij} matrix, recall that for a simple parallel plate capacitor, the
energy stored is U_{c} = Q²/2C,

Thursday 2/10: The parallel plate capacitor. Method of Images. Start of Separation of Variables. Quiz 3 Take-Home on the integral and differential forms of Gauss' Law for Electricity in Spherical Coordinates, due Tuesday 15 February 2011.

- Not assigned for HW, but you should look at Exercise 3.10.

Friday 2/11: Separation of Variables. PHI(x,y,z) = X(x) Y(y) Z(z) from Section 3.2.4.

- Look over Section 3.2.5 which uses prolate spheroidal coordinates (!). Introduction to Legendre Polynomials.

Monday 2/14: Laplace's Equation in Spherical Coordinates. Separation of variables. The Legendre Polynomials -- The Rodriguez Equation.

- Because we moved Exam 1, Exam 2 will be moved to Thursday 24 February 2011.

Tuesday 2/15: Solving for Legendre Polynomials. Spherical Harmonics.

- Alternate Textbook: Introduction to Electrodynamics (3rd Edition) / David J. Griffiths.

Thursday 2/17: Physical vs. "pure" multipoles. Showing that
multipole expansion of an arbitrary charge distribution at large distance gives
us the sum of Legendre polynomials, *P _{l}(cos(theta))*. Quiz 4
Take-Home on orthogonality of sines, due Tuesday 22 February 2011.

- NOTE: 2nd part of Q4 had a problem, so will rewrite as a homework problem. Meanwhile, you might want to consider the function (1 - (3/2) sin²(theta)) and whether you can write it in terms of one or more Legendre polynomials.

Friday 2/18: If a charge distribution has a net charge Q, then for large
values of *r*, the monopole term should dominate the potential *V*.
If Q=0, then the dipole term should dominate for large *r*, unless the
dipole moment **p** is zero. For physical dipoles, the location of the
origin will affect the dipole moment.

**HW 4:**(Click here for a copy.) Due Tuesday 22 February 2011(?)

- Re Q4: The equation you want is I believe Brau p. 147 equation (3.129).
- This is going to be a short week. Do not put off starting to study for Exam 2. Have questions for Tuesday Office Hours.

Monday 2/21: Dr. Phil has canceled his classes due to treacherous roads.

Tuesday 2/22: Return X1.

- Review comments: We'll have a quiz on dipoles after Break. For now, concentrate on separation of variables in Cartesian coordinates (Brau Section 3.2.4, starting on p.145), and the orthogonal integrations of Fourier series and Legendre polynomials.

Thursday 2/24: Exam 2.

Friday 2/25: Spirit Day. (No Classes)

WMU SPRING BREAK

- Hope you got some well-deserved break time in!

Monday 3/7: Inducing a dipole moment in a neutral atom by an externally
applied E-field. CRC Handbook of Chemistry & Physics data: makes sense that
atoms in the periodic table with 1 *s* electrons (H, Li, Na, K, Cs) have
much larger atomic polarizabilities (alpha) than filled shell noble gasses (He,
Ne, Ar, etc.)

Tuesday 3/8: Using atomic polarizability of a spherical shell of electrons to compare to Hydrogen result. (Using a quantum mechanical charge density rho(r) will be HW5 -- see below.) Some molecules have a permanent dipole moment, such as water. Effects of having E-field parallel or perpendicular to the line of the molecule. The general polarizability tensor in 3-D. Torques caused by dipole moments not aligned with applied E-fields.

**HW 5:**Due Monday**14 March 2011**.

Thursday 3/10: Interpretting polarization as bound surface charges (sigma-sub-b) and bound volume charge densities (rho-sub-b).

Friday 3/11: Return X2. The bound surface and volume charge densities are
not "fictitious" charges, like the image charge method we used with
conductors, but actually charge separations as a result of either induced or
permanent polarization. Quiz 5 is actually it's *Griffiths p. 170 Problem
4.11*, assigned Friday 11 March 2011 on orthogonality of sines, due Tuesday
15 March 2011.

- If you try to look up "bar electret" in Wikipedia, one of the articles you'll get is about the Electric Displacement vector, D, which we will cover next week -- the citation? Griffiths, Intro to Electrodynamics, 3rd edition. (grin)
- Barium titanate
is BaTiO
_{3}, by the way. - Time Change on Sunday! 2am Eastern Standard Time magically becomes 3am Eastern Daylight Time. Adjust your clocks accordingly.

Monday 3/14: (1) An argument regarding whether or not it matters that the
work last week essentially used perfect dipoles, rather than physical dipoles.
It turns out we're okay. (2) Development of the Displacement Field vector,
**D**, due to both bound charge densities and free charge densities.
Re-writing Gauss' law for **D** rather than **E**. Note that unlike
**E**, where curl-**E** = 0, that curl-**D** is not necessarily zero,
because curl-**P** isn't necessarily zero -- it isn't for the bar electret,
for example. This means that the Displacement Field vector **D** cannot be
written as the gradient of a scalar potential, unlike **E .**

Tuesday 3/15: *Discussion of situation with Fukushima I Nuclear Plant
after tsunami damage in Japan, historical context with Three Mile Island in
Pennsylvania and Chernobyl in the former Soviet Union.*

- Posted video of tsunami damage on my LiveJournal blog here.
- Japanese Reactors Fukushima I (Units 1-4) (ongoing 2011).
- Three Mile Island (1979).
- Chernobyl (1986).
- Article on Michigan and Midwest nuclear reactors.
- Fears vs Reality Over Radiation in West Michigan. *** Added 3-16-2011
- Chalk River reactor in Canada (1952) and then Navy Lt. Jimmy Carter. *** Added 3-16-2011

Thursday 3/17: The electric susceptility, chi-sub-e, the permitivity of a
material, epsilon-naught × chi-sub-e, and the relative permitivity, (1 -
chi-sub-e) = kappa = dielectric constant. Using the Displacement vector
**D**, to find **E** and **P**.

- HW6 will be Griffiths Problem 4.17. Due Tuesday 22 March 2011.
- Quiz 6 will be Griffiths Problem 4.15. And Griffiths Problem 4.18 (illustration on p.185). Due Thursday 24 March 2011.

Friday 3/18: For linear dielectrics, since **D** and **P** are both
proportional to **E**, then since **curl E** = 0, then are **curl D**
and **curl P** also zero? Not necessarily. For example, if one does a closed
line integral of **P · dl** around a path that goes on both sides of an
interface between two media, then **P** will have two values of chi-sub-e,
and so the parallel legs won't cancel. By Stoke's theorem, therefore **curl
P** is not zero. In a crystal, it is easier to polarize in some directions
than others, so we may get a susceptibility tensor, with 9 terms. For isotropic
media (isotropic homogeneous linear dielectric) only the xx, yy and zz diagonal
terms survive, and they're all the same.

- HW5: actually it's
*Griffiths p. 179 Problem 4.17*, due Tuesday 22 March 2011. - Q6 is a Take-Home, actually it's
*Griffiths p. 177 Problem 4.15*, assigned Thursday 17 March 2011. and*Griffiths p. 184-185 Problem 4.18*, assigned Friday 18 march 2011, and due Thursday 24 March 2011.

Monday 3/21: *Griffiths Example 4.7, pp. 186-188. *A while ago we
looked at a conducting sphere in a uniform external E-field in the
+z-direction. (E = 0 inside, E-field lines must terminate perpendicular to the
conducting sphere's surface -- otherwise there is a parallel E-field and the
surface charges would still be moving and we wouldn't be in electrostatic
equilibrium.) Now we look at a dielectric sphere in the same uniform external
E-field in the +z-direction. Have to solve the Boundary Values problem for the
potential *V*. (E inside is parallel to external E-field. E-field lines do
not have to end up perpendicular to surface.)

**Thought Question:**Since epsilon-sub-r = kappa > 1 for dielectrics, then 3/(kappa + 2) < 1 and E_{inside}= 3/(kappa + 2) E_{0}< E_{0}. Why should this be so?- Exam 3 is on dipoles and dielectrics, through material from Friday 3/18.

Tuesday 3/22: *Griffiths Example 4.8, pp. 188-190. *Put a charge +q at
(0,0,d) on the z-axis above the x-y plane. To find the force on the charge if
there was a semi-infinite conductor at z < 0, we solved this by method of
images by placing a charge -q at (0,0,-d). Now imagine that instead of a
semi-infinite conductor, we put a dielectric.

- Some perspective on radiation, from the brilliant author of the webcomic xkcd -- article and chart.
- One of the problems for
*next*week I have labeled as Quiz 7,*Griffiths p. 190 Problem 4.23*, assigned Tuesday 22 March 2011, and due Thursday 31 March 2011.

Thursday 3/24: Energy stored in a capacitor with dielectric. Note that there is more than one way to consider what we mean by the energy to assemble a system -- one may or may not be including the work to "stretch the springs" in the dielectric. Electric force pulling a dielectric slab into a parallel plate capacitor due to real fringe field effects.

- HW5 Solution. Q6 Solution (complete).

Friday 3/25: Exam 3.

Monday 3/28: Discussion of Electric and Magnetic Forces and Fields of
*Moving* Electric Charges.

- HW7:
, assigned Monday 28 March 2011, and due Thursday or Friday 31 March or 1 April 2011.*Griffiths p. 196-7 Problem 4.28*

Tuesday 3/29: Lorentz Force. Magnetic Force on a Moving Electric Charge - The Cross Product and Right-Hand Rule (R.H.R.). The Cross Product (or Vector Product) is the exact opposite of the Dot Product (or Scalar Product). Multiplying two vectors together by a cross product gives us another vector (instead of a scalar). And the cross product is not commutative, vector-A × vector-B = - (vector-B × vector-A), so the order is paramount. Using Right Hand Rule to assign directions to x,y,z coordinates. Constant speed, perpendicular constant magnetic force --> Uniform Circular Motion. Cyclotron frequency -- no dependence on the radius (constant angular velocity). If there is a component of the velocity along the B-field direction, get helical paths. Charged particles from the sun directed towards poles -- origins of auroras. Radiation exposure on over-the-poles airline flights. Significant that (a) Mars has only a thin atmosphere and (b) not much magnetic field?

- Picture of the first cyclotron.

Thursday 3/31: Discussion of the cyclotron. "Dees" refer to semi-circular (D-shape) magnets. The National Superconducting Cyclotron Lab at MSU. We usually treat the wires in a circuit as having R=0, but they usually are not superconductors. Resistance is a function of temperature. Kammerleigh Onnes 1916 work on extending the R vs. T curve toward T = 0 Kelvin. Discovered Superconductivity, where R=0 identically. High-temperature superconductors.

April 4/1: Velocity Selector - the Magnetic
Force is speed dependent, the Electric Force is not. So we can use an E-field
to create an Electric Force to cancel the Magnetic Force on a moving charged
particle, such that at the speed v = E / B, the particle travels exactly
straight with no net force -- any other speed and the particle is deflected
into a barrier. Hence a velocity selector "selects" velocities...
Velocity Selector. Mass Spectrometer -
different semi-circular paths for ions of different mass but same velocity. Can
determine chemicals, molecules, and separate isotopes (same element, different
number of neutrons in nucleus, so different mass -- cannot be separated by
ordinary chemical means). Mass Spectrometer as Calutron -- detecting or
separating isotopes, something that cannot be done by ordinary chemical means.
1895, J.J. Thompson discovers charge and mass of the electron. *Griffiths
Example 5.2* -- E- and B-fields acting on a charge initially at rest. Get a
cycloid trajectory, similar to a point on the rim of a rolling wheel. Next up,
electric current. **Hall Effect** -- a device with no moving electrical
parts -- proves that charge carriers in a current carrying wire are negative,
not positive.Quiz 8 Take-Home, based on *Griffiths Example 5.2* from
class, due Tuesday 5 April 2011.

- HW7 now has a hint.

Monday 4/4: Current carrying wire. I-vector, K-vector, J-vector.

Tuesday 4/5: Calculating current density J for (a) uniform current, (b) radially dependent current and (c) non-uniform current (!). The Divergance of J-vector is a statement on charge conservation (Continuity Equation). Electrostatics vs. Magnetostatics. The Biot-Savart Law.

- Q8 based on
*Griffiths Example 5.2*from class, assigned Friday 1 April 2011, and now due Thursday 7 April 2011. - HW8:
, assigned Tuesday 5 April 2011, and due Friday 8 April 2011.*Griffiths p. 214 Problem 5.6* - Note that Problem 5.6 (b) has implications for why the electron, which we usually think of as a point charge, actually has a magnetic moment due to its charge density (or surface charge density) spinning either clockwise or counter-clockwise to its direction of travel. Hence its magnetic moment and hence its two values of spin, ±½.

Thursday 4/7: B-field on the z-axis above a circular loop of current. The divergence and curl of B.

Friday 4/8: Ampere's Law. B-field from a long straight wire -- almost a "circular argument". B-field from an infinite sheet of current -- magnetic analog to the infinite sheet of charge. Open vs. closed coils, how we make coils -- and why we model coils as stacks of circular currents.

- Beginning Monday, April 11, the Course/Instructor Evaluation System (ICES Online) will open to students for the spring 2011 administration. (via GoWMU)
- Monday 11 April 2011 is the last day to turn in a Draft paper for your science literacy book report.

- Don't forget about your 2010 taxes, if you have to file.
- Monday is last day to turn in a Draft paper, if you want to.

Monday 4/11: Return X3. Ampere's Law and B-field from a long straight Solenoid, Toroidal coil.

- Quiz 9 is a Take-Home,
*Griffiths Problems 5.13 and 5.16*from class, assigned Monday 11 April 2011, and due Thursday 14 April 2011.

Tuesday 4/12: We're almost to Maxwell's Equations in differential form. Comparisons and differences between E and B -- they seem to be opposites. Still no magnetic monopoles. The Vector Potential A for creating B. Modifying A so as to get cleaner equations. Because A is a vector, ultimately it is not as useful as the scalar potential V is to E.

- With yesterday's work on Ampere's Law, we have closed the book on Exam 4 material.
- Why April 12th is a significant day in the history of Soviet and American space programs.

Thursday 4/14: Griffiths looks at the 5 equations linking J-vector, A-vector and B-vector -- the 6th equation for symmetry's sake is "not very useful". E-field has discontinuity at a surface charge, likewise B-field has discontinuity at a surface current. A-vector is continuous across the boundary, but the first derivative to the normal component is discontinuous. Multi-pole expansion of the vector potential A. The monopole term must be zero, because (a) we have detected no magnetic monopoles and (b) we therefore designed the vector potential A with no magnetic monopoles in mind. First Day to turn in your Topic 1 Paper.

- Current Homework 9: assigned Thursday 14 April 2011, and due Tuesday 19 April 2011.
- HW9 isn't due until next Tuesday -- I'd set it aside until after Exam 4.
- Q7/HW7/Q8/HW8 Solution. Q9 Solution.
- For Exam 4 tomorrow: Magnetism. And the Biot-Savart Law takes too much time to do on the test, so Ampere's Law is more useful for us.

Friday 4/15: Exam 4. Second Day to turn in your Topic 1 Paper.

- Helpful Hint: Remember this is a Science Literacy paper, NOT just a Physics paper. Some of the books don't touch much on Physics at all -- they're on the list to help cover all the sciences, engineering, math, computers, technology, medicine -- and the morality and ethics of using them.

- Monday is the last day to turn in your Topic 1 papers, in class or by 5pm.
- Get your taxes done?
- Reminder that ICES Student Course Evaluations are available online via GoWMU 4/11 Mon through 4/24 Sun.

Monday 4/18: Multipole Expansion of magnetic vector potential **A**.
There is no monopole term. Expect the dipole term to dominate. Magnetic Dipole
Moment, **m** = I **a** , where a-vector is the area enclosed by the
current loop, with the direction taken by the "Mode 2" R.H.R. around
the current. Note that if we did find magnetic monopoles, it might be the case
that we'd try to make a magnetic dipole moment **m** =
q_{m} **d** , in a way similar to the electric dipole moment of
two charges ±q separated by a displacement vector **d** . Finding
magnetic dipole moment for a current loop which can be made from two
perpendicular square loops. Last Day to turn in your
Topic 1 Paper. (Unless you had a Draft paper
looked at by Dr. Phil.)

- Homework 10:
*Griffiths Problems 5.34*from class, assigned Monday 18 April 2011, and due Thursday 21 April 2011. - Quiz 10 is a Take-Home,
*Griffiths Problems 5.35 and 5.36*from class, assigned Monday 18 April 2011, and due Thursday 21 April 2011. - The Final Exam will have FIVE problems on it, of which you get to choose which FOUR will count.

Tuesday 4/19: Griffiths Chapter 6: Magnetization and H-vector. Chapter 7: Ohm's Law. (PDFs of lecture notes.)

- Topic 1 Papers, unless you had a Draft evaluated by Dr. Phil, are now officially LATE -- and will incur a 0.010 point a day penalty.

Thursday 4/21: Return X4. Griffiths Chapter 7:
Faraday's Law of Induction,
Displacement Current correction to Ampere's Law and Maxwell's Equations in
various formulations. **Superconductors**. Once a supercurrent is
established, one does not need an internal E-field to keep it going. A
superconductor cannot support an internal B-field -- Meissner Effect -- which
means that the supercurrents must be on the surface -- i.e., the difference
between Exam 4 Problem 2 parts (b) and (c) for s < a. A superconductor can
fail, lose its superconductivity if any of the critical parameters are
exceeded: critical temperature (T_{c}), critical current density,
critical external B-field.

Friday 4/22: Chapter 9: Traveling E-M wave solutions to Maxwell's Equations -- for free space and in linear media. And we nearly made it up to Wave Guides, p. 405, which was something of a goal had we not had to adjust the course partway through.

- Finals Week Office Hours posted.
- Note that Dr. Phil will NOT be in to campus on Thursday 28 April 2011.
- The Late Final Exam is Friday 29 April 2011, 11:00am-1:00pm, in Bradley Commons next to Dr. Phil's office. Send Dr. Phil and e-mail if you plan on coming to the Late Final Exam, so I can plan to print up enough copies of XFL.