Dr. Phil's Home
Updated: 16 December 2007 Sunday.
Monday 12/10: Office Hours.
Tuesday 12/11: FINAL EXAM 12:30-2:30pm
Wednesday 12/12: Office Hours.
Thursday 12/13: Office Hours.
Friday 12/14: Office Hours. There is a chance that Dr. Phil may work from home on Friday if there is no need to come in on Friday, so you might want to check first.
Monday 12/17: Office Hours CANCELLED. There is a good chance now that Dr. Phil will NOT be in on Monday 17 December 2007. The weather forecasts on Friday suggested strongly that I gather all remaining materials and take home. Not sure how much snow K-zoo has as of Sunday afternoon -- why chance things? If you REALLY need to talk to me on Monday, either send me e-mail OR call me at home OR call the Physics Dept. at 269-387-4940 and have them e-mail or call me at home. Thanks!
Tuesday 12/18: GRADING DAY. Grades are due at Noon.
Monday 9/3: LABOR DAY -- No Classes.
Tuesday 9/4: Class begins. Introduction to Dr. Phil. Distribute syllabus.
Wednesday 9/5: Discuss 19th Century Physics. Demo: Static Electricity -- glass/plastic rods and rubber rods, silk cloth and pieces of fur. As expected, it was too humid for the Demo to work. 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. Occaam's Razor. The Hydrogen Atom. (Atom is neutral, ions are charged.)
Thursday 9/6: 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. 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. The Hydrogen Atom: Gravity loses to Electric Force by a factor of 200 million dectillion (!!!). Q1 - Attendance and choosing a PID (Personal ID number). (If you missed class on this day, check with Dr. Phil sometime soon or send email.)
Friday 9/7: The Hydrogen Atom: Gravity loses to Electric Force by a factor of 200 million dectillion (!!!) The Helium Atom: Putting more than one proton in the nucleus produces enormous forces on the tiny protons -- Need the Neutron and the Strong Nuclear Force (!!!). 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.
Monday 9/10: Remember: In PHYS-1150, Looking at Symmetry and Zeroes (ones where the answer is zero) as a way of solving problems. Review of Vector Force problems (don't blink or you'll miss it). Distribute Topic 1 Handout. (Searchable Web Page; Downloadable PDF File) Please note that the URL on the handout is not correct. It should read http://homepages.wmich.edu/~kaldon/classes/ph113-5-115-6-bl.pdf. The links on the web site are correct.
From PHYS-1130 notes on vectors: Now we need to start dealing with two-dimensional problems in general. Two kinds of numbers: Scalars (magnitude and units) and Vectors (magnitude, units and direction). Adding and subtracting vectors: Graphical method. To generate an analytical method, we first need to look at some Trigonometry. Right Triangles: Sum of the interior angles of any triangle is 180°, Pythagorean Theorem (a² + b² = c²). Standard Angle (start at positive x-axis and go counterclockwise). Standard Form: 5.00m @ 30°. Practical Trigonometry. SOHCAHTOA. Adding and subtracting vectors: Analytical method. (Check to make sure your calculator is set for Degrees mode. Try cos 45° = sin 45° = 0.7071) Why arctangent is a stupid function on your calculator.
Remember: PHYS-1160 Lab Begins This Week.
Tuesday 9/11: 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. 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 in-class quiz. Handout about SI metric system prefixes and Dr. Phil's Practical Significant Figures.
Wednesday 9/12: 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). Strength of E-field is important, in part because in air there is a limit to how big E can get. At breakdown, the E-field is large enough to start ripping electrons from gas molecules and the positive ions go one way, the electrons go another, and then we get a "spark" and no longer are static. Emax in air is 3,000,000 N/C. Little sparks from walking across the carpet. Lightning from big charges accumulating on underside of thunderstorms. Worse, charge tends to accumulate on the ends of "pointy things", which is why the hairs on the back of your arm or neck stand up when the E-field increases and you are more likely to be hit by lightning. Church steeples and lightning rods. NOTE: The syllabus had a typo on p. 14 -- Q3 is a take-home to be handed out tomorrow, not today.
Thursday 9/13: 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 comes from the E-field not Force. More importantly the Potential V (really delta-V) is an observable quantity. Simplified equation V = E d. Example: Lighting. 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. Q3 Take-Home, due Tuesday 18 September 2007.
Friday 9/14: Quick Tour of the PHYS-1130 Class website. 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. 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". While the charge on the tip is less than the charge on the rest, the surface charge density, sigma = q / Area, is much higher. Working toward Gauss's Law for Electricity. Analogy of a bag around a light bulb. All the light rays are contained within the bag, no matter the shape or distance or size. Electric flux. Hand out 1st Sample Exam 1. (Click here for a copy.)
Monday 9/17: Finally go over the four charges-in-a-square vector force problem in class. 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.
Tuesday 9/18: 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. 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.) SUMMARY: 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.) Due date for Q3 Take-Home extended by one day to Wednesday 19 September 2007. Q4 Take-Home due Thursday 20 September 2007. Second Sample Exam 1 handed out. (Click here for a copy.)
Wednesday 9/19: Arrr! It be International Talk Like A Pirate Day, me mateys. Moving from Field Theory to Applications leading to Devices. A battery is a device which stores energy in a chemical reaction. When connected to a circuit, postive charges flow from + terminal to - terminal (or negative charges flow from - terminal to + terminal). There is a potential difference or delta-V between the terminals of a battery. A real battery will run down if used too long or if one tries to work it too hard. We will start with "perfect" batteries which never run down. 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. US Navy seaman vs. the tank capacitor (Cap-2, Seaman-0). Use Gauss' Law for Electricity to find the E-field between the plates. Turns out to be twice the E-field from a single sheet of charge. (Important to know why.)
Thursday 9/20: Capacitor Equation. SI unit
for Capacitance is the Farad. 1F is a large capacitor. Usually deal with
µF (microfarad = 1/1,000,000th of a Farad) and pF (picofarad =
1/1,000,000,000,000th of a Farad). Circuit diagrams represent the elements of a
circuit. So far: battery, wires, capacitor. 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.
Exam 1 moved to Thursday 27 September 2007. Q5
Take-Home and due
Monday 24 September 2007 -- Note the due date,
set so the solution can be posted Monday evening, so you can see it before Exam
1.With the change in the Exam 1 date, the due
date for Q5 will probably be Tuesday 25 September 2007.
Friday 9/21: YES! WE HAVE CLASS TODAY! 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. E = 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! Third Sample Exam 1 handed out. (Click here for a copy.)
Monday 9/24: 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 (Emax). Dielectic constant increases capacitance over air gap. Dielectric strength usually bigger than Emax 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. Using dielectric to change capacitance for detection: Studfinder (for carpentry), some computer keyboard keys, biometrics for security systems.
Tuesday 9/25: Using dielectric to change capacitance for detection: Studfinder (for carpentry), some computer keyboard keys, biometrics for security systems. Review for Exam 1. Q6 Take-Home due Thursday 27 September 2007.
Wednesday 9/26: Electrostatics versus Electrodynamics. Resistors and Resistance. Current defined. Microscopic view of what is going on inside the wire. Positive current with positive charge carriers is the same as negative charge carriers (like electrons) going the other way. Inside the wire, electrons move randomly anyway. There are so many, they don't need to go fast to create a current -- the "drift velocity" of electrons is very slow, << 1 m/s. The Simplest Circuit: Battery, wires, load (resistor). Resistance vs. Conductance. Ohm's Law: V=IR form. (Ohm's "3 Laws").
Thursday 9/27: Exam 1.
Friday 9/28: YES! WE HAVE CLASS TODAY! Simplest circuit, load resistor, Ohm's Law: V=IR form. (Ohm's "3 Laws"). Electrocution -- it's not the voltage, it's the current and the resistance affects the current. Resistivity is a property of the material used in a resistor. Resistance by geometry. R = resistivity × length ÷ area. 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.
Monday 10/1: Yes, WMU will be open even if the State of Michigan shuts down. Power dissipated by Joule heating in a resistor. P = I V (3 forms of Power equation to with Ohm's "3 Laws"). Series and Parallel 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".) 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 10/2: Discussion of types of real batteries, especially the rechargeables (Nicad, NIMH and Li-ion, plus lead-acid) and why things have changed. 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. The actual voltage from the battery is the emf voltage minus the loss from the internal resistance. 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. Q7 Take-Home, due Thursday 4 October 2007.
Wednesday 10/3: 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.
Thursday 10/4: Continue with Kirchhoff Example. Example problem from lecture. Kirchhoff example, where "cross resistor" in a circuit with all identical resistors doesn't really count -- left and right sides of the circuit are identical, so no current flows through cross resistor. Wheatstone Bridge -- takes advantage of null current to find an unknown resistance. 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. Q8 Take-Home quiz on Kirchhoff's Laws, due one week later on Thursday 11 October 2007.
Friday 10/5: YES! WE HAVE CLASS TODAY! Measuring things has the potential to change that which we are measuring. In PHYS-1160 Lab, you are likely 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. 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%.) First Sample Exam 2 handed out. (Click here for a copy.)
Monday 10/8: Columbus Day (Observerd) -- not a WMU Holiday. 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. The natural number e = 2.7182818284590452353602874713527... provides a way for us to calculate exponential curves using the ex function of your calculators. To find t for any given charge q or current i level, you can use the natural log function, ln x, to "cancel" the ex function.
Tuesday 10/9: X1 handed back -- then collected for fixing problem with sig.figs. (Click here for a solution.) "Magnetism is just like Electricity, only different." Most people are familiar with (1) magnets sticking to some metals, not others such as stainless steel and (2) if you have two magnets, they may attract or repel. North and south are analogous to plus and minus charges. Q9 in-class quiz.
Wednesday 10/10: 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. Demos: Cow magnets -- powerful cylindrical, rounded end magnets which get dropped into a cow's first stomach, to collect nails, bits of barbed wire, etc. from continuing on to the cow's other stomachs. Broken cow magnets show a radial crystalline structure due to the alignment of small magnetic domains -- what makes the magnetic field strong also makes the magnet physically weak in some directions, hence the breakage across the radially aligned grains. Dropping a permanent magnet can result in a reduction of its magnetic field as the shock allows some iron atoms to flip 180° and therefore cancel instead of add to an adjacent iron atom's magnetic field. The horizontal compass needle rotates until its North end points North (or rather to the North Magnetic Pole, which is of course a South pole of the Earth's magnetic core); the vertical compass rotates so that it lines up with the B-field along the surface of the Earth at the point. At the Equator, the vertical magnetic should be parallel to the ground, at the magnetic poles, it should be perpendicular to the ground. Is the Earth's magnetic field going to flip some day? And what about Mars? Q8 deadline extended to Friday 12 October 2007.
Thursday 10/11: 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. 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. Q10 Take-Home due Tuesday 16 October 2007.
Friday 10/12: YES! WE HAVE CLASS TODAY! X1 re-handed back again. Check your grading carefully, and feel free to ask Dr. Phil -- you are entitled to all your points. 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... The Velocity Selector works with both positive and negative charges, but there must be a charge. A mass spectrometer -- a device that sorts particles by mass. 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. Q8 deadline extended to Monday 15 October 2007 at 1pm. Second Sample Exam 2 handed out. (Click here for a copy.)
Monday 10/15: 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. 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.Magnetic Torque on a Current Carrying Wire Loop. Torque = IBA or IBAsin(theta), where A = area enclosed by the coil. Though derived for a rectangular coil with sides a and b, it turns out this is a general result. Left as is, this system is an osciallator -- the torque goes to zero after 90° and then points the other way and reaches a maximum at 180°. 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. Discussion of simple DC motors.
Tuesday 10/16: 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 and reaches a maximum at 180°. 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. Discussion of simple DC motors. Point out that we shall reverse this process to create a generator -- that motors and generators are really the same device, depending on which way the work and energy is flowing. The magnetic constant -- the Permeability of Free Space. Magnetic Field loops from a Current Carrying Wire. RHR has "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. 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 the 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.) Q11 Take-Home due Thursday 18 October 2007.
Wednesday 10/17: 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.) Anti-parallel currents (wires parallel, but currents in opposite directions) repel. Crossed currents (wires perpendicular to each other) see no magnetic force on each other. 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.). Third Sample Exam 2 handed out. (Click here for a copy.)
Thursday 10/18: Magnetic field from a single loop of wire. B = (mu0)I / 2 R. Approximating a circular current by using a square of four straight wires. For N loops in the same space, B = N(mu0) I / 2 R. In a Solenoid, the N loops are spread out over a length L, so n = N / L. B-field of a Solenoid: constant and uniform B-field inside (away from edges) and zero outside the coil. Use Ampere's Law to find B-field inside a Solenoid: B = (mu0) N I / L = (mu0) n I. NOTE: Italics added to emphasize that the N-loop coil and the N-loop solenoid are different -- I may have not been clear in lecture. The Solenoid is the magnetic analog of the parallel plate capacitor for E-fields. Comments about making a real velocity selector -- trying to stuff a capacitor for the E-field and a solenoid for the B-field in the same space! Comments about winding real coils with thin, varnish insulation. Faraday's Law of Induction. A changing magnetic flux induces a current in a loop of wire. No new quiz until after Exam 2 on Tuesday.
Friday 10/19: YES! WE HAVE CLASS TODAY! Backtrack to pick up 2½ items: (1) Operational definition of the Ampere using the Magnetic Force between Two Current Carrying Wires. (1½) A single moving electric charge as: (a) a current and (b) as a source of a B-field. Comments about particle accelerators and "beam currents": Any moving stream of charged particles constitutes a current, so sometimes we talk about the beams in particle accelerators in amps. (2) Hall Effect -- a device with no moving electrical parts -- proves that charge carriers in a current carrying wire are negative, not positive. "The 200 Year Hall Effect Keyboards", will last "forever", but made obsolete in two years when Windows 95 added three keys. More on 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. 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. It is Lenz's Law that gives us the minus sign in Faraday's Law of Induction. 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 10/15-16 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).
Monday 10/22: Demo: Lenz Law race between cow magnets dropped through (a) plastic pipe and (b) non-magnetic aluminum pipe. And second race between (b) non-magnetic aluminum pipe and (c) non-magnetic copper pipe. Induced B-fields due to changing B-fields of falling magnets are created by induced currents and induced emf -- as the magnet enters and leaves a circular region of metal pipe, it is slowed by magnetic forces between its magnetic field and the induced B-field. It is Lenz's Law that gives us the minus sign in Faraday's Law of Induction. Demo: "Jumping Rings", making the bulb light, by Eddy Currents and Induction. Note that the metal rings get HOT, because there is a large induced current and metal has a low resistance. Short review for Exam 2.
Tuesday 10/23: Exam 2.
Wednesday 10/24: Demo: "Jumping Rings", continued. The split ring (a) does not get hot and (b) does not jump, because there is no circuit enclosing the changing magnetic flux. Heating the bottom of a metal cooking pot by induction: New type of cooking range uses sealed induction heating elements instead of exposed hot resistors or open gas fed flames -- usable for metal pans only. More 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.
Thursday 10/25: Why induction is a big deal in electronics, industrial motors and electrical power distribution. Back emf, back current. Demo: Hand crank generators use a gear transmission for one turn of the crank turns the rotor with the coils multiple times in the magnetic field. Becomes harder to turn once the lamps light, because you have to do more work. The Inductor (L). (SI units = Henry = H) Self-Inductance. Back emf, back current. Opposing the status quo -- even of its own B-field. Q12+13 "double-Take-Home-quiz" due Tuesday 30 October 2007.
Friday 10/26: YES! WE HAVE CLASS TODAY! 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). Who knew that (Henrys) ÷ (ohms) = (seconds)? 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. 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.
NOTE: The Physics Help Room moves temporarily to 2242 Rood Hall - Oct. 26-Nov. 2, 2007
NOTE: The Physics Help Room moves temporarily to 2242 Rood Hall - Oct. 26-Nov. 2, 2007.
Monday 10/29: For resistive only A.C. 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. 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.
Tuesday 10/30: 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. 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. Q12+13 Double Quiz can be turned in today (Tuesday), Wednesday or Thursday. Q14 Take-Home quiz, due Thursday 1 November 2007.
Wednesday 10/31: Why A.C. power? Because we can make a transformer and easily raise or lower the voltage by using two coils connected magnetically by an iron core. V2 = V1N2/N1. 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.
Thursday 11/1: Maxwell's Equations and Hertz's radio wave LC oscillator -- the spark gap radio. AM (amplitude modulation) radio versus FM (frequency modulation) and digital radio. The Marconi wireless telegraph of the RMS Titanic, and the modern cellphone.
Friday 11/2: YES! WE HAVE CLASS TODAY! 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. 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). Possibility of a "light sail" for traveling in space. 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).
NOTE: The Physics Help Room returns to 0077 Rood Hall - Nov. 5, 2007
Monday 11/5: Pure colors (EM waves, ROYGBIV for visible light) vs. Perceived colors (RGB, CMY, pinks, browns, "white" light). "Normal" human vision, some types of color blindness. 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). These more particle-like forms of light become increasingly dangerous, because they can knock electrons around and change chemical bonds. (UV and tanning, skin cancer; medical X-rays)
Tuesday 11/6: 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). Visible light is 400nm to 750nm (4000 angstroms to 7500 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. Discussion of why Superman's X-ray vision cannot work: Normal human vision -- light either reflected off of objects or directly from light source. Few X-rays get reflected, so what is the source of the X-rays for Superman to see? (If he's projecting the X-rays, he's killing anyone he looks at.) 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. Q15 Take-Home due Thursday 8 November 2007.
Wednesday 11/7: Frequencies LOWER and wavelengths LONGER than visible light (IR infrared, Microwave, Radio waves, ELF extremely low frequency). AM (amplitude modulation) radio versus FM (frequency modulation) and digital radio. Here's a link to a Wikipedia article on Digital Television and the 17 February 2009 U.S. conversion date discussed in class. The energy of a single photon ("particle" of light) is E = h f, where h = 6.63 × 10 -34 J·s is Planck's constant, a fundamental constant involved in Modern Physics. (If there was only Classical Physics, then h = 0.)
NOTE: Just tonight I started seeing a series of public service ads on TV about (a) the conversion to digital television and (b) the government program to give you $40 to buy a converter box, starting in January 2008.
Thursday 11/8: 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. When a light ray reaches a new material, it can undergo (1) reflection, (2) absorption, (3) transmission. The Law of Reflection. Measure all angles from the normal line perpendicular to the surface. Rough surfaces -- scattering. 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".) People tend to not like photographs of themselves, because they are used to seeing their mirror image -- their normal image, which the rest of us sees, looks "wrong".
Friday 11/9: YES! WE HAVE CLASS TODAY! Corner and Corner Cube reflectors. The Law of Refraction - Snell's Law. Light bent at the interface between two media, because the speed of light changes in the media. (Analogy: If you are driving along the road and your right tires go off onto the soft shoulder, they can't go as fast and the car turns towards the shoulder until all four wheels are driving off the road.) First Sample Exam 3 handed out. (Click here for a copy.)
Monday 11/12: The Law of Refraction - Snell's Law. Light bent at the interface between two media, because the speed of light changes in the media. (Analogy: If you are driving along the road and your right tires go off onto the soft shoulder, they can't go as fast and the car turns towards the shoulder until all four wheels are driving off the road.) 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. 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. LAST DAY TO TURN IN DRAFT PAPERS TO DR. PHIL.
Tuesday 11/13: X2 handed back -- then collected for fixing problems. (Click here for a solution.) Dispersion -- in vacuum all speeds of light are the same, but in a medium, there are slighltly different n's for each wavelength. As one goes from a high index of refraction to a low index, increasing the angle of incidence, white light will start breaking into the rainbox spectrum of colors. Rainbows from raindrops -- normal rainbows are 1 reflection, the fainter rainbow of a double-rainbow comes from two reflections in a raindrop. Like the corner reflector, two reflections reverses the order of the colors in the second rainbox. Second Sample Exam 3 handed out. (Click here for a copy.) Q16 Take-Home, due Thursday 15 November 2007.
Wednesday 11/14: 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? 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)... to be continued.
Thursday 11/15: 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. Zone of Confusion: No solution for p = f. Analytic formula for object and image. Magnification: M = h' / h = -q / p. 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. 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).First day to turn in Topic 1 Papers -- continues through Monday 19 November 2007 at 5pm. (Draft papers get extended deadline.) Q17 and Q18 Take-Home handed out Thursday 15 November 2007, each due Tuesday 20 November 2007.
Friday 11/16: YES! WE HAVE CLASS TODAY! Diopters are the reciprocal of focal length in meters. Note that some eyepieces to optical devices have some diopter built in, so that if you add an eyepiece to the eyepiece, the second unit may be marked for the total diopter, not the diopter of that particular lens. In multiple lenses the effective diopter is just the sum of the diopters. A flat piece of glass is 0 diopters. 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. Back to Anti-Reflection and Max-Reflection coatings with 0, 1 or 2 half-wavelength shifts upon reflections. This closes the material for Exam 3. (Special relativity problems on some Sample Exam 3's will be saved for Final Exam.) Third Sample Exam 3 handed out. (Click here for a copy.)
Monday 11/19: Review for X3. Back to Anti-Reflection and Max-Reflection coatings with 0, 1 or 2 half-wavelength shifts upon reflections. Quarter-wave and half-wave coatings.
Tuesday 11/20: Exam 3. Topic 2 Worksheets handed out, due Tuesday 4 December 2007. (Click here for a copy.)
Wednesday 11/21: Classes end at Noon, so No class for PHYS-1150.
Thursday 11/22: <Thanksgiving Day> No classes.
Friday 11/23: No classes.
Monday 11/26: Dark bands due to destructive interference in an air wedge between two pieces of glass -- can be used to measure the thickness of small things, such as a hair or a piece of paper. Newton's rings where a curved surface touches a flat surface.
Tuesday 11/27: 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. Single-Slit Diffraction. Double-Slit plus Single Slit. (Because those two slits separated by a distance d also have a width a.) Resolution limitations due to the circular aperture diffraction pattern of the "hole" in a lens (pupil in the eye). A smaller opening makes picture look "sharper" for a while, due to increased "depth of field". Then diffraction limiting takes over -- far away cannot tell if a bright light is one source or two. Q19 Take-Home, due Thursday 29 November 2007.
Wednesday 11/28: Young's Double-Slit Interference. Demo: Double-hemispherical wave overlaps on the overhead projector. Plane Polarization of E-M waves. Force E-field to oscillate only in one direction. For two Polarizers, Law of Malus: I = I0 cos²(theta). For three Polarizers, it is possible to rotate the E-field vector from one direction to its perpendicular. Circular Polarization -- E- and B-fields rotating, clockwise or counterclockwise. Classical Relativity (two observers, two frames of reference), Special Relativity (speed constant), General Relativity (accelerations or gravity).
Thursday 11/29: Einstein's postulates: (1) All observers see the same Physics laws. (2) All observers measure the speed of light in vacuum as c. Beta, gamma, Length Contraction and Time Dilation. Alpha Centauri is 4.20 LY from Earth (proper length). Those on a starship see a different distance and experience a different time than the observer left on the Earth. But both think the other observer is moving at v < c. No preferred observer in Special Relativity. Two observers cannot agree on what they see, distance or time. One sees the proper length: a length measurement where both ends are measured at the same time. One sees the proper time: a time measurement where beginning and end are measured at the same place. Experimental confirmation of Special Relativity: put atomic clocks on aircraft, spacecraft. Difference in time with identical clocks left on the ground. Q20 Take-Home, handed out Thursday 29 November 2007, due Tuesday 4 December 2007. NOTE: No afternoon office hours -- Dr. Phil has a dentist appointment.
Friday 11/30: 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. Two observers cannot agree on the order of events, either. The concept of "simultaneity" is gone. Another confirmation of Special Relativity: 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. Doppler shifts: (1) for sound in classical physics and (2) for light with relativity. Light is shifted towards higher frequencies (blue shift) when source is heading towards you; shifted to lower frequencies (red shift) when source is heading away from you. First Sample Final Exam handed out. (Click here and here for a copy.)
Monday 12/3: The Correspondence Principle -- at some point our Classical Physics results need to match the Modern Physics results. So when do we need Special Relativity? For eyeball measurements, we have trouble distiguishing the size of things that are only off by 10%. That would correspond to a gamma = 1.10, and a beta = 0.417 c. Relativistic momentum, prel = gamma mv, and relativistic Kinetic Energy, KErel = (gamma - 1) mc². Total Energy, Etotal = gamma mc². The Einstein Relation, E = m c², and conversion between energy and matter (mass). Pair creation of an electron-positron pair from two high energy gamma rays. Once we used to talk of a "relativistic mass", to try to explain why an object of matter cannot be accelerated up to the speed of light in vacuum, c. You can just as easily use the Work-Energy theorem to show that it would take infinite work to get a matter object up to c. (British SF writer Charlie Stross talks about the difficulties of space travel, including traveling to another star here.)
Tuesday 12/4: Final topics: Atomic, Nuclear and Particle Physics. All models of the atom are fundamentally wrong at some level. It's the nature of Quantum Mechanics, which operates at the land of the very small. But we've already used the "planetary" model of the atom back when we looked at the electron in orbit of a hydrogen atom, using U.C.M. and Coulomb's Law. 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). So the deBroglie wavelength only matters for very small objects, not Buicks. 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".) 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 ×10-10 meters) and protons (and neutrons, not yet discovered) concentrated into a nucleus (about 1 femtometer = 1 ×10-15 meters). The Bohr atom is really quite a triumph of the Physics of PHYS-1130 and PHYS-1150: 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. Third Sample Final Exam (click here for a copy). Q21 Take-Home, due Thursday 6 December 2007.
Wednesday 12/5: The notion in Quantum Mechanics that values for things like electrons can only have certain values is foreign to Classical Physics. Indeed, in Classical Physics, Planck's constant h = 0. But think of our lecture hall -- you can only sit in an unoccupied seat. Each seat exists in a row with only so many seats, each row is at a particular height above the lecture floor and a particular distance (radius) from the lecture table. So in our lecture hall, each of you exists in a unique quantized state. And it takes more work and energy to climb out of the lowest level (ground state) up to the top of the lecture hall and walk out the door, freed from 1110 Rood. (grin) Which leads us to... Niels 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. 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. The derivations shown in class are on the backside of the Periodic Table handout. (Click here for a copy.)
Thursday 12/6: Return X3. 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. A (very) brief discussion of Atomic and Nuclear Physics. NOTE: This material is covered more fully in an Atomic & Nuclear Physics handout, along with the Periodic Table with equations sheet which will be handed out on Wednesday. (Click here for the handout (not given in class) and here for the Periodic Table.) Q22 points for attendance sign-in sheet.
Friday 12/7: LAST DAY OF CLASS. At this point, all outside work (Take-Home Quizzes and Worksheets, plus the Paper) has been assigned. Only outstanding item is the Final Exam, including Q23 as the Check-Out form. Course Review. Finish up the day with the course & teacher evaluations for the semester.