Today. Entropy and the Second Law of Thermodynamics Electric and Magnetic Forces; the field concept

Transcription

1 Announcements: Today HW#6 and HW#7 are both due Wednesday March 18th. Entropy and the Second Law of Thermodynamics Electric and Magnetic Forces; the field concept ISP209s9 Lecture 14-1-

2 Energy and Entropy - Pendulum Example Energy The thermal energy (heat) is lost ISP209s9 Lecture 14-2-

3 Entropy Entropy is a measure of the number of ways a system can be arranged. S = Heat/T thermal energy goes toward increasing the entropy Second Law of Thermodynamics The entropy of a closed system always increases. As the pendulum swings useful energy is lost to increasing the random motion of the air and pivot If this is true, we can t go back in time. There is no way to recollect the thermal energy and make the pendulum swing higher (that is with a closed system). ISP209s9 Lecture 14-3-

4 Coin Tosses Suppose we have 10 coins: HHHHHHHHHH S = k ln(1) = 0 Heads Number of ways Entropy (J/K) * ISP209s9 Lecture 14-4-

5 Why? Why does the entropy of a system always have to increase? For now, lets say because that s the way it seems to work. It probably has to do with how the Universe was formed, but that discussion is for later in the term. ISP209s9 Lecture 14-5-

6 Why does time always move in one direction? The Universe was created with very low entropy. Much too low for its size. It is like the Universe started with all heads. Hence, everything in the Universe moves toward reaching the correct amount of entropy. It is very improbable to go the other way. In this case very means so improbably that it never happens. Time has a direction because going back in time would imply the entropy could be decreased. That is very improbable. The Universe tends toward increasing entropy. ISP209s9 Lecture 14-6-

7 A new force Magnetic force Certain objects in nature have magnetic poles. They always come in pairs, north and south. Like poles repel Unlike poles attract N S N S S N N S Near the pole, the strength of the force decreases with the square of the distance. F! 1 r 2 ISP209s9 Lecture 14-7-

8 What causes the magnetic force? Moving charge, current, causes a magnetic field. Current is the flow of charge (electrons) in a wire, similar to water flowing in a pipe. Large scale current in the Earth is due to the liquid core of the earth and its rotation give the Earth a magntic field. The exact nature is not known. The Earth s changing magnetic field: ISP209s9 Lecture 14-8-

9 The Earth s magnetic field N S N S Magnetic field lines point from North magnetic poles to South magnetic poles. Thomas Alerstam Nature 421, 27-28(2 January 2003) ISP209s9 Lecture 14-9-

10 Earth s Magnetic Field and the sun ISP209s9 Lecture

11 The Changing Earth s Magnetic Field ISP209s9 Lecture

12 The Earth s Magnetic field - Really Super computer calculation of field lines Cyan in Gold - out Gary A. Glatzmaier (UCSC) ISP209s9 Lecture

13 The correspondence of a loop of current and magnet Magnets have an internal structure where the motion of the electrons creates small regions with currents. Bar magnet current ISP209s9 Lecture

14 The electric and magnetic forces The magnetic force and the electric force are related. They are two manifestations of what we call the electromagnetic force. There are four equations that give the relationship. These are Maxwell s Equations. Charge creates the electric force Moving charge creates the magnetic force Maxwell s equations unified the electric and magnetic forces. The electric force is what allows us to sit and stand. ISP209s9 Lecture

15 "! r E = 4&' r 4& " % B = c r 1 " % E = $ c r "! B = 0 Maxwell s Equations r J + r # B # t 1 c r # E # t Charge makes an electric field. Moving charge makes a magnetic field. Changing magnetic field makes an electric field Magnets always have a north and a south pole The equations predict the existence of an wave that travels with speed c, the speed of light. ISP209s9 Lecture

16 Electric Charge Electric charge is a property of matter. It is measured in Coulombs The charge on one electron is 1.602E-19 C How many electrons in a charge of 1 C? # Electrons = # Electrons = Total Charge Charge electron 6.215E18 = 1.602E 1C! 19 C electron ISP209s9 Lecture

17 Electric and Magnetic Fields If we move a test charge, q, (or magnet) in the vicinity of another charge (or magnet) we can make a map of the force. Define: Electric field E = F/q Electric field is a vector. Its units are N/C or V/m (volts/meter). It points in the direction of the force. Once we know the electric field we can calculate the force: F=qE F = electric field times charge of the object in the field Which is underlying reality, the force or the field? ISP209s9 Lecture

18 Samples Electric field lines point away from positive charge and toward negative charge. Charge generates an electric field. ISP209s9 Lecture

19 Example of two point charges ISP209s9 Lecture

20 Magnetic Fields N S The SI unit for magnetic field is Tesla, T. At East Lansing the Earth s magnetic field strength is 0.7E-4 T. ISP209s9 Lecture

21 Topographical Maps Sample from TOPO Maps The slope gives a measure of the force and direction on a ball. ISP209s9 Lecture

22 Map for the Electric Field Electric Potential The height is electric potential, V, measured in volts The slope gives a measure of the electric field. ISP209s9 Lecture

23 Another example- 4 charges + charge gives positive potential (V) position position - charge gives negative potential (V) ISP209s9 Lecture

24 Example +20 V -20 V The electric potential is the same everywhere on a conductor. ISP209s9 Lecture

25 The Earth has an electric field The Earth s electric field is about 150 N/C (same as V/m) ISP209s9 Lecture

26 Lightning Potential difference of 100 MV is developed between cloud and ground. In the bolt about 5 C of charge are transferred (on average). ISP209s9 Lecture

27 The Strength of the Electric Field Electric potential SI unit is the Volt (V) Electric field is rate of change of potential E = "! V! x The minus sign means that electric fields point from + to charge. ISP209s9 Lecture

28 Sample Problem What is the magnitude of the electric field at: 0.5 m? 1.5 m? 3.0 m? The field is 0 V/m at 0.5 m and 3.0 m since the slope is zero. " V ( 100V! 0V ) V E( at 1.5m) = = = 100 " x 2m! 1m ( ) m ISP209s9 Lecture

29 A visual picture Electric Potential Positive charge makes a hill + +q Steep slope means a larger force. Negative charge makes a valley. - ISP209s9 Lecture

30 Gravitational (or electric) Potential/Field height The force is related to the rate of change of potential. ISP209s9 Lecture

31 Electric fields and potential In equilibrium the electric field in a metal conductor (electrons to move) is zero. This means that inside a metal the electric potential is flat, like the flat top of a table. Sitting inside a metal cage is like sitting on top of a large, flat table. As long as you are in the center, there is no danger of falling off. This is why being in a car during a thunder storm is relatively safe. ISP209s9 Lecture

32 Electric Field Example Q = -0.5 µc = -0.5x10-6 C What is the magnitude of the electric force on Q? F = qe F = 0.5E-6C x 40 N/C = 20E-6 N Not asked for, but the direction is +, to the right. Electric Field E = -!V/!x =-(50V-90V)/1m= 40 V/m + means to the right in this case ISP209s9 Lecture

33 Flow of Charge - Current Current is the rate of flow of charge. SI units is Ampere = 1 Coulomb/second Batteries are like pumps that lift charge to a higher potential. The charge flows down the hill to the other side of the battery. A battery is like a pump. V Moving Charge does work on the way down ISP209s9 Lecture

34 Types of materials Conductor electrons in the conduction band; electrons relatively free to flow (copper, aluminum, gold, silver) Insulator no electrons is the conduction band; electrons can not flow (wood, most rubber, most glass, most plastic) Semiconductor at finite temperature, some electrons are in the conduction band (used in most electronics; silicon, germanium) Superconductor at very low temperature electrons pair and can move freely without resistance (Niobium, Titanium, Lead) ISP209s9 Lecture

35 Conductor Conduction band V electrons Electrons hit bumps, but are free to roll. energy ISP209s9 Lecture

36 Insulator Conduction band V electrons Electrons are not free to roll. energy ISP209s9 Lecture

37 Semiconductor Conduction band V electrons energy light LED light emitting diode ISP209s9 Lecture

38 Superconductor Conduction band V electrons No resistance to flow (also no use of energy) energy ISP209s9 Lecture

39 The Electromagnetic Spectrum The modern picture of electromagnetism is that the electric force is carried by the photon. A photon is a small bundle of energy. We see photons in the range of 1.8 ev (red) to 3.1 ev (violet) [1 ev = 1.6E-19 J] The full range of different photon energies is called the electromagnetic spectrum. ISP209s9 Lecture

40 The Electromagnetic Spectrum Speed = " f " wavelength f Frequency, Hz (1/period)(1/s) For light Speed c = 3.0E+8m/s Energy = h f h = 6.625E-34 Js = 4.136E-15 evs Prentice-Hall 2005 ISP209s9 Lecture

41 Wavelength and Frequency " = 1.0 m period = 2.0 s Wavelength Frequency = 1/period Distance over which the wave repeats Number of cycles (repeats) per second. ISP209s9 Lecture

42 Why is there always r 2? I hate r 2. Inverse square law intensity = L[Watts] 4! d L is the luminosity (measured in watts), d is the distance to the source 2 This explains why the electric force has the form it does. The strength of the force is related to the probability of being hit by a photon. That decreases as the square of the distance. ISP209s9 Lecture