Announcements l Exam 2 on Thursday March 20 in Wonders Hall C100
We will cover 6 of them in our course.
Polarization of a wave l Consider a slinky l I can send a wave down the slinky by moving one end in and out moving one end up and down l The first type of wave is called a longitudinally polarized wave l The second type is called a transversely polarized wave
Polarization l An electromagnetic wave can also have a polarization l Electromagnetic waves are always transversely polarized l A particular electromagnetic wave may have its electric field oscillating in a certain orientation l That is its plane of polarization
Polarizing filter l Ordinary electromagnetic waves are unpolarized the electric field vectors for each wave are in random (transverse) directions l A polarizing filter lets in only those EM waves with a polarization in a particular direction polymer chains are treated to make them conducting electrons absorb energy from EM waves whose electric fields oscillate in the direction of the chains
Remember the cosmic microwave background radiation
l A new result was announced yesterday from measurements carried out at the South Pole Basically, they observed a particular type of polarization of the microwave radiation that indicates huge gravitational waves 10-35 seconds after the universe began.
From today s New York Times
Wave optics: diffraction l Like water waves passing through a breakwater, light waves spread out when passing through a narrow opening l This is called diffraction l We can say that the light waves spread out a great deal because they are passing through a very narrow opening compared to the size of their wavelength There is a broad central maximum, where the light spreads out, of width~2λl/a, where λ is the wavelength of the light, L is the distance to the screen and a the width of the opening
Inteference A series of bright and dark fringes appears on the screen. Bright for constructive interference and dark for destructive interference.
Diffraction grating: Let s go crazy and put in lots of slits Light diffracts through each of the slits A device like this is called a diffraction grating but there s both diffraction and interference taking place and we get interference between each of the diffracted waves Again, there s a path length difference between light passing through different slits bright lines or spots when d sinθ bright = mλ m=0,1,2,
Ether l Ether had the following properties massless provides no resistance to motion of objects through it has to have properties of a stiff elastic solid had to be considered to be at rest with respect to absolute space electromagnetic waves travel at a speed c with respect to the ether Starting in 1881, Albert Michelson, a young American, began a series of experiments intended to measure the motion of the Earth through the ether, the ether drift strange stuff All of his experiments were unsuccessful.
Basic idea Split a light beam into 2 components at right angles with respect to each other
Ether drift l If light travels at a constant speed with respect to the ether and if the earth is moving with respect to the ether, then light should travel at different speeds along paths I and II (which are arranged to be the same distance) l The light starts out in phase but if it travels at different speeds, then it will be out of phase when it recombines l an interference pattern Orbital speed of the earth is about 3X10 4 m/s, about 10-4 of the speed of light
Ether drift l Of course, we don t know which way the ether wind is blowing with respect to the earth s motion, but the apparatus was designed to be able to rotate l There should be some difference in the interference patterns when the apparatus is set up at different angles l Nope, they found no difference; and the sensitivity of their experiment was 40X as large as the effect they were trying to measure l Sometimes you have to give up old ideas l Sometimes a negative search is still a discovery
Enter Fitzgerald and Lorentz l In 1882, 2 physicists, G.F. Fitzgerald and H.A. Lorentz, suggested a solution to problem posed by Michelson- Morley experiment l Fitzgerald: moving through ether generates a resisting force which compresses apparatus 1/2 millionth of 1 percent enough to explain lack of ether drift caused by Earths motion through the ether l Lorentz was looking for transformation equations between inertial frames of reference that would leave electromagnetic forces invariant l Same transformation as found by Fitzgerald; interesting consequences moving objects would contract time would slow down l Poincare also pointed out that mass would increase with speed and that the maximum speed for any object would be the speed of light
Enter Einstein l 1879-1955 l One of greatest physicists of all time l Teacher once told him: You will never amount to anything Einstein l Began speaking late, but gifts were evident from an early age l In 1905, while working as a patent clerk, he published four papers that revolutionized physics 1 on Brownian motion 2 on special relativity 1 on photoelectric effect for which he received the Nobel prize in 1921 l Over 350 papers in career and a few patents l And a Halloween costume as Costume Kits Albert Enstein Costume Kit costume kit includes: wig and moustache. well as an action figure but no square dance song or does he?
Albert Einstein l All of the previous ideas are in Einstein s theory of special relativity l Significance of Einstein s work is that he was able to show simply and directly that they were natural consequences of a profound and insightful reexamination of some basic assumptions about nature of physical measurements l Circumstances at beginning of 20th century similar to those at time of Newton l Several physicists were close to making a breakthrough but only one (Newton, Einstein) able to master the situation l l In 1905 paper, On the Electrodynamics of Moving Bodies, enumerated 2 special principles that should be applicable in all frames of reference I: laws of physics are invariant (the same) in all inertial reference frames II: It is a law of physics that the speed of light is the same in all inertial reference frames independent of speed of the source or detector Thus, ether can not be detected by experimental means; so should be discarded Einstein realized that it was necessary to reconsider the meaning of space and time, and how they are measured. Space and time are not independent concepts but are intrinsically linked with each other. no such thing as absolute length or absolute time perhaps time is not the same in 2 inertial reference frames
Special relativity l The special theory of relativity can be summarized with two precepts l Some of the consequences are not so intuitive slowing down of clocks lengths contracting masses increasing l The laws of physics are the same in all coordinate systems either at rest or moving at constant speed with respect to one another l The speed of light in a vacuum has the same value regardless of the velocity of the observer or the velocity of the source emitting the light
Review for 2 nd exam: temperature and heat l Understand the Farenheit, Celcius (Centigrade) and Kelvin temperature scales and how to convert from one to the other understand what is meant by absolute zero and what absolute zero is in different temperature scales l Connection between kinetic energy of a molecule and temperature KE=1/2mv 2 =3/2k B T l Units for heat Joules l It takes 4.18 J to raise 1 g of H 2 0 by 1 o C l 1 food Calorie = 1000 calories
Three laws of thermodynamics l First law whenever heat is added to a system, it transforms to an equal amount of some other form of energy l Second law heat never spontaneously flows from a cold substance to a hot substance l Third law no system can reach absolute zero
Entropy l In natural processes, high-quality energy tends to transform into lower-quality energy order tends to disorder entropy, a measure of disorder, always increases for a closed system time s arrow always points from order to disorder l The increase in entropy is equal to the amount of heat added to the system divided by the temperature at which it was added l We can also write the entropy of a system as S=k B ln(w), where k B is the Boltzmann constant and W is the number of possible states for a system ΔS = ΔQ T the larger the number of possible states, the larger the entropy
Specific heat capacity l The specific heat capacity (sometimes just called specific heat) of a substance is the quantity of heat required to change the temperature of a unit mass by 1 degree C can think of it as thermal inertia since it signifies the resistance of a substance to a change in temperature l If the specific heat capacity c is known for a substance, then the heat transferred is equal to the specific heat capacity X mass X change in temperature Q = cmδt where Q is the quantity of heat l Water has a very high specific heat; lots of ways for water molecules to store energy
Heat transfer l Heat transfers from warmer to cooler things l This process occurs in 3 ways conduction convection Radiation
Electrostatics l If outermost electrons are free to move within the material, we call the material a conductor l If they re not free to move (but can still be rubbed off), we call the material an insulator l Coulomb s law for the force between two charges and the similarities and differences with Newton s law for gravitation F = k q eq p r 2 F = G m e m p r 2
Drawing/interpreting electric (and magnetic) field lines l Pretty useful idea but we need some guidelines electric field lines point in direction of field at that point in space the total number of electric field lines is proportional to the size of the charge close to an electric charge, the field lines look like that due to the point charge alone the density of field lines is proportional to the strength of the electric field electric field lines originate on + charges and terminate on - charges no 2 field lines can cross in free space don t cross the streams
Electric potential and potential energy electric potential = l The unit of measurement for electric potential is the Volt, so electric potential is often called voltage 1 Volt = 1 Joule/Coulomb l Know how a battery works the electrons are not supplied by the battery, they re already in the conductor electric potential energy amount of charge the battery just supplies the work necessary to move the electrons from a lower potential to a higher potential
Ohm s law l I=V/R l V=IR l R=V/I relates the current, voltage and resistance l How much current flows through a lamp with a resistance of 60 Ω when the voltage across the lamp is 12 V? I=V/R=12 V/60 Ω = 0.2 A l What is the resistance of a toaster that draws a current of 12 A when connected to a 120 V circuit? R=V/I=120 V/12 A= 10 Ω
Resistors in series and parallel ΔV ab = ΔV a + ΔV b = IR 1 + IR 2 I = ΔV ab R 1 + R 2 = ΔV ab R eq R eq = R 1 + R 2 (+R 3 +...) I = I 1 + I 2 = ΔV R 1 + ΔV R 2 = ΔV R eq 1 = 1 + 1 " + 1 % +... R eq R 1 R 2 # $ R 3 & '
Power in electrical circuits l Can write the power in the following forms 2 P = IΔV R = I 2 R = ΔV R R l If I integrate power over time, I have units of energy kw-hr 1000 J/s*3600s =3.6X10 6 J/kW-hr
Electric and Magnetic Fields Note some similiarities: magnetic field lines originate on N poles and terminate on S poles But there are differences: I can separate the + charge and the - charge of an electric dipole, leaving me with a single electric charge Can t do that with a magnetic dipole: a N pole is always accompanied by a S pole and vice versa; unfortunately there are no magnetic monopoles, or maybe just one And we found that magnetism is caused by the movement of electrons inside of atoms
Magnetic forces on electric charges l So we believe in the existence of magnetic fields and magnets exert forces on each other l What kind of force is exerted on an electric charge? l Suppose I do a series of experiments involving electric charges and magnetic fields a charge q in a region of magnetic field q 1. The force on q is proportional to the magnitude of q 2. The force on q is proportional to the magnitude of B 3. The force on a negative charge is opposite the force on a positive charge 4. The force is proportional to the velocity v 5. The magnitude and direction of F depends on the angle between v and B F=qvBsinθ
Electric motors l How does an electric motor work? l A current flows through a loop inside a magnetic field l There s a force (actually a torque) because of the current interacting with the magnetic field that causes the loop to rotate current in the motor made to change direction every time the coil makes a half rotation l The rotating coil can be used to run clocks, operate gadgets etc electricity goes in, work comes out (plus heat)
Magnetism in materials l What causes magnetism in materials? l We said it has something to do with current loops l Where do the current loops come from? l Well the electrons are orbiting around the nucleus and each electron is spinning like a top l Both of these actions produce current loops, which then produce magnetic moments l In most materials, the magnetic effects from the electrons cancel each other out l For some materials this doesn t happen, and they have magnetic properties
Faraday s law of induction l A strong magnetic field does not create an electric current l But he did notice a current in the meter when he first closed the switch and just after he opened it again l So it s not a magnetic field that creates an electric current; it s a changing magnetic field l And not the magnetic field per se, but the magnetic flux just think of the flux as the number of magnetic field lines ε = Δφ Δt = Δ(BA) Δt
l The force on the bar magnet resulting from the current induced in the coil A) opposes the motion causing the change in flux B) is in the same direction as the motion causing the change in flux C) is independent of the motion causing the change in flux
Generators and motors What s the difference between them? A generator turns mechanical work into electrical energy. A motor turns electrical energy into mechanical work. A motor is a generator run in reverse.
Electromagnetic waves
Review: refraction and dispersion
Why is the sky blue? l l l l Light from the Sun has all of the colors of the visible spectrum (but is peaked towards yellow) The cross section (probability) for scattering of light from air molecules goes as f 4 (frequency to the 4th power) So blue light is scattered preferentially and when you look away from the sun, all you see is the scattered blue component of sunlight The sky is paler towards the horizon You should also understand about sunsets, clouds, etc.
Wave optics: diffraction l Like water waves passing through a breakwater, light waves spread out when passing through a narrow opening l This is called diffraction l We can say that the light waves spread out a great deal because they are passing through a very narrow opening compared to the size of their wavelength λ a angles of dark fringes are given by formula asinθ = mλ (m=+/-1,+/-2, ), so angle from center to first dark fringe is approximately λ/a
Interference A series of bright and dark fringes appears on the screen. Bright for constructive interference and dark for destructive interference. d
Special theory of relativity l Applies at all speeds, slow and fast l What do we mean by fast? approaching the speed of light 186,000 miles per sec 3 X 10 8 m/s not your typical highway speeds but ones approached for example by the particles at Fermilab l Einstein came up with the special theory of relativity while thinking about light
Special relativity l The special theory of relativity can be summarized with two precepts l Some of the consequences are not so intuitive slowing down of clocks lengths contracting masses increasing l The laws of physics are the same in all coordinate systems either at rest or moving at constant speed with respect to one another l The speed of light in a vacuum has the same value regardless of the velocity of the observer or the velocity of the source emitting the light