## Lectures in PHYS-207 (8)

Updated: 18 April 2003 Friday.

### Week of April 14-18, 2003.

Monday 4/14: Refraction con't. If going from an high index of refraction media to a lower index media, have a chance for Total Internal Reflection (T.I.R.). Thin Lenses. Positive, biconvex, converging lens. Concentrating sunlight: burning paper or popping ants? Q20/21 Double take-home quiz, due Wednesday 16 April 2003.

Tuesday 4/15: Real image formed by passing rays through a positive thin lens

Wednesday 4/16: Q1 (Part II of II) (8000 points automatically for participating.)

Thursday 4/17: Physical Optics. Based on wave properties of light. Young's Double-Slit Interference. Single-Slit Diffraction. Double-Slit plus Single Slit. Use of Muliple Lenses -- Focal lengths in series add like series capacitors (by reciprocals) -- one can adjust the working distance to the object or image, or compact or expand the physical size of the lens. Anti-Reflection coating for lenses. Step 1 - A thin coating of thickness t applied to a glass surface, means that light rays coming in from the air make two reflections (air to coating, and coating to glass). If the roundtrip distance of the 2nd reflection is out of phase with the 1st reflection (off by ½ wavelength) then the two reflections can cancel each other. Thickness = half the round-trip distance, yields a "quarter-wave coating". Step 2 - But the roundtrip distance is done in the coating, so need to find the wavelength in the coating, not the air or glass. Step 3 - When a light ray goes from a low index of refraction to a higher index of refraction, the reflection gains a ½ wavelength phase shift. If both reflections are the same kind (low to high, or high to low), then we still get the same quarterwave anti-reflection solution. If both reflections are different, we get halfwave anti-reflection coatings. Q22 take-home quiz, due Friday 18 April 2003. Q23 take-home quiz, THE LAST QUIZ, due at Your Final Exam.

Friday 4/18: THE LAST DAY OF CLASS. Demo: Crossed Polarizers, Double-hemispherical wave overlaps on the overhead projector. Review.

### Week of January 6-10, 2003.

Monday 1/6: OFFICE DAY. No Classes.

Tuesday 1/7: Class begins. Introduction to Dr. Phil. Distribute syllabus. Discuss 19th Century Physics.

Wednesday 1/8: The Realization that Electricity and Magnetism were part of the same Electromagnetic Force was a great triumph of 19th century physics. Franklin's One-Fluid Model of Electricity.

Thursday 1/9: Q1 (Part I of II) (7000 points automatically for participating.)

Friday 1/10: Four Fundamental Forces in Nature: Gravity, E & M, Weak Nuclear Force, Strong Nuclear Force. Real Electric Charges. Two charges: like charges repel, unlike (opposite) charges attract. 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 (!!!).

### Week of January 13-17, 2003.

Monday 1/13: Coulomb's Law continued. Remember: In PHYS-207, always be on the lookout for Zero Problems (ones where the answer is zero). Review of Vector Force problems (don't blink or you'll miss it). Conductors (metals) versus non-conductors (insulators). Charging a conductor by induction.

Tuesday 1/14: 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 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.)

Wednesday 1/15: Distribute Topic 1 (Blue Handout - Book & Movie List). 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.

Thursday 1/16: 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). Rod perpendicular to line from point P.

Friday 1/17: 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. Coulomb's constant k versus Permitivity of Free Space (epsilon-naught). Review of 2-D and 3-D Integration. 1st Sample Exams for Exam 1.

### Week of January 20-24, 2003.

Monday 1/20: Dr. Martin Luther King, Jr. memorial observance [No Class Today]

Tuesday 1/21: Electric Flux: Electric field times Area, modified by the angle. Review of Dot Product. Gauss' Law for Electricity. Q3 in class.

Wednesday 1/22: Lecture Handout: Gauss' Law.

Thursday 1/23: Second set of Sample Exam pages for Exam 1. Q4 in class. NOTE: No Thursday afternoon office hours.

Friday 1/24: 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. Example: Lighting. Finding V by direct integration (started). Q5 Take-Home Quiz, Due Monday 27 January 2003 by 5pm.

### Week of January 27-31, 2003.

Monday 1/27: Discussion of Exam 1 format. More on finding Potential V by direct integration. Q5 now due by 5pm on Tuesday.

Tuesday 1/28: Find components of E by partial derivative of Electric Potential function V. 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.

Wednesday 1/29: Direct integration of V for a quarter of circular line of charge -- V really is a scalar, not a vector. 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. Q6 in class.

Thursday 1/30: Exam 1.

Friday 1/31: Capacitor Equation. Stories: US Navy seaman vs. the tank capacitor (Cap-2, Seaman-0). Parallel Plate 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!

### Week of February 3-7, 2003.

Monday 2/3: 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. Work to assemble charges on a capacitor = Energy stored in the capacitor. Q7 take-home due Wednesday 5 February 2003.

Tuesday 2/4: Work to assemble charges on a capacitor = Energy stored in the capacitor. Energy density is the energy stored in the E-field per volume. 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).

Wednesday 2/5: 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. Using dielectric to change capacitance for detection: Studfinder (for carpentry), some computer keyboard keys, biometrics for security systems. Electrolytic capacitors. Electrostatics versus Electrodynamics. Resistors and Resistance.

Thursday 2/6: 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. We usually treat the wires in a circuit as having R=0, but they usually are not superconductors. Q8 in-class.

Friday 2/7: Resistance by geometry. 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. 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".) Q9 take-home quiz. Originally due Tuesday 11 February 2003, now due Thursday 13 February 2003. Get a copy of quiz from Dr. Phil, if you need one.

### Week of February 10-14, 2003.

Monday 2/10: Continuing with Resistors. Power dissipated by Joule heating in a resistor. P = I V (3 forms of Power equation to with Ohm's "3 Laws"). For example given in class on Friday, 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. (Story of radio "repair" call from 4,000,000,000 miles.) 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. Q9 take-home quiz originally due Tuesday 11 February 2003, now due Thursday 13 February 2003. Get a copy of quiz from Dr. Phil, if you need one.

Tuesday 2/11: Exam 1 returned. Q8 in-class.

Wednesday 2/12: ***Unofficial SN*W Day*** Dr. Phil apologizes for being unable to get down to Kalamazoo due to weather, roads and the snow in his driveway that took two hours to dig out from under. These things happen.

Thursday 2/13: 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. 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.) 1st Sample Exams for Exam 2. Quiz 9 take-home finally, really due today.

Friday 2/14: 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. Quiz 10 take-home, due Monday 17 February 2003.

### Week of February 17-21, 2003.

Monday 2/17: [President's Day -- NOT a WMU holiday -- Classes will meet] RC series circuit. Calculus derivation of q(t) for charging capacitor . 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. Q10 take-home due today.

Tuesday 2/18: Discharging capacitor. RC current I(t). 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.

Wednesday 2/19: 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. Finally, we checked to see if, in putting a real ammeter and voltmeter in a circuit, whether the very act of measuring V and I changes their values. (Finish this calculation at home, if you have the numbers from class.) Yes and no -- the changes in the readings with both meters present didn't change the values in our example by more than 0.01%. Q11 on series RC circuits in class.

Thursday 2/20: Finish up Ammeter/Voltmeter problem. "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.

Friday 2/21: 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... One more step on Monday to turn this into a mass spectrometer -- a device that sorts particles by mass. Q12 take-home, due Monday 24 February 2003.

### Week of February 24-28, 2003.

Monday 2/24: 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.

Tuesday 2/25: Magnetic Force on a Current Carrying Wire. For a Closed Loop, the net Magnetic Force from a constant B-field is zero. Q12 take-home, due Tuesday 25 February 2003. Q13 in-class. Four quizzes returned.

Wednesday 2/26: 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 electric motor. Hall Effect -- a device with no moving electrical parts -- proves that charge carriers in a current carrying wire are negative, not positive.

Thursday 2/27: Exam 2

Friday 2/28: WMU Spirit Day [No Classes Today] [Effective Start to Spring Break]

### Week of March 3-7, 2003.

[SPRING BREAK - NO CLASSES THIS WEEK]

### Week of March 10-14, 2003.

Monday 3/10: Semi-circular current loop in a constant B-field. We know that the magnetic force should be zero, but integrate around the loop and show it. Sources of Magnetic Fields. A current (moving electric charges) creates a magnetic field. The Biot-Savart Law.

Tuesday 3/11: The Biot-Savart Law. Circular loop of current carrying wire. 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. Operational definition of the Ampere.

Wednesday 3/12: Magnetic Force between Two Current Carrying Wires (con't.): Operational defnition of the Coulomb.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).

Thursday 3/13: B-field of a Solenoid. 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! Q14 Take-home quiz, due Monday 17 March 2003.

Friday 3/14: Return X2. Q14 Take-home quiz, due Monday 17 March 2003.

### Week of March 17-21, 2003.

Monday 3/17: B-field of an infinite sheet of current. Gauss' Law for Magnetism. Not as useful as Gauss' Law for Electricity, because it is always zero (no magnetic monopoles). Ampere-Maxwell equation. We need to define a displacement current to describe what is happening in the gap of a charging or discharging capacitor. And again we are linking E-fields and B-fields together. Q14 Take-Home quiz, due Monday 17 March 2003.

Tuesday 3/18: 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. Q15 in-class.

Wednesday 3/19: 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. 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.

Thursday 3/20: Demostration Day -- Magnetic force on a current carrying wire. "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. Q16 in-class.

Friday 3/21: The General form of Faraday's Law of Induction. Maxwell's Equations in integral form. Turning coil in a constant magnetic field -- creates a generator (A.C. or D.C.). Motor-Generator set. Why induction is a big deal in electronics, industrial motors and electrical power distribution. The Inductor (L). (SI units = Henry = H) Self-Inductance. Back emf, back current. Opposing the status quo. First set of Sample Exam 3 problems handed out.

### Week of March 24-28, 2003.

Monday 3/24: 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. RL Circuit, similar to RC Circuit, except that energy is stored in the magnetic field at the maximum current. Last day to turn in a Draft Paper for evaluation.

Tuesday 3/25: Energy is stored in the magnetic field of an inductor at the maximum current. Mutual Inductance between two inductors. 2nd coil responds only to changes in magnetic flux coming from 1st coil. Start talking about LC Oscillator circuit. Q17 in class.

Wednesday 3/26: LC Oscillator circuit. Same 2nd order differential equation as the Simple Harmonic Oscillator (PHYS-205), such as a mass on a spring. Comments ONLY about the RLC Damped Harmonic Oscillator and the Driven RLC Harmonic Oscillator (Amplifier).

Thursday 3/27: 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. First day to turn in Topic 1 Papers. Quiz 18 in class.

Friday 3/28: Alternating Current (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. REMINDER: There is an error in one place of the Syllabus, regarding the date/time of the PHYS-207 Final Exam.

### Week of March 31- April 4, 2003.

Monday 3/31: 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°. RC Circuits: I and V out of phase by -90°. Inductive Reactance, 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). Topic 1 Papers due by 5pm for all Dr. Phil students, except those who had a Draft Paper evaluation.

Tuesday 4/1: 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. 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. Efficiency = Power Used ÷ Total Power Generated. Power lines run at higher voltages to minimize power losses due to Joule heating in the powerlines. Q19 take-home, due Thursday by 5pm.

Wednesday 4/2: NOTE: Special office hours from 1pm to 4pm today only for PHYS-207 students.

Thursday 4/3: Exam 3.

Friday 4/4: Maxwell's Equations and Hertz's radio wave LC oscillator -- the spark gap radio.

### Week of April 7-11, 2003.

Monday 4/7: 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. Poynting Vector, S. Traveling E-M Wave, Poynting Vector and Intensity.

Tuesday 4/8: Poynting Vector, S. Momentum and Pressure of light waves absorbed or reflected on contact. The Great 19th Century Debate: Is Light a Particle or a Wave? (Wave-Particle Duality did not seem obvious at the time.) The Electromagnetic Spectrum. Visible light (ROYGBIV=red orange yellow green blue indigo violet).

Wednesday 4/9: The Electromagnetic Spectrum. (ROYGBIV=red orange yellow green blue indigo violet). Frequencies LOWER and wavelengths LONGER than visible light (IR infrared, Microwave, Radio waves, ELF extremely low frequency).

Thursday 4/10: Optics: Geometric Optics (empirical) and Physical Optics (more wave and fieldlike). Ray Tracing: Rays from a spherical source become essentially parallel rays when you are far away. The Law of Reflection. Rough surfaces. Corner and Corner Cube reflectors. The Optical Lever -- move a mirror by 10° and the reflected ray moves by 20°. (Dr. Phil's theory on the origin of "seven years of bad luck for breaking a mirror".)

Friday 4/11: (Dr. Phil's It's-All-Going-Wrong-Day!) X3 Returned -- problems with grading -- go over Star Problems. The Law of Refraction - Snell's Law. Light bent at the interface between two media, because the speed of light changes in the media.