Dr. Phil's Home
Updated: 28 April 2009 Tuesday.
Monday 4/20: Office Hours.
Tuesday 4/21: Office Hours. PHYS-2070(12) Noon section Final Exam 2:45-4:45pm.
Wednesday 4/22: Office Hours. PHYS-2070(13) 2pm section Final Exam 2:45-4:45pm.
Thursday 4/23: Dr. Phil working at home.
Friday 4/24: Office Hours.
Monday 4/27: Office Hours.
Tuesday 4/28: Grades due at Noon.
Monday 1/5: Class begins. Introduction to Dr. Phil.
Tuesday 1/6: Static electricity. The Two-Fluid Model of Electricity. Franklin's One-Fluid Model of Electricity. Occaam's Razor. The simple hydrogen atom -- whatever charge is, the charge on the electron (-e) and the proton (+e) exactly cancel.
Wednesday 1/7: Real Electric Charges. Two charges: like charges repel, unlike (opposite) charges attract. 1 Coulomb of charge is an enormous amount of charge. "Action at a distance" -- Gravity and the Electric Force are not contact forces. The Electric Force between two point charges, Coulomb's Law looks like Newton's Law of Universal Gravity. Four Fundamental Forces in Nature: Gravity, E & M, Weak Nuclear Force, Strong Nuclear Force. Distribute syllabus.
Thursday 1/8: 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 (!!!).
Friday 1/9: 1 Coulomb of charge is an enormous amount of charge. Two 1.00 C charges separated by 1.00 meters have a force of nine-billion Newtons acting on each other. Finding the net vector electric force FE for a system of point charges. Remember: In PHYS-2070, Looking at Symmetry and Zeroes (problems where the answer is zero) as a way of solving problems. Four pages of Topic 1 assignment handed out. (Full 27-page Handout as PDF File -- Searchable HTML Page ) Q1 in-class, for attendance purposes. (If you missed class today, click here to print out a form to bring to class next time.)
FYI: Handout: SI Prefixes and Dr. Phil's Simplified Significant Figures. List of Topics covered in PHYS-2050 when Dr. Phil taught it last.
Monday 1/12: Demo these class web pages. Review of vectors and vector forces. Review of vector notation for components and Standard Form. Right Triangles and 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. Solving a vector Electric Force problem when there isn't symmetry to render the problem zero. 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.)
Remember: PHYS-2080 Lab Begins This Week.
Web comic XKCD's take on Guide To Converting To Metric. (Both funny and true, but there is some bad language.)
Tuesday 1/13: Conductors (metals) versus non-conductors (insulators). Conduction electrons in metals -- free to move around. 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. Charging a conductor by induction. Electric Field is a vector. FE = q E. For a point charge, E = k q1 /r2. SI units for E-field: (N/C). E-field lines radiate away from a positive point charge; converge towards a negative point charge. If the universe is charge neutral, can have all E-field lines from + charges terminating on - charges.Why use E-fields, when you need the force F = q E anyway? Because it allows us to examine the environment without needing another charge. E-field lines allow us to qualitatively sketch what happens when two charges are near to each other. (1) +q and -q, (2) +q and +q. Very close to each point charge, the E-field lines are radial outward, evenly spaced. In the system, the E-field lines interact with each other -- but E-field lines can never cross. Long range, the system of point charges looks like a single net charge. The density of E-field lines in an area gives you an indication of the strength of the E-field line. The numbers of E-field lines attached to a point charge is proportional to the charge. E-field lines radiate away from positive charges and terminate on negative charges. Q2 Take-Home, due in class on Thursday 15 January 2009.
Wednesday 1/14: Q2 comments about parts (a) and (b): You may be making this too hard. Part (a) is just asking what the net or total charge of the system is. Part (b) wants to know how to make the charge in (a) by either adding or subtracting electrons to a neutral system. See lecture notes about Real Electric Charges. E-field lines allow us to qualitatively sketch what happens when two charges are near to each other. (3) +2q and -q. Why use E-fields, when you need the force F = q E anyway? Because it allows us to examine the environment without needing another charge. 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. Direct integration of Electric Force and Electric Field are similar. Charge distributions -- lamda (linear charge density, C/m), sigma (surface charge density, C/m²), rho (volume charge density, C/m³). Examples: Rod in-line with line from point P (1-dimensional integration).
FYI for Future Physics Teachers -- brochures for the PhysTEC NOYCE Scholarship Program. Application Deadline: Friday February 27, 2009. You can also contact Prof. Al Rosenthal in Physics for further information.
Thursday 1/15: Direct integration of Electric Field continued. Rod perpendicular to line from point P. Note that in all these cases, we can predict the long range behavior (E-field behaves as a single point net charge), and anticipate the close-in short range behavior. Check Serway's examples (that's your textbook) -- watch out that his notation may be different.
Friday 1/16: Review of 2-D and 3-D Integration. Rectangular (area, volume), Polar (circumference, area), Cylindrical (volume, surface area). 1st Sample Exams for Exam 1. (Click here and here for a copy.) Q3 In-Class.
NOTE: Monday 19 January 2009 -- MLK Day activities on WMU campus. No classes.
NOTE: Tuesday 20 January 2009 -- Physics Help Room starts in 0077 Rood.
NOTE: Tuesday 20 January 2009 -- Obama inauguration shown live in Miller Auditorium.
NOTE: Tuesday 20 January 2009 -- Dr. Phil is still sick. Tuesday classes canceled.
Monday 1/19: Dr. Martin Luther King, Jr. Memorial Observance -- No Classes.
Tuesday 1/20: Dr. Phil's sick day -- Class canceled.
Wednesday 1/21: Review of 2-D and 3-D Integration (cont.) -- Spherical Co-ordinates. Direct integration of Electric Field continued. Thin ring of charge to center point P. (Symmetry!) Thin ring of charge perpendicular to line from point P. Note that in all these cases, we can predict the long range behavior (E-field behaves as a single point net charge), and anticipate the close-in short range behavior. Check Serway's examples (that's your textbook) -- watch out that his notation may be different.
Thursday 1/22: Return Q2. Direct integration of Electric Field continued. Disk of charge to center point P. Harder to see 1/r² dependence at long range, but it is clear that E goes to zero. Electric Flux: Electric field times Area. Analogy of a bag or box around a light, captures all the light rays no matter the size or shape. Use known E-field of a point charge to evaluate what the Electric Flux must be equal to. Review of Dot Product. Gauss' Law for Electricity.
Friday 1/23: Q4 in-class quiz (mini-exam).
Monday 1/26: Gauss' Law for Electricity. Using Gauss' Law for Point Charge, Conducting Sphere, Insulating Sphere, Infinite Line of Charge. Gauss' Law for Infinite Sheet of Charge.
Tuesday 1/27: . 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: Lightning. Conductor in equilibrium is an equipotential throughout. Equipotential lines, where V is constant, are always perpendicular to E-field lines. Q5 Take-Home, due Thursday 29 January 2009.
Wednesday 1/28: Return Q3. Find components of E by negative of the partial derivative of Electric Potential function V. Finding V by direct integration. Direct integration of V for a whole and a half of a circular line of charge -- V really is a scalar, not a vector. In electrostatic equilibrium, E = 0 inside a charged conductor, but V = constant, not V = 0 automatically. Why charge accumulates on the tips of "pointy things". NOTE: The book is effectively closed for Exam 1 topics now.
Thursday 1/29: Return Q4A and Q4B. 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. This is different from a battery, which has energy stored in its chemical reaction. Dr. Phil & the camera flash. Stories: US Navy seaman vs. the tank capacitor (Cap-2, Seaman-0). Review Exam 1.
Friday 1/30: Exam 1.
Monday 2/2: 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. Apply Gauss' Law for Electricity to the constant E-field of the Parallel Plate Capacitor. We now have an "operational equation", true for all capacitors, and a "by geometry" equation for the special case of the parallel plate capacitor. Two devices connected together in a circuit can only be connected two ways: series or parallel. In Series, same charge, share voltage. Equivalent capacitor is always smaller. NOTE: Remember to take the last reciprocal!
Tuesday 2/3: 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! Work to assemble charges on a capacitor = Energy stored in the capacitor = U = ½CV² . 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. Extend the example in class with a fourth column, U=½CV², and find the energy stored in the equivalent capacitor and the sum of the energy stored in all four of the real capacitors -- if they agree, then our analysis and calculations are correct -- the battery cannot tell the difference! Q6 Take-Home, due Thursday 5 February 2009.
Wednesday 2/4: Making a real capacitor. What if not filled with air? Filling with conductor, must have at least one gap, otherwise will short outthe plates. A conducting slab inside a parallel plate capacitor makes two capacitors in series. Charge neutral slab stays charge neutral, but +Q of top plate attracts -Q on top of slab, and -Q of bottom plate attracts +Q on bottom of slab. Dielectrics -- an insulator where the +/- charge pairs are free to rotate, even if they do not move. Dielectric constant (kappa) and Dielectric strength (E-max). Dielectic constant increases capacitance over air gap. Dielectric strength usually bigger than E-max in air. Both allow you to (a) make bigger capacitors (or smaller for the same values) and (b) make non-hollow, self-supporting components. Examples of the uses of capacitors and dielectrics.
Thursday 2/5: Capacitive studfinder, uses edge effects of E-field from a capacitor to "see" the dielectric material behind the wall. Electrostatics to Electrodynamics (moving charges). Current defined: i = delta-Q/delta-t = dq/dt. The Simplest Circuit: Battery, wires, load (resistor). Resistance vs. Conductance. Discussion of microscopic theory of charges in a conductor. Drift velocity is the very slow net movement of the electrons moving randomly in the wire. Ohm's Law: V=IR form. (Ohm's "3 Laws") We usually treat the wires in a circuit as having R=0, but they usually are not superconductors. Joule Heating, Power Law: P = IV (also 3 forms). Q7 Take-Home, due Tuesday 10 February 2009.
Friday 2/6: Resistance by geometry. Discussion of heat from resistors. Our electronic devices generate heat, but heat can also kill them. Story of early "hot" 486 laptops. Discussion of microscopic theory of charges in a conductor. Drift velocity is the very slow net movement of the electrons moving randomly in the wire. This microscopic theory becomes more important as we go to smaller and smaller circuit elements in our microchips. Moore's Law. 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.
Monday 2/9: Go over Series and Parallel rules for Capacitors. Finish discussion of high temperature superconductors. "High temperature" superconductors (liquid nitrogen temperature, not liquid helium). The "Woodstock of Physics" in 1987. Discuss power cords -- flexible but hot cords for hair dryers, why power cords get recalled. Continuing with Simple Circuits... 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".) In this example, Resistor R1 sees the largest current and dissipates the largest amount of energy per second (Power in Watts). This means it is also the most vulnerable. Fault tolerant design. (Story of radio "repair" call from 4,000,000,000 miles.)
Tuesday 2/10: Real batteries consist of a "perfect" battery (Electromotive force = emf) in series with a small internal resistance, r. As chemical reaction in battery runs down, the internal resistance increases. Don't cut open batteries. Comments on different types of disposable (carbon-zinc, alkaline, lithium) and rechargable (Rayovac Renewal alkaline, NiCad, NiMH, Li-ion) batteries. 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. First Sample Exam 2. (Click here and here for a copy.) Q8 Take-Home, due Thursday 12 February 2009.
Wednesday 2/11: Class canceled by Dr. Phil. Reading Assignment: Sections 28.3 and 28.4 in Serway.
Thursday 2/12: 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 by going around the perimeter of each "puzzle piece", then (2) will give you sufficient 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-2100 (?) may know a "better" way to solve Kirchhoff's problems. But the brute force algebra approach has the advantage of being based on the Physics, so has instructional value. Example in class had 3 equations in 3 unknowns -- finish algebra and find i1, i2 and i3 for tomorrow. NOTE: I am providing a PDF of the problem worked out -- the order of the algebra might not be the same as on the board, but I believe the answers to be correct. Other examples of systems which require Kirchhoff Laws. Sometimes a resistor has zero current, in which case it does not contribute to the circuit. Proper procedure for jump starting a car. (And why doing it wrong ranges from dangerous to deadly.) Q9 Take-Home, due Thursday 19 February 2009.
Friday 2/13: FRIDAY THE THIRTEENTH (Not a WMU holiday) Return X1. RC series circuit. Calculus derivation of q(t) for charging capacitor .
Monday 2/16: PRESIDENT'S DAY (Not a WMU holiday). Calculus derivation of q(t) for charging capacitor and discharing circuit. RC current i(t). 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. Either way the current will be down to 5% of its maximum value.
Tuesday 2/17: Discussion of Christmas tree lights and what happens when one or more burns out. Building an ammeter or voltmeter -- non-digital version with a needle. The Galvanometer is a generic meter. It has a resistance and the needle moves in response to a current through a tiny coil. Since meters must be connected to the circuit, technically they change the circuit. However, we will show that the design of an ammeter and a voltmeter minimizes these changes. 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. The full-scale deflection current, iFS , is the current needed to move the needle to the maximum value on the scale -- it is very small. Second set of Sample Exam 2's handed out: (Click here and here for copies.)
NOTE: Thursday's weather may be heavy rain and snow = slush. Kirchhoff Law Q9 due date shifted to Friday 20 February 2009, just in case.
Wednesday 2/18: 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. The full-scale deflection current, iFS , is the current needed to move the needle to the maximum value on the scale -- it is very small. Ammeter: a galvanometer and a very small shunt resistor in parallel, together connected in series with the circuit. Voltmeter: a galvanometer amd a very large resistor in series, together connected in parallel with the circuit. In both cases, the role of the second resistor is to limit the current to the galvanometer, no matter what the design criteria of the meter in question. Does putting a real ammeter and voltmeter in a circuit, whether the very act of measuring V and I changes their value? It can't by much, because the full-scale deflection current and the voltage drop across the galvanometer are so small, compared to the values we are measuring.
NOTE: The numbers we found for the ammeter and voltmeter resistors were: rs = 0.001262 ohms and Rv = 49,940 ohms. The galvanometer had a resistance RG = 63.1 ohms and a full-scale deflection current iFS = 1.00 ×10-4 A. The high resistance wire we used for the shunt resistor in the ammeter had an R/L = 0.000147 ohm/cm.
Thursday 2/19: "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. 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:
qM , 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. 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? Q10 Take-Home,
due on Friday 20 February 2009 now due
Monday 23 February 2009.
NOTE: Exam 2 moved from Thursday 26 February 2009 to Wednesday 25 February 2009, due to memorial service for the late President Diether Haenicke.
Friday 2/20: Magnetic Force on a Moving Electric Charge - The Cross Product and Right-Hand Rule (R.H.R.). The Cross Product (or Vector Product) is the exact opposite of the Dot Product (or Scalar Product). Multiplying two vectors together by a cross product gives us another vector (instead of a scalar). And the cross product is not commutative, vector-A × vector-B = - (vector-B × vector-A), so the order is paramount. Using Right Hand Rule to assign directions to x,y,z coordinates. Constant speed, perpendicular constant magnetic force --> Uniform Circular Motion. Cyclotron frequency -- no dependence on the radius (constant angular velocity). 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... 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.
Monday 2/23: A current carrying wire consists of moving electric charges, and so therefore would see a magnetic force from a magnetic field. Discussion of microscopic theory of charges in a conductor. Drift velocity is the very slow net movement of the electrons moving randomly in the wire. Magnetic Force on a Current Carrying Wire. Demo -- hey it works and even in the right direction! Technically current is not a vector, despite the fact we talk of direction of current. J = current density = current/cross-sectional area is the vector related to current. NOTE: J-vector = sigma × E-vector (current density = conductivity × E-field) is the vector version of Ohm's Law. This will NOT be on Exam 2. For a Closed Loop, the net Magnetic Force from a constant B-field is zero. Magnetic Torque on a Current Carrying Wire. Left as is, this system is an osciallator -- the torque goes to zero after 90° and then points the other way. But if we can reverse the direction of the current after the torque goes to zero, then the rotation can continue -- and we have a primitive DC electric motor. Q11 Take-Home quiz, due on Tuesday 24 February 2009.
Tuesday 2/24: 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 little/no glow from bigger bulb -- remember that light bulb filaments heat up and are non-ohmic resistors), and RC CIRCUITS (start with three caps in series, connected in series with a light bulb. large (bright) initial current, fades over time as delta-V on plates builds up. 1 cap or 3 caps in parallel, takes longer -- RC constant is larger.). Review for X2.
Wednesday 2/25: Exam 2.
Thursday 2/26: Classes canceled due to Pres. Diether Haenicke memorial service.
Friday 2/27: Spirit Day - No Classes
WMU SPRING BREAK
Monday 3/9: 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. Discussion of Mid-Term Grades. Reset the course after Spring Break.
NOTE: Physics Help Room is moved from 0077 Rood to Bradley Commons 2202 Everett Tower -- next to Dr. Phil's office -- THIS WEEK ONLY.
Tuesday 3/10: The Biot-Savart Law. B-field from a infinitely long straight current carrying wire by direct integration. (Serway has a similar example, but rather than do the integral in x, he does this theta substitution which Dr. Phil does not think is straight forward.) Circular loop of current carrying wire by integration for P at the center of the loop. (Serway's example allows for P to be on a line perpendicular to the loop.) B-field for a circular current carrying wire at the center -- or any part of a circle. Gauss' Law for Magnetism. Not as useful as Gauss' Law for Electricity, because it is always zero (no magnetic monopoles).Q12 Take-Home, due Thursday 12 March 2009.
Wednesday 3/11: Return X2. 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. 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. Operational defnition of the ampere and the Coulomb.
Thursday 3/12: Gauss' Law for Magnetism. Not as useful as Gauss' Law for Electricity, because it is always zero (no magnetic monopoles). However, there is something we can use in a similar way which involves involving a path integral along a B-field and the current(s) contained inside -- Ampere's Law. Use in a way similar to the way we used Gauss' Law for Electricity. Use symmetry and geometry to select your Amperean Loop to your advantage. B-field of a Torroid (torroidal coil; a torus is like a donut). B-field of a Solenoid. (NOTE: The integrals for the L and R sides of the Amperean Loop for Ampere's Law are zero because: (1) the B-field is zero outside the solenoid and (2) for that part of the path which is inside the solenoid, the B-field and the ds-vector are perpendicular, so the dot product is zero as well.) Coils can have right-hand or left-hand turns -- but it is the direction that the current wraps around the coil which determines which way the B-field points. 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!
Friday 3/13: Demo: Magnet moving into a coil, causing current to flow through galvanometer. Faraday's Law of Induction. A changing magnetic flux induces a current, induces an e.m.f., in the circuit, substituting for the battery as the power source. Lenz's Law "of maintaining the status quo." The coil acts as if it opposes any change of the magnetic flux inside, by inducing a magnetic field to cancel and increasing flux or maintain a decreasing flux. It is Lenz's Law that gives us the minus sign in Faraday's Law of Induction. Turn a coil in a magnetic field and the flux changes, thereby inducing a B-field, emf and current. Has same 180° problem that a DC motor has. Hand-crank generators. Electric generators and electric motors differ in which way the arrow points toward or away from mechanical energy. Regenerative braking -- turn electric motors into generators. An Inductor is a coil in a circuit. Why an Inductor has Self-Inductance -- running a current through a coil creates a magnetic field and therefore changes the magnetic flux in the coil. The inductor has to respond to that change. Inductance can be a big deal. Even our Simplest Circuit (a resistor hooked up to a battery) forms a loop, and the loop must respond to the circuit being turned on. Why induction is a big deal in electronics, industrial motors and electrical power distribution. Where they got it right (and wrong) regarding electrical power in the movie Jurassic Park. Q13 Take-Home, due Tuesday 17 March 2009.
Monday 3/16: Demonstration Day -- Hand-crank generators. Electric generators and electric motors differ in which way the arrow points toward or away from mechanical energy. Lenz Law race between cow magnets dropped through (a) plastic pipe, (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. Place bundle of iron rods in an AC coil and light bulb dims -- analogous to lights dimming when large electric motors drive vacuum cleaners and compressors for refrigerator, air conditioning and dehumidifiers. 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. Adding metal increases the mass, but provides more eddy currents and therefore more induced B-fields repelling the solenoid's B-field. A split metal ring (a) does not get hot and (b) does not jump, because there is no circuit enclosing the changing magnetic flux. 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: 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.
Tuesday 3/17: 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. An Inductor is a coil in a circuit. Why an Inductor has Self-Inductance -- running a current through a coil creates a magnetic field and therefore changes the magnetic flux in the coil. The inductor has to respond to that change. Inductance can be a big deal. Even our Simplest Circuit (a resistor hooked up to a battery) forms a loop, and the loop must respond to the circuit being turned on. The Inductor (L). (SI units = Henry = H) Self-Inductance. Back emf, back current. Opposing the status quo. Equations for Inductance. Q14 Take-Home quiz, due Thursday 19 March 2009.
Wednesday 3/18: RL Circuit, similar to RC Circuit, except that energy is stored in the magnetic field at the maximum current. UL = ½ L I ². RL Circuit for energizing the coil. Equation for current i(t) is similar in appearance to the equation for q(t) for a charging capacitor. Now we will de-energize the coil. NOTE: In class I used my usual brute force approach, instead of Serway's. The Kirchhoff Loop for the de-energining coil is -iR -L(di/dt) = 0. Since the current is decreasing, di/dt is negative and the induced emf from the coil becomes a voltage gain. Solution for i(t) the same form as the current i(t) for charging/discharging capacitor. Mutual Inductance between two inductors. 2nd coil responds only to changes in magnetic flux coming from 1st coil. And vice versa.
Thursday 3/19: LC Oscillator circuit. Same 2nd order differential equation as the Simple Harmonic Oscillator (PHYS-2050), such as a mass on a spring. Solutions are sines and cosines. Energy is held constant for all t between the capacitor and the inductor. Can't really have a true LC oscillator, since normal wires and coils have a resistance which dissipates energy through Joule heating. LC Oscillator solution: q(t) = Q0 cos(omega t + phi). Energy is held constant for all t between the capacitor and the inductor. Can't really have a true LC oscillator, since normal wires and coils have a resistance which dissipates energy through Joule heating. Comments ONLY about the RLC Damped Harmonic Oscillator. Mechanical analogue is the mass-on-a-spring with shock absorbers. First Sample Exam 3. (Click here for a copy.)
Friday 3/20: 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. Why A.C. power? (1) Transformers allow voltage to be raised or lowered. D.C. voltage can only be lowered by the voltage drop of a resistor, or raised by adding power sources. The transformer consists of two coils connected magnetically by an iron core. V2 = V1N2/N1. (2) D.C. power lines have huge power losses due to Joule heating, very low efficiency. Actual Efficiency = Power Used ÷ Total Power Generated. Power lines run at higher voltages to minimize power losses due to Joule heating in the powerlines (P = I²R). Q15 Take-Home quiz, due Tuesday 24 March 2009.
Monday 3/23: For resistive only circuits, can still use Ohm's Law, V = I R. Current and Voltage are both sine waves. Real A.C. circuits may have a Resistive nature, a Capacitive nature and an Inductive nature. For A.C. circuits with a Resistor only: I and V stay in phase with each other. RL Circuits: I and V out of phase by 90°. Inductive Reactance. Phasor diagrams -- taking the y-component of a rotating vector gives the sine function. RC Circuits: I and V out of phase by -90°. Capacitive Reactance. Many A.C. circuits have features of all three components (R, L and C), so we have to deal with Impedance, Z. Phasor diagrams (see textbook for diagrams).
Tuesday 3/24: 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. Phase angle, phi, for resultant Vmax vector relative to the Imax vector, is phi = tan-1((XL-XC)/R). For impedance matching , where XL=XC, we get the same equation for the angular frequency omega = 1/SQRT(LC) as for the LC oscillator. This is why power companies have to worry about maintaining their frequency -- it affects the impedance of the circuits. For DC circuits, P = IV. For AC, it is a little more complicated. Paverage = Irms Vrms cos(phi) -- because of the phase angle between V and I. For a purely resistive circuit, or one which looks like a purely resistive circuit, phi = 0°, and so get Paverage = Irms Vrms .
Wednesday 3/25: The problem with Ampere's Law -- it doesn't work properly in the gap between the plates of a capacitor while it is charging. So James Clerk Maxwell fixed it with a "displacement current" term, involving the time derivitive of the Electric flux in the gap. Maxwell's Equations in integral form. Note that Maxwell didn't invent the four equations, only half of one, but he figured out what todo with them. E & M Waves. Turning Maxwell's Equations in E and B, into 2nd order differential equations (Wave Equation) in E or in B. A constantly changing B-field creates a changing E-field, and a constantly changing E-field creates a changing B-field. The Great 19th Century Debate: Is Light a Particle or a Wave? (Wave-Particle Duality did not seem obvious at the time.) Second set of Sample Exam 3. (Click here for a copy.) Q16 Take-Home, now due Friday 27 March 2009.
Thursday 3/26: Looking at the solution to Traveling E-M Wave, with v in x-direction, E in y-direction and B in z-direction. Angular frequency omega, wave number k. c = Emax / Bmax. Derivation of c = E / B. Similar to the relationship between the E-field and the B-field in the velocity selector, where v = E / B. Poynting Vector, S. Traveling E-M Wave, Poynting Vector and Intensity. Energy stored equally in E- and B-fields of the E-M wave. Momentum and Pressure of light waves absorbed or reflected on contact. (Complete absorption like totally inelastic collision; complete reflection like totally elastic collision).
Friday 3/27: Light pressure and momentum transfer, despite the fact that light as mass = zero. NASA used solar panels as solar sails on Mariner 10 near the planet Mercury. 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. Q17 Take-Home, due Tuesday 31 March 2009.
Monday 3/30: Light as a wave. v = frequency × wavelength = c = 2.998 × 108 m/s (in vacuum). Light as a particle. The energy of a single photon ("particle" of light) is E = h f, where h = 6.626 × 10 -34 J·s is Planck's constant, a fundamental constant involved in Modern Physics. (If there was only Classical Physics, then h = 0.) The Electromagnetic Spectrum. Visible light (ROYGBIV=red orange yellow green blue indigo violet). 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. Frequencies LOWER and wavelengths LONGER than visible light (IR infrared, Microwave, Radio waves, ELF extremely low frequency). 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. Radio includes what we consider consumer radio (AM and FM), television (analog and digital), WiFi, Bluetooth, cellular/wireless services, etc.
Tuesday 3/31: 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.) Gamma rays and food irradiation. Q18 Take-Home, due Thursday 2 April 2009.
Wednesday 4/1: April Fool's Day (Not a WMU holiday). Review of Sig. Figs. Comments on Optics: Transmission, Reflection (Scattering), Absorption. Optics: Geometric Optics (ray tracing, light as stream of particles), Physical Optics (wave nature of light). Constructive and Destructive Interference.
FYI: Handout: SI Prefixes and Dr. Phil's Simplified Significant Figures.
Thursday 4/2: Review for X3.
Friday 4/3: Exam 3.
Monday 4/6: 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".) 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.)
Tuesday 4/7: 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. 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. This is due to dispersion, a change in the speed of light for each wavelength. 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. 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!
Wednesday 4/8: 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! A biconcave lens is also called a negative or diverging lens. Parallel light rays will diverge, coming together at the near focal point, not the far focal point -- you can only see the bright spot by looking through the lens. 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. Physical Optics. Based on wave properties of light. Constructive and Destructive Interference. 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. Q19-20 Double Take-Home Quiz, due Friday 10 April 2009.
Thursday 4/9: White light getting two reflections off a thin coating of oil on water -- wavelength associated with maximum reflection will be the strongest irridescent color. Modern Physics -- goes to size/time/length scales far outside our normal experience. Classical Relativity (two observers, two frames of reference), Special Relativity (speed constant), General Relativity (accelerations or gravity). 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. 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. First set of Sample Final Exams handed out. (Click here and here for a copy.) FIRST DAY to turn in Topic 1 Book Reports.
Friday 4/10: 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. Two observers cannot agree on the order of events, either. The concept of "simultaneity" is gone. SECOND DAY to turn in Topic 1 Book Reports.
Monday 4/13: 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. 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.) LAST DAY to turn in Topic 1 Papers. Second set of Sample Final Exams handed out. (Click here and here for a copy.) Q21-22 Double Take-Home, due Wednesday 15 April 2009.
Tuesday 4/14: 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. 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. 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. 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.)
Wednesday 4/15: Return X3. Some comments about the Periodic Table of Elements. 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. 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 which was handed out 4/15.)
Thursday 4/16: 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 ×10-10 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 ×10-18 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. 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.)
Friday 4/17: Last Day of Class.