Dr. Phil's Home

## Lectures in PHYS-2070 (9/10)

Updated: 02 December 2005 Friday.

### Week of 28 November - 2 December, 2005.

Monday 11/28: 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). 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). Second set of Sample Final Exams handed out.

Tuesday 11/29: Waves in air, water, require a medium. 19th century "ether" for light. Michaelson-Morley Experiment found no evidence of ether. Special Relativity. Beta, gamma, Length Contraction and Time Dilation. Alpha Centauri is 4.2 LY from Earth (proper length). Those on a starship see a different distance and experience a different time. 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. 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. Experimental confirmation of General Relativity: on 29 May 1919 during a total solar eclipse, when the light from a star was bent around the edge of the Sun by the Sun's gravity, so the star appeared early from behind the eclipse. Also the orbit of Mercury and GPS satellites. Q20 was going to be in-class, ended up Take-Home due tomorrow 30 November 2005.

Wednesday 11/30: Return X3. 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. Relativistic momentum and relativistic Kinetic Energy. Total Energy. The Einstein Relation, E = m c². Two observers cannot agree on the order of events, either. The concept of "simultaneity" is gone. Red shift (Doppler shift of light source moving away from us) and blue shift (Doppler shift of light source moving towards us) can tell how fast a star or galaxy is moving relative to us. Q21 Take-Home quiz, due Friday 2 December 2005. (Click here for a copy.)

Thursday 12/1: Q22 in-class points. NOTE: If you are registered for the 11am lecture, but plan on taking the Final on Tuesday OR you are registered for the 1pm lecture, but plan on taking the Final on Monday -- please send Dr. Phil an e-mail by Sunday night, so I know how many finals to print for Monday. More quizzes handed back.

Friday 12/2: Last Regularly Scheduled Class. DO NOT MISS. (Earned Q23 in-class points!) For casual observations, we usually cannot distinguish measurements that are within 10% of each other. For a gamma of 1.10, this translates to a beta of 0.4167 or about 42% the speed of light. Q21 part (c) comments: The event here is the time for the (front end of the ) pole to go through the barn. For proper time, it's not a question of whether the clock is at rest with respect to the observer, but whether the event occurs in the same place. The farmer, for example, starts timing when the pole enters the front of the barn and stops timing when the pole emerges from the rear of the barn. Is this a proper time? Finish up the day with the course & teacher evaluations for the semester.

• Announcements! (Monday 5 December 2005 - SED Students can join ScMaTa for Finals Pizza, 10am-2pm, Rood 3375)

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NOTE: If you are registered for the 11am lecture, but plan on taking the Final on Tuesday OR you are registered for the 1pm lecture, but plan on taking the Final on Monday -- please send Dr. Phil an e-mail by Sunday night, so I know how many finals to print for Monday.

Sunday 12/4: Hope to have link to estimated grading online after 5pm...

There are TWO Final Exams -- There will be TWO Final Exam Curves (since the Monday group gets shortchanged for office hours.)

Monday 12/5: Office Hour 9-10am; 11am PHYS-2070 Final Exam 10:15am-12:15am (2 hours)

Tuesday 12/6: Office Hours 10am-2:15pm; 1pm PHYS-2070 Final Exam 2:45pm- 4:45pm (2 hours)

### Week of August 29-September 2, 2005.

Monday 8/29: Office Day -- No Classes before 4pm.

Tuesday 8/30: Class begins. Introduction to Dr. Phil. Discuss 19th Century Physics.

Wednesday 8/31: Demo: Static electricity. The Two-Fluid Model of Electricity. Franklin's One-Fluid Model of Electricity. Occaam's Razor.

Thursday 9/1: 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. Find number of free conduction electrons, and number of Coulombs of positive and negative charges. "Action at a distance" -- Gravity and the Electric Force are not contact forces. The Electric Force between two point charges, Coulomb's Law.

Friday 9/2: "Quiz 1" in class. Topic 1 handout. (Searchable HTML booklist) (Full handout with booklist)

### Week of September 5-9, 2005.

Monday 9/5: LABOR DAY -- No Classes

Tuesday 9/6: Conductors (metals) versus non-conductors (insulators). Charging a conductor by induction. Finally hand out Syllabus. Take-Home Q2, due Thursday 8 September.

Wednesday 9/7: Four Fundamental Forces in Nature: Gravity, E & M, Weak Nuclear Force, Strong Nuclear Force. Coulomb's Law looks like Newton's Law of Universal Gravity. The Hydrogen Atom: Gravity loses to Electric Force by a factor of 200 million dectillion (!!!).

Thursday 9/8: 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.) 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. Handout: SI Prefixes and Dr. Phil's Simplified Significant Figures.

Friday 9/9: SI units for E-field: (N/C). Review of vector notation for components and Standard Form. 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. Examples: Rod in-line with line from point P (1-dimensional integration). Discussion of allowed Formula Cards for all quizzes and exams (see Syllabus). Q3 Take-Home, due Tuesday 12 September 2005.

### Week of September 12-16, 2005.

Monday 9/12: Direct integration of Electric Field continued. Rod perpendicular to line from point P. Thin ring of charge to center point P. (Symmetry!) 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. Review of 2-D and 3-D Integration. 1st Sample Exams for Exam 1.

Tuesday 9/13: Thin ring of charge perpendicular to line from point P. Thin plate of charge perpendicular to line from point P (2-D integration). 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. Coulomb's constant k versus Permitivity of Free Space (epsilon-naught).Q4 Take-Home, due Thursday 15 September 2005.

Wednesday 9/14: Review of 2-D and 3-D Integration. Electric Flux: Electric field times Area, modified by the angle.

Thursday 9/15: Review of Dot Product. Gauss' Law for Electricity. Using Gauss' Law for Point Charge, Conducting Sphere, Insulating Sphere, Infinite Line of Charge.

Friday 9/16: Using Gauss' Law for Infinite Sheet of Charge. Q5 in-class.

### Week of September 19-23, 2005.

Monday 9/19: 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. Second Sample Exam 1 handout.

Tuesday 9/20: Simplified equation V = E d. Example: Lighting. 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". Q6 take-home, due Thursday 22 September 2005.

Wednesday 9/21: Ben Franklin & lightning rods. 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.

Thursday 9/22: 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. Stories: Dr. Phil & the camera flash. Capacitor Equation. Stories: US Navy seaman vs. the tank capacitor (Cap-2, Seaman-0). Parallel Plate Capacitor

Friday 9/23: Work to assemble charges on a capacitor = Energy stored in the capacitor. 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! 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. For "homework" (NOT to be turned in), 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! Q7 take-home, due Tuesday 27 September 2005.

### Week of September 26-30, 2005.

Monday 9/26: Essentially no one from either section did the "homework" mentioned in class on Friday. Sigh. Recap capacitor network reduction problem. Comparing energy stored in each of the four capacitors, with the energy stored in the single equivalent capacitor of the reduced circuit. The sum of the energy stored in the parts must be same as for the equivalent capacitor -- the battery cannot tell the difference. 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. Electrolytic capacitors.

• Announcements! (for those interested in being physics teachers)

Tuesday 9/27: Examples of the uses of capacitors and dielectrics. Some comments on dipoles -- dipole moment will NOT be covered on any exam, but we will continue to treat systems of point charges as systems of point charges. Example from sample exam of rigid cluster of charges in an E-field and whether it translates, rotates, both, neither. Q8 will not be an in-class quiz today, but will be a take-home to be due next week after Exam 1.

• Announcements! (WMU has changed the start dates for the Spring 2006 semester)

Wednesday 9/28: Current defined. The Simplest Circuit: Battery, wires, load (resistor). Resistance vs. Conductance. 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. Q8 Take-Home, due Tuesday 4 October 2005 Wednesday 5 October 2005.

Thursday 9/29: Go over Q2 through Q7 in class. Review for Exam 1.

Friday 9/30: Exam 1.

### Week of October 3-7, 2005.

Monday 10/3: Reset/review: Simplest circuit, load resistor, Ohm's Law. Resistance by geometry. 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".) Power dissipated by Joule heating in a resistor. P = I V (3 forms of Power equation to with Ohm's "3 Laws").

Tuesday 10/4: For example given in class on Monday, 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.) Heating of microprocessor chips. Superconductivity, where R=0 identically. "High temperature" superconductors (liquid nitrogen temperature, not liquid helium). Real batteries (start of discussion). Q8 now due Wednesday 5 October 2005.

Wednesday 10/5: 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, and multi-cell batteries (9V transistor/smoke alarm, 510V dry cell). 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.

• Announcements! (Program on the Space Shuttle Columbia Thursday night)

Thursday 10/6: 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. Proper procedure for jump starting a car. (And why doing it wrong ranges from dangerous to deadly.) 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-210 (?) 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. Q9 Take-Home, due Tuesday 11 October 2005.

Friday 10/7: 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. RC series circuit. Calculus derivation of q(t) for charging capacitor . Hand back Q4. First Sample Exam 2 handouts (two exams, a third is a duplicate). Q10 Take-Home, due Thursday 13 October 2005 -- now due Monday 17 October 2005.

### Week of October 10-14, 2005.

Monday 10/10: (Columbus Day -- no U.S. mail delivery, but classes meet) RC series circuit. 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).

Tuesday 10/11: 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. 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.

Wednesday 10/12: "Magnetism is just like Electricity, only different." 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: 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. Extend deadline for Q10 Take-Home to Monday 17 October 2005.

Thursday 10/13: Magnetic Force on a Moving Electric Charge - Right-Hand Rule & Uniform Circular Motion. Cyclotron frequency -- no dependence on the radius (constant angular velocity). The origin of Auroras (aurora borealis = northern lights, aurora australis = southern lights): charged particles from the Sun end up following the Earth's B-field lines in helical (screwlike) paths towards the poles -- when these fast moving particles hit the upper atmosphere, they cause a glow. 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... Q11 Take-Home, due Tuesday 18 October 2005.

Friday 10/14: 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.

### Week of October 17-21, 2005.

Monday 10/17: Return X1. Extend dates for take-home quizzes Q10 and Q11 by two days: Q10 now due Wednesday 19 October 2005 and Q11 now due Thursday 20 October 2005 -- these are the final extensions for these quizzes. Q12 in-class Tuesday 18 October 2005 on the magnetic force on a moving electric charge in a magnetic field.

Tuesday 10/18: 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. Q12 in-class.

• Announcements! (for those interested in being physics teachers - PhysTec Meeting on Thursday 10/20 5:30-7pm Rood 2242)

Wednesday 10/19: 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. Q10 Take-Home FINALLY Due Today!

Thursday 10/20: Hall Effect -- a device with no moving electrical parts -- proves that charge carriers in a current carrying wire are negative, not positive. 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. Q11 Take-Home FINALLY Due Today.

Friday 10/21: 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.) Magnetic Force between Two Current Carrying Wires. Two current carrying wires in OPPOSITE directions are repelled by each other. Quiz Solutions for all the network quizzes are available in a single PDF file: (Click here for Quiz Solutions 8-12.) Second set of Sample Exam 2's handed out: (Click here and here for copies.) Q13 Take-Home, due Tuesday 25 October 2005.

### Week of October 24-28, 2005.

Monday 10/24: Gauss' Law for Magnetism. Not as useful as Gauss' Law for Electricity, because it is always zero (no magnetic monopoles). 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 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!

• Announcements! (just a reminder in case anyone was planning on graduating in Spring 2006 -- new deadline for applying for graduation)
• Announcements! (Friday 28 October 2005 - SWMSES Conference, 8am-4pm, Portage Northern HS)

Tuesday 10/25: Magnetic Force between Two Current Carrying Wires (con't.): Operational defnition of the ampere and the Coulomb. B-field of a Solenoid. Comments about winding real coils with thin, varnish insulation. 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. Review some of the Sample Exam 2 problems.

Wednesday 10/26: B-field of an infinite sheet of current. Ampere-Maxwell equation. We need to define a displacement current to describe what is happening in the gap of a charging or discharging capacitor, using the change in the electric flux with respect to time to convey the sense of "current" across the gap. And again we are linking E-fields and B-fields together. Q14 on Ampere's Law in class.

Thursday 10/27: 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. Review for Exam 2. Note: If you are fretting about the "truncated cone resistor & current density" star problem on one of the sample exams, don't worry -- it won't be on your Exam 2. (grin)

Friday 10/28: Exam 2.

### Week of October 31-November 4, 2005.

Monday 10/31: 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.

Tuesday 11/1: Demonstration Day -- "Jumping Rings", making the bulb light, by Eddy Currents and Induction. Lenz Law race between cow magnets dropped through (a) plastic pipe and (b) non-magnetic aluminum pipe. It is Lenz's Law that gives us the minus sign in Faraday's Law of Induction. Magnetic force on a current carrying wire. Ford test electric vehicle with inductive charger -- no exposed metal contacts, everything covered in smooth plastic. Heating the bottom of a metal cooking pot by induction. 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. Q15 Take-Home, due Thursday 3 November 2005.

• Announcements! (Thursday 17 November 2005 - Joint PhysTEC Meeting with ScMaTa, 7pm, Rood 3302)

Wednesday 11/2: Motional emf = - Blv. The area is changing due to the motion, so the magnetic flux IS changing in time, even if the B-field is constant. The General form of Faraday's Law of Induction. Review November dates for Exam 3 and Topic 1 paper. Maxwell's Equations in integral form. 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.

Thursday 11/3: 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. RL Circuit, similar to RC Circuit, except that energy is stored in the magnetic field at the maximum current. UL = ½ L I ².

• NOTE: If you're looking for Dr. Phil before about Noon on Friday you probably won't find me. I'll be getting a flu shot at GVSU in the morning, so will be arriving late on campus.

Friday 11/4: Yesterday we did the RL Circuit for energizing the coil. Now we will de-energize the coil. Solution for i(t) the same form as the current i(t) for charging/discharging capacitor. Equations for Inductance -- like C and R, we have an "in use" equation with the operational variables phi-B and I, and a "by geometry" equation for a standard geometry, in this case an air-filled solenoid. 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. First set of Sample Exam 3's handed out. Q16 Take-Home, due Tuesday 8 November 2005.

### Week of 7-11 November, 2005.

Monday 11/7: 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.

Tuesday 11/8: 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. 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.

Wednesday 11/9: CLASS WAS CANCELLED. Dr. Phil was running a fever and had a doctor's appointment for 10am. Sorry for the inconvenience.

Thursday 11/10: 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. 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. Q18 Take-Home, due Monday 14 November 2005.

• Announcements! (Friday 11 November to Friday 18 November 2005 - Physics Help Room temporarily moves to Bradley Commons, 2202 Everett)
• Announcements! (Monday 21 November 2005, "What Makes Einstein So Smart", 7:00-8:00pm, 1104 Rood)

Friday 11/11: Why A.C. power? Transformers allow voltage to be raised or lowered. 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. Downsides of having high voltage power lines around. Second set of Sample Exam 3's handed out. Q17 in-class quiz today.

### Week of 14-18 November, 2005.

Monday 11/14: The Diode and Rectifier -- devices which allow current to flow only in one direction. Useful for power supplies which convert AC to DC. Single diode provides pulsed power -- top halves of sine waves. Four diode bridge rectifier inverts the bottom halves of sine waves. Adding a capacitor can help even out the current and voltage to produce a result closer to the average -- and more like the flat V vs. t graph of a battery. Driven RLC oscillators: omega ("w") is the angular frequency of the AC, while omega-naught ("w0") is the natural resonant angular frequency of the LC oscillator. When the two are equal, Z is minimized and the rms current and power are maximized. Analogy of tuning a radio. Maxwell's Equations and Hertz's radio wave LC oscillator -- the spark gap radio. Last day to turn in a Draft paper...

Tuesday 11/15: 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. The Great 19th Century Debate: Is Light a Particle or a Wave? (Wave-Particle Duality did not seem obvious at the time.)

Wednesday 11/16: Review for Exam 3.

Thursday 11/17: Return X2. (finally!)

Friday 11/18: Exam 3.

### Week of 21-25 November, 2005.

Monday 11/21: 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...).

Tuesday 11/22: The Electromagnetic Spectrum. Frequencies LOWER and Wavelengths LONGER than visible light (IR infrared, Microwave, Radio waves, ELF extremely low frequency). Poynting Vector, S. Traveling E-M Wave, Poynting Vector and Intensity. Hand out first Sample Final Exams. Q19 in-class.

Wednesday 11/23: WMU closes at Noon for Thanksgiving Recess. Since 1pm class is canceled, the 11am class is, too.

Thursday 11/24: THANKSGIVING -- No Classes --

Friday 11/25: Recovery from THANKSGIVING DINNER -- No Classes -- (grin)