## Lectures in PHYS-207 (H7)

Updated: 8 December 2002 Sunday

### Week of December 2-6, 2002.

Monday 12/2: Thin Lenses. Positive, biconvex, converging lens. Concentrating sunlight: burning paper or popping ants? Negative, biconcave, diverging lens. Real image formed by passing rays through a positive thin lens.

Tuesday 12/3: 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. Physical Optics. Based on wave properties of light. 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

Wednesday 12/4: Young's Double-Slit Interference. Single-Slit Diffraction. Double-Slit plus Single Slit.

Thursday 12/5: A quick revisit (for PHYS-205 Honors students) of Relativity. Classical Relativity (two observers, two frames of reference), Special Relativity (speed constant), General Relativity (accelerations or gravity). Beta, gamma, Length Contraction and Time Dilation. Armed with this knowledge, we can look at a moving electric charge and a parallel current carrying wire. In the rest frame of the wire, the charge can experience a magnetic force due to the B-field coming from the current carrying wire. But if we look at the rest frame of the charge, then fixed positive charged ions of the metal will appear to be moving at -v, while the negavtive charge carries go the same way as the charge. Length contraction makes it appear that the wire has a net positive charge, and the charge q will be repelled by the E-field from this apparent "offset" in the charges. Q22 take-home quiz, due Friday 6 December 2002.

Friday 12/6: Course Review. Q23 take-home quiz, due at Your Final Exam.

### Week of September 2-6, 2002

Monday 9/2: LABOR DAY

Tuesday 9/3: OFFICE DAY

Wednesday 9/4: Class begins. Introduction to Dr. Phil. Distribute Syllabus. Discuss 19th Century Physics.

Thursday 9/5: Four Fundamental Forces in Nature: Gravity, E & M, Weak Nuclear Force, Strong Nuclear Force. 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.

Friday 9/6: 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 (!!!). Q1 given as Take-Home, due Monday 9/9.

### Week of September 9-13, 2002

Monday 9/9: Coulomb's Law continued. Review of Vector Force problems. Q1 due. Q2 in-class.

Tuesday 9/10: Conductors (metals) versus non-conductors (insulators). "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.

Wednesday 9/11: 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.

Thursday 9/12: Thin ring of charge perpendicular to line from point P. Review of polar co-ordinates and differentials for Area (dA) and Volume (dV). 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. Q3 in-class.

Friday 9/13: Inducing a charge on a conductor. Electric Flux: Electric field times Area, modified by the angle. Review of Dot Product.

### Week of September 16-19, 2002

Monday 9/16: Gauss' Law for Electricity. Coulomb's constant k versus Permitivity of Free Space (epsilon-naught). Review of cylindrical and spherical co-ordinates.

Tuesday 9/17: Lecture Handout 2-D and 3-D Integration. Lecture Handout: Gauss' Law. Q4 Take-Home handed out, Due probably Thursday 9/19 (Click here if you need a copy).

Wednesday 9/18: Continue standard Gauss' Law problems. 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.

Thursday 9/19: Finding V by direct integration. Find components of E by partial derivative of Electric Potential function V. Conductor in equilibrium is an equipotential throughout. Q5 in-class.

Friday 9/20: Equipotential lines, where V is constant, are always perpendicular to E-field lines.

### Week of September 23-27, 2002

Monday 9/23: Moving from Field Theory to Applications leading to Devices. The Capacitor stores charge +Q on one plate and -Q on second plate, stores energy in the E-field between the plates. Capacitor Equation. Stories: Dr. Phil & the camera flash, US Navy seaman vs. the tank capacitor (Cap-2, Seaman-0). Parallel Plate Capacitor.

Tuesday 9/24: 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 (Started -- finish Wednesday).

Wednesday 9/25: Finish 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. Q6 in-class.

Thursday 9/26:

Friday 9/27: Work to assemble charges on a capacitor = Energy stored in the capacitor. Energy density is the energy stored in the E-field per volume. Some Exam 1 review.

### Week of September 30 - October 4, 2002

Monday 9/30: Electrostatics versus Electrodynamics. Current defined. Resistors and Resistance. The Simplest Circuit: Battery, wires, load (resistor). Ohm's Law (Vector form with current density J). Conductivity vs. Resistivity.

Tuesday 10/1: Ohm's Law: V=IR form. (Ohm's "3 Laws"). 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. 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. Short Circuit defined.

Wednesday 10/2: Exam 1.

Thursday 10/3: Continuing with Resistors. 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"). Q8 Take-Home, Due Monday 7 October.

Friday 10/4: For example given in class on Thursday, 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.) 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. 1st Sample Exams for Exam 2.

### Week of October 7-11, 2002

Monday 10/7: 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.)

Tuesday 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-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.

Wednesday 10/9: Setup a Kirchhoff's Law problem from the textbook (28.27?) -- turns out it is essentially the circuit as we did before. 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.

Thursday 10/10: 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.

Friday 10/11: Ammeter: a galvanometer and a very small shunt resistor in parallel, together connected in series with the circuit. Voltmeter: a galvanometer amd a very larger 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. 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%.

### Week of October 14-18, 2002.

Monday 10/14: "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. Magnetic Force on a Moving Electric Charge - Right-Hand Rule & Uniform Circular Motion. Cyclotron frequency -- no dependence on the radius (constant angular velocity).

Tuesday 10/15: 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). Q9 due today, but it is clear that people are still have problems. Will turn back on Wednesday & give more time.

Wednesday 10/16: Mass Spectrometer as Calutron -- detecting or separating isotopes, something that cannot be done by chemical means. Q10 in-class.

Thursday 10/17: Magnetic Force on a Current Carrying Wire. For a Closed Loop, the net Magnetic Force from a constant B-field is zero. Q11 in-class.

Friday 10/18: Exam 1 returned.

### Week of October 21-25, 2002.

Monday 10/21: 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.

Tuesday 10/22: 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. Hall Effect -- a device with no moving electrical parts -- proves that charge carriers in a current carrying wire are negative, not positive. Q12 in-class.

Wednesday 10/23: Sources of Magnetic Fields. The Biot-Savart Law. Circular and semi-circular loop of current carrying wire. Magnetic Force between Two Current Carrying Wires. Operational definition of the Ampere and the Coulomb.

Thursday 10/24: Exam 2 (rescheduled to today).

Friday 10/25: 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).

### Week of October 28-November 1, 2002.

Monday 10/28: 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.) B-field of a Solenoid. Comments about winding real coils with thin, varnish insulation.

Tuesday 10/29: 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.

Wednesday 10/30: Exam 2 returned. Q13 in-class.

Thursday 10/31: B-field of an infinite sheet of current. 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.

Friday 11/1: Demostration Day -- Magnet moving into a coil, causing current to flow through galvanometer. Magnetic force on a current carrying wire. Broken cow magnet, showing the weakened radial metal grain structure of the aligned magnetic moments that allowed it to break when dropped. "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

### Week of November 4-8, 2002.

Monday 11/4: The General form of Faraday's Law of Induction. Maxwell's Equations in integral form. First set of Sample Exam 3 problems handed out.

Tuesday 11/5: Move Exam 3 to Thursday 21 November 2002. 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. Q14 in-class. Second set of Sample Exam 3 problems handed out.

Wednesday 11/6: 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. LC Oscillator circuit. Same 2nd order differential equation as the Simple Harmonic Oscillator (PHYS-205), such as a mass on a spring.

Thursday 11/7: Comments ONLY about the RLC Damped Harmonic Oscillator and the Driven RLC Harmonic Oscillator (Amplifier).

Friday 11/8: 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.

### Week of November 11-15, 2002.

Monday 11/11: 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.

Tuesday 11/12: 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). Q15 take-home quiz due today.

Wednesday 11/13: Why A.C. power? D.C. power lines have huge power losses due to Joule heating, very low efficiency. Efficiency = Power Used ÷ Total Power Generated. Q16 take-home, due Friday.

Thursday 11/14: Power lines run at higher voltages to minimize power losses due to Joule heating in the powerlines.

Friday 11/15: Transformers allow voltage to be raised or lowered.

### Week of November 18-22, 2002.

Monday 11/18: Maxwell's Equations and Hertz's radio wave LC oscillator -- the spark gap radio. Aside: The Electromagnetic Spectrum. Visible light (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).

Tuesday 11/19: E-M Spectrum (continued). Finish radio & ELF waves. Frequencies HIGHER and wavelengths SHORTER than visible light: (UV ultraviolet, X-rays, Gamma rays).

Wednesday 11/20: Review Star Problems for Exam 3.

Thursday 11/21: Exam 3 (rescheduled date)

Friday 11/22: 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. Momentum and Pressure of light waves absorbed or reflected on contact. Traveling E-M Wave, Poynting Vector and Intensity.

### Week of November 25-29, 2002.

Monday 11/25: 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. Q17 in-class.

Tuesday 11/26: 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".) The Law of Refraction - Snell's Law. Light bent at the interface between two media, because the speed of light changes in the media. If going from an high index of refraction media to a lower index media, have a chance for Total Internal Reflection (T.I.R.). Q18-19 take-home, now due Tuesday 3 December 2002.

Wednesday 11/27: WMU Closes at Noon. We moved Noon back an hour. (grin)

Thursday 11/28: It's Thanksgiving. Go eat something. Be Thankful.

Friday 11/29: No classes.