Lectures in PHYS-115 (4)

Updated: 18 April 2005 Monday.

Week of April 18-22, 2005.


Monday 4/18, Tuesday 4/19: OFFICE HOURS 10am-3pm.

Wednesday 4/20: PHYS-115 Final Exam (2 hours) 2:45-4:45pm, 1104 Rood Hall

Thursday 4/21: Dr. Phil may not drive in today -- if you have to make up the Final Exam, please contact Dr. Phil ASAP

Friday 4/22: OFFICE HOURS 10am-3pm. Last chance to make-up Final Exam before a Zero or Incomplete.

Week of January 3-7, 2005.

Monday 1/3: OFFICE DAY. No Classes.

Tuesday 1/4: Class begins. Introduction to Dr. Phil. 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. Static Electricity -- glass/plastic rods and rubber rods, silk cloth and pieces of fur. Two different ways to "charge" up an object, sometimes they attract, sometimes they repel. The Two-Fluid Model of Electricity, call them A & B. Franklin's One-Fluid Model of Electricity. 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. Q1 - Attendance and choosing a PID (Personal ID number).

Thursday 1/9: The Hydrogen Atom: Gravity loses to Electric Force by a factor of 200 million dectillion (!!!). 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.

Friday 1/10: A Nickel coin has a mass of 5 grams, so about 1/10th of a mole. Find the number of Coulombs of positive and negative charges. 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 (!!!). Handout about SI metric system prefixes and Dr. Phil's Practical Significant Figures. Distribute syllabus.

Week of January 10-14, 2005.

Monday 1/10: Remember: In PHYS-115, 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. Semi-Conductors sit in the middle. Sometimes they conduct and sometimes they don't. This means they act like a switch or valve, and this is the basis for the entire electronics semi-conductor industry.

Tuesday 1/11: NOTE: We are changing rooms from 1110 Rood Hall to 1104 Rood Hall today. Looking at Symmetry and Zeroes as a way of solving problems. How does q1 know that q2 is there? -- "Action at a Distance" -- Gravity and the Electric Force are not contact forces. The mathematical construct of the Electric Field. E is not an observable quantity. (Side example: Methods of measuring speed v, do not directly measure speed v.) Q2 became a Take-Home, now due Wednesday 12 January 2005, in class or by 5pm.

Wednesday 1/12: E-field diagrams. E-field lines radiate away from positive point charges, towards negative point charges. E-field lines allow us to qualitatively sketch what happens when two charges are near to each other. (1) +q an-q, (2) +q and +q, (3) +2q and -q. Note that far from the charges, these systems look like just a single point charge with a net charge of (1) 0, (2) +2q and (3) +q. Finite objects: Near distances, Far distances (looks like a point charge) and inbetween (requires PHYS-207 and calculus).

Thursday 1/13: E-Fields and Conductors (in Electrostatic Equilibrium). Charges accumulate on outside of conductors. (1) E-Field lines terminate normal (perpendicular) to the conductor's surface. (2) E = 0 inside the conductor. (3) Charges tend to accumulate more on pointy tips of things, which means more E-field lines and stronger E-fields. Easy to show for a uniformly charged sphere that (2) is true at center of the sphere, harder to show (2) is true everywhere inside the sphere. 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. E-max in air is 300,000,000 N/C. Little sparks from walking across the carpet. Lightning from big charges accumulating on underside of thunderstorms. Distribute Topic 1 Handout. (Searchable Web Page; Downloadable PDF File). Q3 Take-Home, due Tuesday 18 January 2005, in class or by 5pm.

Friday 1/14: Electric Flux: Electric field times Area, modified by the angle. Simplest examples are E-field perpendicular to surface, max flux and parallel to surface, no flux. The permitivity of free space, epsilon-naught. Gauss's Law for Electricity. Derive for point charge, turns out to be general equation. Take advantage of geometry and symmetry. For conducting charged metal sphere of radius R, all the charge is on the outside. Two cases: (1) r < R, no q-inside Gaussian suface, no E-field and (2) r > R, q-inside = Q, so E-field same as a point charge.

Week of January 17-21, 2005.

Monday 1/17: Dr. Martin Luther King, Jr. memorial observance [No Class Today]

Tuesday 1/18: Two more Gauss's Law cases: A line of charge, lamda = Q / L. E-field falls off as 1/r, not 1/r². A sheet of charge, sigma = Q / A. E-field is constant. Infinite line or sheet of charge versus finite line or sheet (need to stay close to charge and near center, away from edges.) Extend deadline for Q3 to Wednesday 19 January 2005.

Wednesday 1/19: Two terms with unfortunately close sounding names: Electric Potential Energy (in Joules) and Electric Potential (in Volts).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. Q4 Take-home, due Friday 21 January 2005. (Click here for a copy.)

Thursday 1/20: If a charged conducting sphere has E = 0 on the inside, as we saw from Gauss's Law for Electricity, then E = constant on the inside and therefore delta-V = 0, so V = constant. We call this an "equipotential." (1) We can use this to show why charge accumulates on the tip of pointy things. (2) Or plot equipotential contours around a +q and a -q point charges, sketch in our E-field lines and discover that E-field vectors are ALWAYS perpendicular to equipotential lines/surfaces. Equipotential lines can be plotted like altitude on topological maps, equipotential surfaces can be plotted in 3-D to look like ski slopes on mountains. (See Figure 16-5 in textbook.) Examples in real world of E-field measurements by taking voltage readings -- E-field emissions from computer CRT monitors. First Sample Exam 1 handed out. Q5 Take-home, due Monday 24 January 2005.

Friday 1/21: 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).

Week of January 24-28, 2005.

Monday 1/24: 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! 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.

Tuesday 1/25: Finish the table. How a camera flash works -- why a battery and a capacitor are different. Q6 in-class.

Wednesday 1/26: 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. Polarization. Dielectric constant (kappa) and Dielectric strength (E-max).

Thursday 1/27: 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.Q7 Take-Home, due Tuesday 1 February 2005.

Friday 1/28: 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.

Week of January 31-February 4, 2005.

Monday 1/31: 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"). For example given in class, 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.)

Tuesday 2/1: Exam 1 review, Q3-6 solutions. Q8 Take-Home, due Monday 7 February 2005.

Wednesday 2/2: 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.) (Some Sample Exam 1 solutions, click here for a copy.)

Thursday 2/3: Exam 1 rescheduled to here.

Friday 2/4:

Week of February 7-11, 2005.

Monday 2/7: 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 problem from lecture.

Tuesday 2/8: RC series circuit. Circuit diagram for charging capacitor (ignore the calculus part). 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. The current, for both charging and discharging capacitor in an RC circuit, is maximum at time = 0 and goes to zero over time. Q9 take-home, due Monday 14 February 2005. NOTE: you can get most of the points even if you don't or can't do the algebra and get a solution to part (d). (Click here for a copy.)

Wednesday 2/9: Demo Day: Light bulb boxes for PARALLEL RESISTORS (unscrew a bulb, remainder stay lit at same brightness), SERIES RESISTORS (unscrew a bulb and they all go out; put a 100W and a 15W bulb in series and the smaller bulb lights up okay, but no glow from bigger bulb), and RC CIRCUITS (start with two caps in parallel, connected in series with a light bulb. large (bright) initial current, fades over time as delta-V on plates builds up. 3 caps in parallel, takes longer -- RC constant is larger. 1 cap or 3 caps in series, short and shorter times to charge or discharge.). Discuss modern Christmas tree lights. Bulbs in series, but each bulb is in parallel with a small resistor, to keep whole string lit when one bulb burns out.

Thursday 2/10: Measuring things has the potential to change that which we are measuring. In PHYS-116 Lab, you are using digital multimeters. 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 2/11: Ammeter: a galvanometer and a very small shunt resistor in parallel, together connected in series with the circuit. Voltmeter: a galvanometer amd a very 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. (If you have the numbers from class, you can show that for a resistor expected 5.00 A and 5.00 V that the changes in the readings with both meters present won't change the values in our example by more than 0.01%.) Intended to hand out First Sample Exam 2, but wouldn't print. (You can get an advance copy from this PDF.)

Week of February 14-18, 2005.

Monday 2/14: Resistance of people varies with quality of contact surface -- could be as high as 1,000,000 ohms or as low as 20,000 - 40,000 ohms. 11 mA (0.011 A) is fatal, because it burns out the natural pacemaker of the heart. Why European 240 V is more dangerous than North American 120 V. Electrical outlets in the U.S. 2-prongs versus 3-prongs (versus 2-polarized prongs). How grounding helps. "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.

Tuesday 2/15: X1 returned (finally, after re-grade). 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 is 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. Likewise, placing a piece of steel, such as a screwdriver tip, against a powerful magnet may allow some iron atoms to line up with the magnetic field, thereby magnetizing the screwdriver tip. 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.

Wednesday 2/16: 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. Example of the 4T NMR magnet at Michigan Tech and the 10-foot radius line on the floor and erasing ATM cards within that circle. Magnetic Force on a Moving Electric Charge - Right-Hand Rule & Uniform Circular Motion.

Thursday 2/17: 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... A mass spectrometer -- a device that sorts particles by mass. 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. Q11 Take-Home, due Monday 20 February 2005 by 5pm. (Click here for a copy.) There was an error in the filename on the class web page and this link was missing on this page -- must've been interupted in the middle of updating this. Dr. Phil

Friday 2/18: Magnetic Force on a Current Carrying Wire. An electric current is a series of moving electric charges, after all. See text, p.594, for microscopic argument using drift velocity of charge carriers. The magnetic constant -- the Permeability of Free Space. Magnetic Field loops from a Current Carrying Wire. Because there are no magnetic monopoles, Gauss's Law for Magnetism simply tells us that the total magnetic flux through any closed surface equals zero. Ampere's Law, however, is more useful: Any closed Amperean Loop will have the sum of all the B-field pieces parallel to the Amperean Loop be proportional to current I which is enclosed by the Amperean Loop. Magnetic Force between Two Current Carrying Wires. Combining problems, we find that for two parallel current carrying wires, with the currents in the same direction, the magnetic field from wire 1 creates an attractive magnetic force on wire 2. And the magnetic field from wire 2 creates an attractive magnetic force on wire 1. (Two forces, equal and opposite, acting on each other -- this is exactly as it should be with Newton's 3rd Law.) Second sample Exam 2.

Week of February 21-25, 2005.

Monday 2/21: Magnetic Force between Two Current Carrying Wires (con't.). Magnetic field from a single loop of wire. B-field of a Solenoid: constant and uniform B-field inside (away from edges) and zero outside the coil. 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!

Tuesday 2/22: Comments about winding real coils with thin, varnish insulation. Operational definition of the Ampere using the Magnetic Force between Two Current Carrying Wires. A single moving electric charge as: (1) a current and (2) as a source of a B-field. Comments about particle accelerators and "beam currents." Q12 on Right-Hand Rule and Current Carrying Wire, in-class.

Wednesday 2/23: Review RHR as applied to Q12 and other examples. Remember, there are "two modes". Mode 1 uses three mutually perpendicular directions for when you have three vectors (A × B = C is 1-2-3, x-y-z). Mode 2 uses the curling of the fingers to represent the circulation of a field or the motion of a current, etc., with the thumb representing the relevent vector or direction. Magnetic Torque on a Current Carrying Wire Loop. 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 2/24: Exam 2. (Handed out Worksheet 1 - click here for a copy.)

Friday 2/25: <Spirit Day> No classes. Effective start to Spring Break.

Week of February 28-March 4, 2005.

Monday 2/28 - Friday 3/4: WMU Spring Break -- No classes.

Week of March 7-11, 2005.

Monday 3/7: Faraday's Law of Induction. A changing magnetic flux induces a current in a loop of wire. Think of the coil as wanting to maintain "the status quo". So if the magnetic flux is increasing, the induced current creates an induced magnetic field to try to cancel the flux. If the magnetic flux is decreasing, the induced current creates an induced magnetic field to try to bolster the flux. Demo: Magnet moving into a coil, causing current to flow through galvanometer. Turning coil in a constant magnetic field -- creates a generator (A.C. or D.C.). See notes for 2/23 on a primitive electric motor. Essentially electric motors and generators are the same devices. Dynamic or Regenerative Braking turns electric motors into generators -- it takes energy (work) to turn the generator and this energy is robbed from the vehicle's Kinetic Energy. Hybrid gas-electric cars use this as do most railroad trains (either electric or diesel-electric).

Tuesday 3/8: 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. 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. Q13 take-home, due Thursday 10 March 2005.

Wednesday 3/9: 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.

Thursday 3/10: Return X2. Why induction is a big deal in electronics, industrial motors and electrical power distribution. Back emf, back current.

Friday 3/11: The Inductor (L). (SI units = Henry = H) Self-Inductance. Back emf, back current. Opposing the status quo -- even of its own B-field. The Series RL Circuit. Very much like the Series RC Circuit, but everything the opposite. RC: Charges stored on capacitor plates. The current stops when fully charged. Energy is stored in the electric field between the plates (PE = ½ C V²). RL: Current (moving charges) moving through coil. The current is at a maximum when fully energized. Energy is stored in the magnetic field inside the coil (PE = ½ L I²). NOTE: Technically it is very hard to have a purely inductive circuit, that is just a battery and an inductor L, because the long thin wire used in the coil's windings generally has a resistance. Therefore real L circuits are really RL circuits. This is analagous to the capacitor, where there is a resistance in the wire connected to the plates of the capacitor, and therefore real C circuits are really RC circuits. In both cases this means it takes a finite, non-zero time for the device (L or C) to store energy in its respective field.

Week of March 14-18, 2005.

Monday 3/14: Back to trying to understand why A.C. circuits are different than D.C. 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. For A.C. circuits with a Resistor only: I and V stay in phase with each other. RC Circuits: I and V out of phase by -90°. (We say the voltage lags the current.) RL Circuits: I and V out of phase by 90°. (We say the voltage leads the current.) Inductive Reactance, Capacitive Reactance.

Tuesday 3/15: 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). Treat Resistive Voltage as one vector and Inductive Voltage minus Capacitive Voltage as a perpendicular vector. Whole structure rotates and we take the y-components to get the sine-function of the voltage. V-max and Phase angle (phi) just like finding the magnitude and standard angle from an x- and y-components of a vector. Q14 in-class on inductors. Q15 Take-Home, due Thursday 17 March 2005.

Wednesday 3/16: 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. Maxwell's Equations and Hertz's radio wave LC oscillator -- the spark gap radio.

Thursday 3/17: For Repeating Waves, we have a Repeat Length (wavelength) and a Repeat Time (Period). Frequency = 1/Period. Wave speed = frequency x wavelength. The Electromagnetic Wave travels at the speed of light. c = 300,000,000 m/s = 186,000 miles/sec, in vacuum. Speed of light in air nearly the same. The Electromagnetic Spectrum. Visible light (ROYGBIV=red orange yellow green blue indigo violet). Frequencies HIGHER and wavelengths SHORTER than visible light (UV ultraviolet, X-rays, Gamma rays).

Friday 3/18: EM Spectrum continued. (X-rays, Gamma rays). Visible light is 400nm to 700nm (4000 angstroms to 7000 angstroms). Cannot "see" atoms with visable light, because the atom is about 1 angstrom across (1.00E-10 meters). The visible light wave is too large to see something that small. So use X-rays. Discussion of why Superman's X-ray vision cannot work. Frequences LOWER and wavelengths LONGER than visible light (IR infrared, microwaves, ...). Microwave ovens have metal screens in their windows -- the centimeter-range sized EM waves cannot see the "small" holes in the screen, so they bounce off the window as if it were just like the metal in the other five walls. Discussion of how microwave ovens "cook" food.

Week of March 21-25, 2005.

Monday 3/21: Finish up E-M spectrum. Frequencies LOWER and wavelengths LONGER than visible light (IR infrared, Microwave, Radio waves, ELF extremely low frequency). 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.

Tuesday 3/22: Rough surfaces. 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. Quiz 16 Take-Home, due Thursday 24 March 2005. Worksheet 2 -- Due Tuesday 29 March 2005. (Click here for a copy.)

Wednesday 3/23: 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.). This is a "perfect" reflection, better than a mirror. Used in high-end optical systems instead of mirrors. Also useful in fiber optics cables. Light going through a parallel-plano sheet of glass. Two interfaces: air-to-glass and glass-back-to-air. Coming down the normal, 0°, no deviation. At any other angle from the normal in air, the ray is refracted towards the normal in glass and then back out at the original angle when back in air. However, the light ray is offset from the line the ray would've followed had the glass not been there. Discussion of trying to see forward (large angle from normal) through the windows of a bus, train or plane. Very hard and very expensive to make true parallel-plano surfaces.

Thursday 3/24: Corner and Corner Cube reflectors. Thin Lenses. Simplest lens surfaces are spherical (convex = bows out, concave = bows in) and flat (plano). So some lenses might appear to be biconvex, plano-convex, biconcave, convex-concave. A biconvex lens is also called a positive or converging lens. Parallel light rays coming into such a lens will all pass through the focal point, a distance f from the center of the lens. By itself, could use as a magnifying lens. Concentrating sunlight: burning paper or popping ants? First Sample Exam 3 to be handed out.

Friday 3/25: For practical considerations for many students, there will be no 3pm PHYS-115 class on Friday 25 March 2005.

Week of March 28-April 1, 2005.

Monday 3/28: Ray tracing gets same results as doing Snell's Law on mulitple curved lens surfaces. Handy not to have to do all that refraction calculations! Real image formed by passing three rays through a positive thin lens. Three cases: object distance p > 2f (real, inverted, reduced image), 2f < p < f (real, inverted, magnified image), p < f (virtual, upright, magnified image = magnifying glass) -- latter two not shown here.

Tuesday 3/29: Analytic formula for object and image. Magnification: M = h' / h = -q / p. The Lens-Maker Formula (really for use in air/vacuum, where n = 1.00). Problem of lenses underwater. Dispersion -- in vacuum all speeds of light are the same, but in a medium, there are slighltly different n's for each wavelength. See prism problem in second Sample Exam 3. Ways to make lenses much more expensive: aspherical (non-spherical curved surfaces), ED glass (extra-low dispersion, allows color pictures with huge telephoto lenses to be in focus). Quiz 17 take-home, due Thurday 31 March 2005, but you can turn in until Monday 4 April 2005 at 5pm.

Wednesday 3/30: 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.

Thursday 3/31: Exam 3.

Friday 4/1: 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 the same quarterwave anti-reflection solution. If both reflections are different, we get halfwave anti-reflection coatings.

Week of April 4-8, 2005.

Monday 4/4: Light from two slit sources -- classically the light should travel in a straight line, get two "light shadows" or bright spots on the target wall. In wave theory, however, light from two coherent (in-phase) point sources will reach a point along the centerline, both traveling the same distance so get constructive interference and a bright spot. At some place offset from centerline, the two distances will vary by half a wavelength and get destructive interference and a dark spot. Alternating bright and dark spots as the two distances change. Young's Double-Slit Interference.

Tuesday 4/5: Single-Slit Diffraction. Double-Slit plus Single Slit. Demo: Double-hemispherical wave overlaps on the overhead projector. Q19 Take-Home, due Thursday 7 April 2005, but can still be turned in Monday 11 April 2005.

Wednesday 4/6: Classical Relativity (two observers, two frames of reference), Special Relativity (speed constant), General Relativity (accelerations or gravity). 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. Q18 in-class (no time on Tuesday).

Thursday 4/7: 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.

Friday 4/8: Two observers cannot agree on the order of events, either. The concept of "simultaneity" is gone. 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. Return some quizzes. Hand out first Sample Final Exam. (Click here for a copy.)

Week of April 11-15, 2005.

Monday 4/11: Relativistic momentum and relativistic Kinetic Energy. Total Energy. The Einstein Relation, E = m c². The deBroglie wavelength -- Wave/Particle Duality for Matter. Planck's constant -- a very small number, but it is NOT zero ( h = 0 in Classical Physics). Q20 Take-Home, due Wednesday 13 April 2005. Q21 Take-Home, due Thursday 14 April 2005. Second Sample File exam. (Click here for a copy.)

Tuesday 4/12: Energy of a photon, a single particle of light is E = h f. Momentum of a massless photon. Heisenberg Uncertainty Principle -- at the level of the atom and its parts, one cannot simultaneous measure certain pairs of quantities to any level of accuracy. Measuring one, means one loses information of the other. Position and momentum: (delta-x)(delta-p) is greater than or equal to h / 4pi. Energy and time: (delta-E)(delta-t) is greater than or equal to h / 4pi. (Note: the quantity h / 2pi shows up so often, we call this h-bar and run a line through the "h" as if we were crossing a "t".) The consequence is that the electron's position around the atom ends up being smeared and we end up talking about probabilities of quantities. For most classical quantities, you can have any value you want. In the realm of quantum mechanics, very small dimensions, values must be quantized -- analogy of the lecture hall and the stairs and the levels with the seats, as opposed to a ramp. Chemistry suggests a finite number of elements or starting blocks for all materials. Everything made of individual atoms, as opposed to say the Velveeta cheese model, where you can forever slice the Velveeta ever finer. Plum pudding model of the atom -- some hard bits in a matrix. Rutherford experiment -- firing particles at a very thin piece of gold foil (discussion of gold leaf), some of the particles rebounded at nearly 180°. "It was as if I had fired cannonballs at a piece of paper and some bounced back towards me." Better model of the atom: electrons on the outside (size of the atom is about 1 angstrom = 1 ×10E-10 meters) and protons (and neutrons, not yet discovered) concentrated into a nucleus (about 1 femtometer = 1 ×10E-15 meters). The Bohr atom is really quite a triumph of the Physics of PHYS-113 and PHYS-115: We showed early in the semester that the gravitational attraction between an electron and a proton doesn't matter in the hydrogen atom, so if we have an electron in a circular orbit about the proton (or better yet, the nucleus with a total proton charge Q = +Z e, so we can do elements other than hydrogen), then the Coulomb Force provides the centripetal force for Uniform Circular Motion (UCM). That allows us to find the speed v as a function of the radius r. Bohr postulated that the electron could only exist in certain orbits, so he proposed that the angular momentum (mvr) can only have integer values of h-bar. This introduces the principle quantum number n. This also means that the circumference of the orbital is some integer of the electron's deBroglie wavelength -- and we have a circular standing wave only for those orbits which are allowed.

Wednesday 4/13: Handout: Dr.Phil's Periodic Table and Derrivation of Radius and Energy Levels in the Bohr Atom. (Click here for a copy.) By the time we get the radius equation, there are only two variables (and both are integers!): the quantum state number n and the proton/element number Z. All the other items are fundamental constants, which when multiplied together give us "a0", the radius of the n=1 innermost state of the hydrogen atom, equal to 0.528 ×10E-10 meters. Twice that is the diameter, so the size of the hydrogen atom is about an angstrom, as advertised. Note that the radius goes as n², so the orbitals get big quite fast. Since this is UCM, knowing the radius means we know the speed v. And that allows us to calculate the classical Kinetic Energy, KE = ½mv². (It turns out that the speeds remain below 0.42 c for all n and Z's for about half the periodic table, so we don't have to deal with Relativity.) The total energy of each state, En = KE + PE, and in this problem I shall state that the PE = -2KE. So En = -KE and it ends up being Z²/n² times more constants. The ground-state or n=1 energy for hydrogen is -2.18 ×10E-18 J or -13.6 eV. Now for an electron to move from one orbit to another, it must gain or lose energy. Going from a higher n to a lower n, the difference in the energy is release as a photon with E = hf. To go from a lower n to a higher n, the electron has to absorb a photon of E=hf. And now we have an explanation of the spectral lines which we had once described as "fingerprints for elements". Burn hydrogen and the light emitted, when run through a prism will split not into a rainbow, but individual lines of individual colors -- these are emission lines. Take white sunlight, shine it through a prism and look at the rainbow of colors under a microscope and you will see that individual lines of color are missing -- these are absoption lines caused by the hydrogen gas in the Sun's atmosphere removing those colors and moving their electrons to higher orbits or ionizing completely. Atomic spectra were known for decades before the Bohr atom, so they were trying to solve the puzzle backwards -- what they didn't know was that any transition involving the n=1 innermost orbit in hydrogen gave photons in the UV and so the scientists couldn't see them at the time. If we try to solve the helium atom (Z=2) in a similar way, we find that with one nucleus and two electrons, we have a three-body problem and we can't solve that in closed form. However, we can use our Bohr equations for hydrogenic ions (hydrogen-like) which have only one electron, so we can solve for He+, Li+2, Be+3, B+4, C+5, ... , U+91, etc. Third Sample Final Exam. (Click here for a copy.)

Thursday 4/14: A (very) brief discussion of Atomic and Nuclear Physics. Double Take-Home Quiz 22-23, due Friday 15 April 2005 -- but I'll accept them on Monday 18 April 2005 by 5pm. I'd like to be able to publish the solution Monday night. Worksheet 4 -- due at Final Exam, Wednesday 20 April 2005. (Click here for a copy.) At this point, all outside work (Take-Home Quizzes and Worksheets, plus the Paper) has been assigned. Only outstanding item is the Final Exam. X3 just came in -- will be handed back tomorrow.

Friday 4/15: LAST DAY OF CLASS - AND ALSO DAY THAT FEDERAL AND STATE INCOME TAXES ARE DUE. -- X3 Returned. (Click here for a solution set.) Course Review. Finish up the day with the course & teacher evaluations for the semester.