Dr. Phil's Home

## Lectures in PHYS-4400 (1)

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
```

### Week of April 25-29, 2011.

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.

### Week of May 2-6, 2011.

Monday 5/2: Office hours.

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

### Week of January 10-14, 2011.

• 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 FE 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 q1 know that q2 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. FE = q E. For a point charge, E = k q1 /r2. 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). Emax = 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: FE (vector, 2 charges), E (vector, 1 charge), UE (scalar, 2 charges), V (scalar, 1 charge) .Simplified equation V = E d. (But remember that it's really delta-V = - E d .) Example: Lightning.

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 Emax 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.

• 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.

### Week of January 17-21, 2011.

• 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 = Emax / Bmax.

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.

### Week of January 24-28, 2011.

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:

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

• Note: The actual Topic 1 Handout is 27 pages long. You've been given pages 1,2,11 and 27, and the link to the Topic 1 Assignment webpage. There you can see the whole handout as a PDF or as a Searchable HTML page with links to jump to the main topics.
• If this all seems like Too Much Information, come see Dr. Phil and he'll help you find something of interest.
• 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.

### Week of January 30-February 4, 2011.

• 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)

### Week of February 7-11, 2011.

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 Cij matrix is the inverse of the Kij matrix, recall that for a simple parallel plate capacitor, the energy stored is Uc = 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.

### Week of February 14-18, 2011.

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, Pl(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(?)

### Week of February 21-25, 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)

### Week of February 28-March 4, 2011.

WMU SPRING BREAK

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

### Week of March 7-11, 2011.

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 BaTiO3, by the way.
• Time Change on Sunday! 2am Eastern Standard Time magically becomes 3am Eastern Daylight Time. Adjust your clocks accordingly.

### Week of March 14-18, 2011.

• Did you remember to reset your clocks an hour ahead for Daylight Saving Time?
• Mid-Term Grades are now available via GoWMU.
• 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.

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.

• 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.
• ### Week of March 21-25, 2011.

• 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 Einside = 3/(kappa + 2) E0 < E0. 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.

### Week of March 28-April 1, 2011.

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

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

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?

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.

### Week of April 4-8, 2011.

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: Griffiths p. 214 Problem 5.6, assigned Tuesday 5 April 2011, and due Friday 8 April 2011.
• 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.

### Week of April 11-15, 2011.

• 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.

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.

### Week of April 18-22, 2011.

• Monday is the last day to turn in your Topic 1 papers, in class or by 5pm.
• 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 = qm 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 (Tc), 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.