Dr. Phil's Home
Updated: 27 December 2008 Saturday.
Monday 12/1: Poynting Vector, S. Traveling E-M Wave, Poynting Vector and Intensity. Energy stored equally in E- and B-fields of the E-M wave. Momentum and Pressure of light waves absorbed or reflected on contact. (Complete absorption like totally inelastic collision; complete reflection like totally elastic collision).
Tuesday 12/2: Despite some of the sample exam problems, we will not be doing geometric or physical optics in PHYS-2070 this semester. However, a taste of 20th century physics to finish the course: Classical Relativity (two observers, two frames of reference), Special Relativity (speed constant), General Relativity (accelerations or gravity). Waves in air, water, require a medium. 19th century "ether" for light. Michaelson-Morley Experiment found no evidence of ether. Quiz 20 is a Take-Home quiz, handed out Tuesday 2 December 2008 and due Wednesday 3 December 2008. (Click here for a copy.)
Wednesday 12/3: 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. One sees the proper length: a length measurement where both ends are measured at the same time. One sees the proper time: a time measurement where beginning and end are measured at the same place. Experimental confirmation of Special Relativity: put atomic clocks on aircraft, spacecraft. Difference in time with identical clocks left on the ground. Two observers cannot agree on the order of events, either. The concept of "simultaneity" is gone. Second set of Sample Final Exams handed out. (Click here and here for a copy.) Quiz 21+22 Double-Quiz is a Take-Home handed out Wednesday 3 December 2008, due Friday 5 December 2008. (Click here for a copy.)
Thursday 12/4: Return X3. (Click here for a solution.) A photon traveling at the speed of light sees in its rest frame a universe going past it at the speed of light. A universe with an improper length of zero. The photon's clock never changes, t = 0 forever. A matter object has mass -- can never actually accelerate to the speed of light. 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. Relativistic momentum, prel = gamma mv, and relativistic Kinetic Energy, KErel = (gamma - 1) mc². Total Energy, Etotal = gamma mc². The Einstein Relation, E = m c², and conversion between energy and matter (mass). Pair creation of an electron-positron pair from two high energy gamma rays. Once we used to talk of a "relativistic mass", to try to explain why an object of matter cannot be accelerated up to the speed of light in vacuum, c. You can just as easily use the Work-Energy theorem to show that it would take infinite work to get a matter object up to c. (British SF writer Charlie Stross talks about the difficulties of space travel, including traveling to another star here.)
Friday 12/5: Last Regularly Scheduled Class. Discuss last quizzes and Final Exam. Review course topics in brief and look at a couple of Sample Final Exam Problems. Finish up the day with the course & teacher evaluations for the semester.
Monday 9/1: Labor Day <No Classes>
Tuesday 9/2: Class begins. Introduction to Dr. Phil. Static electricity. The simple hydrogen atom -- whatever charge is, the charge on the electron (-e) and the proton (+e) exactly cancel. The Two-Fluid Model of Electricity. Franklin's One-Fluid Model of Electricity.
Wednesday 9/3: The Two-Fluid Model of Electricity versus Franklin's One-Fluid Model of Electricity (continued). Occaam's Razor. Distribute syllabus.
Thursday 9/4: Real Electric Charges. Two charges: like charges repel, unlike (opposite) charges attract. A Nickel coin has a mass of 5 grams, so about 1/10th of a mole. "Action at a distance" -- Gravity and the Electric Force are not contact forces. The Electric Force between two point charges, Coulomb's Law looks like Newton's Law of Universal Gravity. 1 Coulomb of charge is an enormous amount of charge. Two 1.00 C charges separated by 1.00 meters have a force of one-billion Newtons acting on each other. "Quiz 1" in class.
Friday 9/5: Conductors (metals) versus non-conductors (insulators). Conduction electrons in metals -- free to move around. 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 (!!!).
Monday 9/8: Demo: Fur rubbing Rubber Rod, Silk rubbing Glass Rod - two kinds of static electricity. Charging a conductor by induction. Review of vectors and vector forces (Newton's 3rd Law). 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.
Tuesday 9/9: 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. "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.) Handout: SI Prefixes and Dr. Phil's Simplified Significant Figures. Q2 Take-Home, due Thursday 11 September 2008, in class or by 5pm.
Wednesday 9/10: 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. Strength of E-field is important, in part because in air there is a limit to how big E can get. At breakdown, the E-field is large enough to start ripping electrons from gas molecules and the positive ions go one way, the electrons go another, and then we get a "spark" and no longer are static. Emax in air is 3,000,000 N/C. Little sparks from walking across the carpet. Lightning from big charges accumulating on underside of thunderstorms. Worse, charge tends to accumulate on the ends of "pointy things", which is why the hairs on the back of your arm or neck stand up when the E-field increases and you are more likely to be hit by lightning. E-field lines allow us to qualitatively sketch what happens when two charges are near to each other. (1) +q and -q.
Thursday 9/11: News: CERN's Large Hadron Collider -- not going to destroy the Earth. E-field lines allow us to qualitatively sketch what happens when two charges are near to each other. (1) +q and -q, (2) +q and +q, (3) +2q and -q. Very close to each point charge, the E-field lines are radial outward, evenly spaced. In the system, the E-field lines interact with each other -- but E-field lines can never cross. Long range, the system of point charges looks like a single net charge. The density of E-field lines in an area gives you an indication of the strength of the E-field line. The numbers of E-field lines attached to a point charge is proportional to the charge. E-field lines radiate away from positive charges and terminate on negative charges. Direct integration of Electric Force and Electric Field are similar. Charge distributions -- lamda (linear charge density, C/m), sigma (surface charge density, C/m²), rho (volume charge density, C/m³). Examples: Rod in-line with line from point P (1-dimensional integration). Set up integral, will continue tomorrow. Q3 Take-Home, due Tuesday 16 September 2008, in class or by 5pm.
Friday 9/12: E&M represents a triumph of 19th century Physics. Electricity and magnetism turn out to be two sides of the same coin. Coulomb constant k is not the fundamental constant for electricity -- epsilon-naught is. Coulomb's constant k versus Permitivity of Free Space (epsilon-naught). Direct integration of Electric Field continued. 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. Check Serway's examples (that's your textbook) -- watch out that his notation may be different.
Monday 9/15: Review of 2-D and 3-D Integration. Start: Thin ring of charge perpendicular to line from point P.
Tuesday 9/16: Direct integration of Electric Field continued. Thin ring of charge to center point P. (Symmetry!) Thin ring of charge 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. Check Serway's examples (that's your textbook) -- watch out that his notation may be different. 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. Q4 Take-Home, due Thursday 18 September 2008, in class or by 5pm.
Wednesday 9/17: Review of Dot Product. Gauss' Law for Electricity. Using Gauss' Law for Point Charge. 1st Sample Exams for Exam 1. (Click here and here for a copy.)
Thursday 9/18: Gauss' Law for Electricity. Using Gauss' Law for Point Charge, Conducting Sphere, Insulating Sphere, Infinite Line of Charge. Q5 Take-Home, due Tuesday 23 September 2008, in class or by 5pm. NOTE: Follow what we did for the direct integration of the line of charge centered off-axis, only for a 2-D plate instead of a 1-D line of charge.
Friday 9/19: Using Gauss' Law for Infinite Insulated Rod of Charge, Gauss' Law for Infinite Sheet of Charge. Electric Potential versus Electric Potential Energy. 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. Simplified equation V = E d. Four pages of Topic 1 assignment handed out. (Full 27-page Handout as PDF File -- Searchable HTML Page )
Monday 9/22: Simplified equation V = E d. Example: Lightning. Conductor in equilibrium is an equipotential throughout. Equipotential lines, where V is constant, are always perpendicular to E-field lines. Why charge accumulates on the tips of "pointy things". Ben Franklin & lightning rods. NOTE: We may give you an extra day on Q5, but mainly because we want you to try this integration. Will probably not grade this on getting exactly the right answer. (grin)
Tuesday 9/23: Regarding Q5 -- oops, much harder than I had planned. Just get double-integral set up and try to get first intergration. Find components of E by negative of the partial derivative of Electric Potential function V. Finding V by direct integration. Direct integration of V for a whole and a quarter of a circular line of charge -- V really is a scalar, not a vector. Q6 Take-Home, due Thursday 25 September 2008, in class or by 5pm.
Wednesday 9/24: 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. Electrolytic capacitors. Stories: Dr. Phil & the camera flash. Capacitor Equation. Stories: US Navy seaman vs. the tank capacitor (Cap-2, Seaman-0). Parallel Plate Capacitor. Second Sample Exam 1. (Click here and here for a copy.)
Thursday 9/25: Work to assemble charges on a capacitor = Energy stored in the capacitor = U = ½CV² . Energy density, uE = U/vol. = ½(epsilon-naught)E² . While this was derived for the parallel plate case, it turns out to be true in general. Two devices connected together in a circuit can only be connected two ways: series or parallel. In Parallel, same voltage, share charge. Equivalent capacitor is always larger. In Series, same charge, share voltage. Equivalent capacitor is always smaller. NOTE: Remember to take the last reciprocal! Q7 Take-Home due Tuesday 30 September 2008, in class or by 5pm.
Friday 9/26: Capacitor Network Reduction problem. Use table with columns for Q = C V. By going back through the intermediate diagrams, it is possible to know every value of every capacitor in the network. Extend the example in class with a fourth column, U=½CV², and find the energy stored in the equivalent capacitor and the sum of the energy stored in all four of the real capacitors -- if they agree, then our analysis and calculations are correct -- the battery cannot tell the difference!
Monday 9/29: Making a real capacitor. What if not filled with air? 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). 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. Examples of the uses of capacitors and dielectrics.
Tuesday 9/30: Example from sample exam of rigid cluster of charges in an E-field and whether it translates, rotates, both, neither. Current defined. The Simplest Circuit: Battery, wires, load (resistor). 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. Joule Heating, Power Law: P = IV (also 3 forms). Q8 Take-Home, due Tuesday 7 October 2008, in class or by 5pm.
Wednesday 10/1: Resistance by geometry. Discussion of heat from resistors. Our electronic devices generate heat, but heat can also kill them. Story of early "hot" 486 laptops. 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. This microscopic theory becomes more important as we go to smaller and smaller circuit elements in our microchips. Moore's Law. Ohm's Law: V=IR form. (Ohm's "3 Laws"). If R=constant over operating range, then we say the material is "ohmic". If R is not constant, it is "non-ohmic". Example: Because of the temperature dependence of R, the filament of an incandescent light bulb has a very different R when lit or dark. Therefore measuring the resistance of a light bulb with an ohm meter is useless. Kammerleigh Onnes 1916 work on extending the R vs. T curve toward T = 0 Kelvin. Discovered Superconductivity, where R=0 identically. We usually treat the wires in a circuit as having R=0, but they usually are not superconductors.
Thursday 10/2: NOTE: Due a fatal flaw in the exam I wrote, Exam 1 scheduled for Thursday 2 October 2008 will be rescheduled for Friday 3 October 2008. Dr. Phil apologizes for the inconvenience, but it's way better that it works this way. Continuing with Simple Circuits... Two devices connected together in a circuit can only be connected two ways: series or parallel. In Series, same current, share voltage. Equivalent resistance is always larger. In Parallel, same voltage, share current. Equivalent resistance is always smaller. Resistor Network Reduction. (Similar rules to Capacitor Network Reduction except "opposite".) In this example, Resistor R1 sees the largest current and dissipates the largest amount of energy per second (Power in Watts). This means it is also the most vulnerable. Fault tolerant design. (Story of radio "repair" call from 4,000,000,000 miles.)
Friday 10/3: Exam 1 (Rescheduled)
Monday 10/6: "High temperature" superconductors (liquid nitrogen temperature, not liquid helium). The "Woodstock of Physics" in 1987. Real batteries consist of a "perfect" battery (Electromotive force = emf) in series with a small internal resistance, r. As chemical reaction in battery runs down, the internal resistance increases. Don't cut open batteries. Comments on different types of disposable (carbon-zinc, alkaline, lithium) and rechargable (Rayovac Renewal alkaline, NiCad, NiMH, Li-ion) batteries. Tip for weak car battery on cold day: Run headlights for 30 to 90 seconds. High internal resistance will warm the battery and make it more efficient.
Tuesday 10/7: Batteries in Series: Same current, voltages add. Batteries in Parallel: Same voltage, currents add. Multiple battery devices: many consumer products put batteries in series. Why you should replace all the batteries at the same time. Hidden batteries in PCs and laptops. Multi-cell batteries (6V lattern battery, 9V transistor/smoke alarm, 510V dry cell). Proper procedure for jump starting a car. (And why doing it wrong ranges from dangerous to deadly.) Q9 Take-Home, due Thursday 9 October 2008, in class or by 5pm.
Wednesday 10/8: Not all circuits can be reduced by serial and parallel network analysis. Kirchhoff's Laws: (1) The sum of all currents in and out of any junction must be zero. (2) The sum of all voltage gains and voltage drops about any closed loop is zero. Practically speaking, if there are N junctions, then (1) will give you (N-1) unique equations, and if there are M loops that can be made in the circuit, then (2) will give you (M-1) unique equations. You will get the same number of equations as you unknown currents through the resistors. NOTE: EE students and those who have had ECT-2100 (?) may know a "better" way to solve Kirchhoff's problems. But the brute force algebra approach has the advantage of being based on the Physics, so has instructional value. Example in class had 3 equations in 3 unknowns -- finish algebra and find i1, i2 and i3 for tomorrow. NOTE: Someone pointed out an error on the board in the equation, I believe R3 accidentally became an R2 in one divisor. So I am providing a PDF of the problem worked out -- the order of the algebra might not be the same as on the board, but I believe the answers to be correct.
Thursday 10/9: Interesting results from yesterday's Kirchhoff's Law example:
i2 ends up slightly negative. That tells us that our assumption of which way i2
points wasn't correct, but that's okay. PTPBIP -- running a current through a
battery backwards (+ to -, rather than - to +) is bad for the battery. In any
event, the batteries each see an equivalent resistance, which you can find via
V = IR. Other examples of systems which require Kirchhoff Laws. Sometimes a
resistor has zero current, in which case it does not contribute to the circuit.
RC series circuit. Calculus derivation of q(t) for charging capacitor .Q10 Take-Home, due next
Thursday 16 October 2008 Monday 20
October 2008, in class or by 5pm.
Friday 10/10: Calculus derivation of q(t) for charging capacitor and discharing circuit. Who knew that (ohms) × (farads) = (seconds)? By time t=3RC, a charging capacitor will reach 95% of its top charge, or a discharging capacitor will be down to 5% of its original charge. RC current I(t). First Sample Exam 2. (Click here and here for a copy.)
Monday 10/13: (Columbus Day -- no U.S. mail delivery, but classes meet) Demo Day: Light Bulbs in Parallel, Light Bulbs in Series, RC circuit. Discussion of Christmas tree lights and what happens when one or more burns out. Building an ammeter or voltmeter -- non-digital version with a needle. The Galvanometer is a generic meter. It has a resistance and the needle moves in response to a current through a tiny coil. Since meters must be connected to the circuit, technically they change the circuit. However, we will show that the design of an ammeter and a voltmeter minimizes these changes.
Tuesday 10/14: Ammeters measure current by connecting in series to the circuit. Voltmeters measure potential difference by connecting in parallel to the circuit. The Galvanometer is a generic meter. It has a resistance and the needle moves in response to a current through a tiny coil. The full-scale deflection current, iFS , is the current needed to move the needle to the maximum value on the scale -- it is very small. Ammeter: a galvanometer and a very small shunt resistor in parallel, together connected in series with the circuit. Voltmeter: a galvanometer amd a very large resistor in series, together connected in parallel with the circuit. In both cases, the role of the second resistor is to limit the current to the galvanometer, no matter what the design criteria of the meter in question. Does putting a real ammeter and voltmeter in a circuit, whether the very act of measuring V and I changes their value? It can't by much, because the full-scale deflection current and the voltage drop across the galvanometer are so small, compared to the values we are measuring.Q11 Take-Home, due Friday 17 October 2008, in class or by 5pm.
NOTE: I think the numbers we found for the ammeter and voltmeter resistors were: rs = 0.001262 ohms and Rv = 49,940 ohms. I had the numbers written down from what should have been the same problem in a different semester.
Wednesday 10/15: "Magnetism is just like Electricity, only different." Most people are familiar with (1) magnets sticking to some metals, not others such as stainless steel and (2) if you have two magnets, they may attract or repel. North and south are analogous to plus and minus charges. Real Magnets are dipoles (North and South ends, linked). Break a magnet in half, and you either get two new magnets -- or nothing. So far, there is no evidence that there are Magnetic Monopoles (magnetic charges: qM , isolated North or South poles). Rules similar to Electric Charges: Unlike poles attract, like poles repel. SI Units for B-field: (1 Tesla = 1 T). "Other" unit for B-field: ( 1 Gauss = 1 G ; 1 T = 10,000 G ). Earth's B-field is about 1 Gauss at the Earth's surface. Demos: Cow magnets -- powerful cylindrical, rounded end magnets which get dropped into a cow's first stomach, to collect nails, bits of barbed wire, etc. from continuing on to the cow's other stomachs. Broken cow magnets show a radial crystalline structure due to the alignment of small magnetic domains -- what makes the magnetic field strong also makes the magnet physically weak in some directions, hence the breakage across the radially aligned grains. Dropping a permanent magnet can result in a reduction of its magnetic field as the shock allows some iron atoms to flip 180° and therefore cancel instead of add to an adjacent iron atom's magnetic field. The horizontal compass needle rotates until its North end points North (or rather to the North Magnetic Pole, which is of course a South pole of the Earth's magnetic core); the vertical compass rotates so that it lines up with the B-field along the surface of the Earth at the point. At the Equator, the vertical magnetic should be parallel to the ground, at the magnetic poles, it should be perpendicular to the ground. Is the Earth's magnetic field going to flip some day? And what about Mars?
Thursday 10/16: Magnetic domains, temporarily magnetising steel objects,
making permanent magnets. Note that permanent magnets may lose some or all of
their magnetic strength when dropped or struck. 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.
Q10 (Kirchhoff) Take-Home, due next
Thursday 16 October 2008
Monday 20 October 2008, in class or by 5pm.
Friday 10/17: YES! WE HAVE CLASS TODAY! 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... 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 chemical means). Mass Spectrometer as Calutron -- detecting or separating isotopes, something that cannot be done by chemical means. This closes the book on material eligible for Exam 2.
Monday 10/20: 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. 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. We talk of "beam currents" in accelerators and TV cathode ray picture tubes -- moving electric charges without a wire, which can be steered by magnetic fields. If the B-field is constant, then the net magnetic force on an arbitrary current carrying wire from point a to point b is the SAME as if the wire ran straight from point a to point b. For a Closed Loop, the net Magnetic Force from a constant B-field is zero. Q10 Take-Home FINALLY Due Today! NOTE: J-vector = sigma × E-vector (current density = conductivity × E-field) is the vector version of Ohm's Law. This will NOT be on Exam 2.
Tuesday 10/21: Magnetic Force on a Current Carrying Wire. If the B-field is constant, then the net magnetic force on an arbitrary current carrying wire from point a to point b is the SAME as if the wire ran straight from point a to point b. For a Closed Loop, the net Magnetic Force from a constant B-field is zero. Magnetic Torque on a Current Carrying Wire. Left as is, this system is an osciallator -- the torque goes to zero after 90° and then points the other way. But if we can reverse the direction of the current after the torque goes to zero, then the rotation can continue -- and we have a primitive DC electric motor. Hall Effect -- a device with no moving electrical parts -- proves that charge carriers in a current carrying wire are negative, not positive. Q12 Take-Home, due Thursday 23 October 2008, in class or by 5pm.
Wednesday 10/22: Sources of Magnetic Fields. A current (moving electric charges) creates a magnetic field. The Biot-Savart Law. Circular loop of current carrying wire. Magnetic Force between Two Current Carrying Wires (qualitative description). Two current carrying wires in the SAME direction are attracted to each other. Two current carrying wires in OPPOSITE directions are repelled by each other.
Thursday 10/23: The Biot-Savart Law. B-field from a infinitely long straight current carrying wire by direct integration. (Serway has a similar example, but rather than do the integral in x, he does this theta substitution which Dr. Phil does not think is straight forward.) Circular loop of current carrying wire by integration for P at the center of the loop. (Serway's example allows for P to be on a line perpendicular to the loop.) 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. Q13 Take-Home, due Tuesday 28 October 2008, in class or by 5pm.
Friday 10/24: 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. Demo: Jumping wire -- current carrying wire between the poles of a large U-magnet. Magnetic Force between Two Current Carrying Wires (con't.): Operational defnition of the ampere and the Coulomb.
Monday 10/27: Return X1. Read the Riot Act to One and All. MOVE EXAM 2 TO MONDAY 3 NOVEMBER 2008.
ALERT! If your last name falls in the range from HENGESBACH to MALTAS, your Mid-Term grade on GoWMU has now been CORRECTED as of 2pm 10/28/08 Tue. There was an error inputting the Exam 1 grades, at one point Dr. Phil was off by one line. They've extended the time for instructors to submit Mid-Term grades, so I was able to make the update.
Tuesday 10/28: Review fundamentals of Physics, Algebra and Calculus.
Wednesday 10/29: Review some of the Sample Exam 2 problems.
Thursday 10/30: 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. B-field of a Torroid (torroidal coil; a torus is like a donut). B-field of a Solenoid. (NOTE: The integrals for the L and R sides of the Amperean Loop for Ampere's Law are zero because: (1) the B-field is zero outside the solenoid and (2) for that part of the path which is inside the solenoid, the B-field and the ds-vector are perpendicular, so the dot product is zero as well.) Comments about winding real coils with thin, varnish insulation. Comments about making a real velocity selector -- trying to stuff a capacitor for the E-field and a solenoid for the B-field in the same space!
Friday 10/31: Comments about making a real velocity selector -- trying to stuff a capacitor for the E-field and a solenoid for the B-field in the same space! Comments on the "right-handedness" of the universe. Coils can have right-hand or left-hand turns -- but it is the direction that the current wraps around the coil which determines which way the B-field points. Michael Faraday and Induction. Dr.Phil's "status quo" explanation for why a coil responds to a changing magnetic flux through its interior area by creating an induced B-field from an induced current in the coil.
Monday 11/3: Exam 2.
Tuesday 11/4: Election Day! Demo: Magnet moving into a coil, causing current to flow through galvanometer. 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. Practical uses for induction: (First, how regular fuses and circuit breakers work -- and why that isn't fast enough to prevent some types of accidents.) Ground Fault Interupt -- if the current doesn't return via the return wire, because it has found another conductive path, then the 2 wires (hot and return) total a net-enclosed-current for Ampere's Law, generating a B-field in a metal ring, detected by an induction coil wrapped around the ring and this sets off the relay which breaks the circuit. 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. It is Lenz's Law that gives us the minus sign in Faraday's Law of Induction.
Wednesday 11/5: 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. It is Lenz's Law that gives us the minus sign in Faraday's Law of Induction. Demonstration Day -- Lenz Law race between cow magnets dropped through (a) plastic pipe, (b) non-magnetic aluminum pipe and (c) non-magnetic copper pipe. "Jumping Rings", making the bulb light, by Eddy Currents and Induction. Ford test electric vehicle with inductive charger -- no exposed metal contacts, everything covered in smooth plastic. Q14 was supposed to be an In-Class quiz today on Ampere's Law, but I talked too long, so Q14 will be given on Thursday. Q15 Take-Home quiz, due FRIDAY 7 November 2008.
Thursday 11/6: Turn a coil in a magnetic field and the flux changes, thereby inducing a B-field, emf and current. Has same 180° problem that a DC motor has. Hand-crank generators. Electric generators and electric motors differ in which way the arrow points toward or away from mechanical energy. Regenerative braking -- turn electric motors into generators. Motional emf -- skipping for now. (Will try to come back to this later.) The General form of Faraday's Law of Induction. Q14 In-Class quiz.
Friday 11/7: An Inductor is a coil in a circuit. Why an Inductor has Self-Inductance -- running a current through a coil creates a magnetic field and therefore changes the magnetic flux in the coil. The inductor has to respond to that change. Inductance can be a big deal. Even our Simplest Circuit (a resistor hooked up to a battery) forms a loop, and the loop must respond to the circuit being turned on. Why induction is a big deal in electronics, industrial motors and electrical power distribution. Where they got it right (and wrong) regarding electrical power in the movie Jurassic Park. The Inductor (L). (SI units = Henry = H) Self-Inductance. Back emf, back current. Opposing the status quo. Equations for Inductance.
Monday 11/10: RL Circuit, similar to RC Circuit, except that energy is stored in the magnetic field at the maximum current. UL = ½ L I ². RL Circuit for energizing the coil. Equation for current i(t) is similar in appearance to the equation for q(t) for a charging capacitor. Now we will de-energize the coil. NOTE: In class I followed Serway's lead, where I should've used my usual brute force approach. The Kirchhoff Loop for the de-energining coil is -iR -L(di/dt) = 0. Since the current is decreasing, di/dt is negative and the induced emf from the coil becomes a voltage gain. Solution for i(t) the same form as the current i(t) for charging/discharging capacitor.
Tuesday 11/11: Veteran's Day (not a WMU holiday). Mutual Inductance between two inductors. 2nd coil responds only to changes in magnetic flux coming from 1st coil. And vice versa. LC Oscillator circuit. Same 2nd order differential equation as the Simple Harmonic Oscillator (PHYS-205), such as a mass on a spring. Solutions are sines and cosines. Energy is held constant for all t between the capacitor and the inductor. Can't really have a true LC oscillator, since normal wires and coils have a resistance which dissipates energy through Joule heating. Q16 Take-Home, due Thursday 13 November 2008.
Wednesday 11/12: LC Oscillator solution. Energy is held constant for all t between the capacitor and the inductor. Can't really have a true LC oscillator, since normal wires and coils have a resistance which dissipates energy through Joule heating. Timing circuits, blinkers, AC, diodes. Comments ONLY about the RLC Damped Harmonic Oscillator. Mechanical analogue is the mass-on-a-spring with shock absorbers. A.C. Circuits. Voltage is a sine or cosine functions, as is the Current. Problem: Average voltage is ZERO. Need to define a new average, the Root-Mean-Square. It is the RMS Voltage and Current that are usually reported in A.C. circuits. Typical A.C. frequency in U.S. is 60 Hz. Need to specify what type of A.C. For sine wave, define RMS Voltage as 0.7071 Maximum Voltage. Similar for RMS Current. First Sample Exam 3. (Click here for a copy.)
Thursday 11/13: Why A.C. power? (1) Transformers allow voltage to be raised or lowered. D.C. voltage can only be lowered by the voltage drop of a resistor, or raised by adding power sources. The transformer consists of two coils connected magnetically by an iron core. V2 = V1N2/N1. (2) D.C. power lines have huge power losses due to Joule heating, very low efficiency. Actual Efficiency = Power Used ÷ Total Power Generated. Power lines run at higher voltages to minimize power losses due to Joule heating in the powerlines (P = I²R). Downsides of having high voltage power lines around. Where they got it right (and wrong) regarding electrical power in the movie Jurassic Park.
Friday 11/14: For resistive only circuits, can still use Ohm's Law, V = I R. Current and Voltage are both sine waves. Real A.C. circuits may have a Resistive nature, a Capacitive nature and an Inductive nature. For A.C. circuits with a Resistor only: I and V stay in phase with each other. RL Circuits: I and V out of phase by 90°. Inductive Reactance. Phasor diagrams -- taking the y-component of a rotating vector gives the sine function. Quiz 17 is a Take-Home quiz, handed out Friday 14 November 2008 and due Wednesday 19 November 2008.
Monday 11/17: RC Circuits: I and V out of phase by -90°. Capacitive Reactance. Many A.C. circuits have features of all three components (R, L and C), so we have to deal with Impedance, Z. Phasor diagrams (see textbook for diagrams). Minimum impedance is when purely Resistive or when the two Reactances cancel each other -- the latter is frequency dependent. Can run into problems if expecting f=60Hz but get f=50Hz or f=25Hz.
Tuesday 11/18: Phasor diagrams (see textbook for diagrams). Minimum impedance is when purely Resistive or when the two Reactances cancel each other -- the latter is frequency dependent. Can run into problems if expecting f=60Hz but get f=50Hz or f=25Hz. Phase angle, phi, for resultant Vmax vector relative to the Imax vector, is phi = tan-1((XL-XC)/R). For impedance matching , where XL=XC, we get the same equation for the angular frequency omega = 1/SQRT(LC) as for the LC oscillator. This is why power companies have to worry about maintaining their frequency -- it affects the impedance of the circuits.
Wednesday 11/19: The problem with Ampere's Law -- 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. Maxwell's Equations in integral form and Hertz's radio wave LC oscillator -- the spark gap radio. Note that Maxwell didn't invent the four equations, only half of one, but he figured out what todo with them. Q18 Take-Home quiz, due Friday 21 November 2008.
Thursday 11/20: E & M Waves. Turning Maxwell's Equations in E and B, into 2nd order differential equations (Wave Equation) in E or in B. Both give sine or cosine solutions in space and time. Traveling E-M Wave. A constantly changing B-field creates a changing E-field, and a constantly changing E-field creates a changing B-field. The Great 19th Century Debate: Is Light a Particle or a Wave? (Wave-Particle Duality did not seem obvious at the time.)
Friday 11/21: 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. The Electromagnetic Spectrum. Visible light (ROYGBIV=red orange yellow green blue indigo violet). Frequencies HIGHER and wavelengths SHORTER than visible light (UV ultraviolet, X-ray, Gamma-ray). Frequencies LOWER and Wavelengths LONGER than visible light (IR infrared, Microwave, Radio waves, ELF extremely low frequency).
Monday 11/24: E-M waves continued. Derivation of c = E / B. Similar to the relationship between the E-field and the B-field in the velocity selector, where v = E / B. Energy of a photon is E = h f, where h = Planck's constant = 6.636 × 10-34 J·s. Though h is small, it is not zero. If there were no Modern Physics, h would be zero. Review Sample Exam 3 problems.
Tuesday 11/25: Exam 3.
Wednesday 11/26: <No Class> WMU Closes for Thanksgiving Holiday at Noon. Since my 1pm class is canceled, the 11am class is, too. Classes resume as usual on Monday 1 December 2008.
Thursday 11/27: THANKSGIVING -- No Classes --
Friday 11/28: Recovery from THANKSGIVING DINNER -- No Classes -- (grin)