PHY101: Major Concepts in Physics I

Transcription

1 Welcome back to PHY101: Major Concepts in Physics I Photo: J. M. Schwarz

2 Announcements In class today we will finish Chapter 20 (sections 3, 4, and 7). and then move to Chapter 13 (the first six sections). There is a lab this week on the direct current electric motor. HW 9 on Chapters 18/19 is posted and is due on Friday, the 16 th, by 5PM in your TA mailboxes across from PB201. Next week is our break for Thanksgiving. Our third in-class exam is on Monday, December 3. Don t forget about that the Physics Clinic in PB112 is open from 9-9 Monday-Thursday and 9-5 Friday. In addition to my office hours, you can also contact your lab TA or me to schedule alternate meeting times when needed.

3 Ninth set of Three Big Questions What are magnetic fields? How can we harness magnetic fields to do work? How do magnetic fields affect the motion of certain objects? 3

4 Magnetic field due to a bar magnet A bar magnet is one instance of a magnetic dipole. By dipole we mean two opposite poles. Slide 4

5 Magnetic field due to two bar magnets

6 Magnetic field due to current in a long straight wire Slide 6

7 Magnetic field due to a solenoid Curl your fingers of your right hand inward toward your palm following the direction of the current. Your thumb points in the direction of the magnetic field in the solenoid interior. Another Slide 7

8 Ninth set of Three Big Questions What are magnetic fields? How can we harness magnetic fields to do work? How do magnetic fields affect the motion of certain objects? 8

9 A Changing Field Can Cause an Induced Voltage! In 1831, Faraday discovered two ways to produce an induced voltage. One is to move a conductor in a magnetic field. The other does not involve movement of the conductor. Instead, Faraday found that a changing magnetic field induces a voltage in a conductor even if the conductor is stationary. Slide 9

10 It s Demo Time!

11 Magnetic flux through a flat surface of area A: Slide 11

12 Faraday s Law Faraday s law says that the magnitude of the induced emf (induced voltage) around a coil of wire with N turns is equal to the rate of change of the magnetic flux through the loop times the number of turns: Slide 12

13 Jumping ring demo and Faraday s Law!

14 Faraday's law of induction states that the voltage induced in a rectangular loop of wire is proportional to A. the magnetic flux. B. the time variation of the magnetic flux. C. current divided by the time. D. the magnetic flux density times the area of the loop.

15 A loop of wire is moved through a region of uniform magnetic field. As it is moved, its orientation with respect to the magnetic field direction does not change. The induced current at this time in the loop: A. depends on the shape of the loop B. depends on the magnitude of the field C. depends on the speed with which it is moved D. is zero

16 20.3 Example problem: A 40.0-turn coil of wire of radius 3.0 cm is placed between the poles of an electromagnet. The field increases from 0 to 0.75 T at a constant rate in a time interval of 225 s. What is the magnitude of the induced emf in the coil if the field is perpendicular to the plane of the coil? Slide 16

17 20.3 Strategy First we write an expression for the flux through the coil in terms of the field. The only thing changing is the strength of the field, so the rate of flux change is proportional to the rate of change of the field. Faraday s law gives the induced emf. Slide 17

18 LENZ S LAW What about the minus sign in Faraday s Law? The directions of the induced emfs and currents caused by a changing magnetic flux can be determined using Lenz s law. The direction of the induced current in a loop always opposes the change in magnetic flux that induces the current. Note that induced emfs and currents do not necessarily oppose the magnetic field or the magnetic flux; they oppose the change in the magnetic flux. Slide 18

19 20.5 A circular loop of wire moves toward a bar magnet at constant velocity. The loop passes around the magnet and continues away from it on the other side. Use Lenz s law to find the direction of the current in the loop at positions 1 and 2. Slide 19

20 20.5 Strategy The magnetic flux through the loop is changing because the loop moves from weaker to stronger field (at position 1), and vice versa (at position 2). We can specify current directions as counterclockwise or clockwise as viewed from the left (with the loop moving away). Slide 20

21 The south end of a bar magnet is pushed downward toward a wire loop in the plane of the paper. In which direction is the induced current, and which way is the induced magnetic field? A. clockwise, into the paper B. clockwise, out of the paper C. counter-clockwise, into the paper D. counter-clockwise, out of the paper

22 EDDY CURRENTS Whenever a conductor is subjected to a changing magnetic flux, the induced emf causes currents to flow. In a solid conductor, induced currents flow simultaneously along many different paths. These eddy currents are so named due to their resemblance to swirling eddies of current in air or in the rapids of a river. Though the pattern of current flow is complicated, we can still use Lenz s law to get a general idea of the direction of the current flow (clockwise or counterclockwise). Slide 22

23 We can also determine the qualitative effects of eddy current flow using energy conservation. Since they flow in a resistive medium, the eddy currents dissipate electric energy. Slide 23

24 Eddy current demo! Slide 24

25 Can cusher demo!

26 Can cusher demo! Plausible explanations?

27 So now you know, in principle, how

28 So now you know, in principle, how metal detectors work,

29 So now you know, in principle, how metal detectors work, electric generators work,

30 So now you know, in principle, how metal detectors work, electric generators work, transformers work,

31 So now you know, in principle, how metal detectors work, electric generators work, transformers work, and many more things.

32 Tenth (and final) set of Three Big Questions What is temperature and what is its molecular basis? How does temperature allow one to tune between gases, liquids, and solids? What are the laws of thermodynamics? And how can we use them to do work? 32

33 TEMPERATURE AND THERMAL EQUILIBRIUM The definition of temperature is based on the concept of thermal equilibrium. Suppose two objects or systems are allowed to exchange energy. The net flow of energy is always from the object at the higher temperature to the object at the lower temperature. As energy flows, the temperatures of the two objects approach one another. When the temperatures are the same, there is no longer any net flow of energy; the objects are now said to be in thermal equilibrium. Thus, temperature is a quantity that determines when objects are in thermal equilibrium. Slide 33

34 The energy that flows between two objects or systems due to a temperature difference between them is called heat. If heat can flow between two objects or systems, the objects or systems are said to be in thermal contact. To measure the temperature of an object, we put a thermometer into thermal contact with the object. Temperature measurement relies on the zeroth law of thermodynamics. Slide 34

35 Zeroth Law of Thermodynamics Zeroth Law of Thermodynamics: If two objects are each in thermal equilibrium with a third object, then the two are in thermal equilibrium with one another. Slide 35

36 TEMPERATURE SCALES The SI unit of temperature is the kelvin. 0 K represents absolute zero there are no temperatures below 0 K. Slide 36

37 Slide 37

38 Slide 38

39 MOLECULAR PICTURE OF A GAS The number of molecules per unit volume, N/V, is called the number density to distinguish it from mass density. In SI units, number density is the number of molecules per cubic meter, m 3 (read per cubic meter ). If a gas has a total mass M, occupies a volume V, and each molecule has a mass m, then the number of gas molecules is and the average number density is: Slide 39

40 It is common to express the amount of a substance in units of moles (abbreviated mol). The mole is an SI base unit and is defined as follows: one mole of anything contains the same number of units as there are atoms in 12 grams (not kilograms) of carbon-12. This number is called Avogadro s number and has the value Slide 40

41 KINETIC THEORY OF THE IDEAL GAS The ideal gas is a simplified model of a dilute gas in which we think of the molecules as point-like particles that move independently in free space with no interactions except for elastic collisions. This simplified model is a good approximation for many gases under ordinary conditions. Many properties of gases can be understood from this model; the microscopic theory based on it is called the kinetic theory of the ideal gas. Slide 41

42 Microscopic Basis of Pressure Slide 42

43 Maxwell-Boltzmann Distribution Collisions keep the kinetic energy distributed among the gas molecules in the most disordered way possible, which is the Maxwell-Boltzmann distribution. O 2 Slide 43

44 ABSOLUTE TEMPERATURE AND THE IDEAL GAS LAW Both Charles s law and Gay-Lussac s law are valid only for a dilute gas a gas where the number density is low enough (and, therefore, the average distance between gas molecules is large enough) that interactions between the molecules are negligible except when they collide. Slide 44

45 ABSOLUTE TEMPERATURE AND THE IDEAL GAS LAW absolute zero Slide 45

46 ABSOLUTE TEMPERATURE AND THE IDEAL GAS LAW Boyle s law: Avogadro's law: Slide 46

47 Ideal Gas Law (Microscopic Form) Ideal Gas Law k = J/K Boltzmann s constant Slide 47

48 Slide 48

49 Ideal Gas Law (Macroscopic Form) Many problems deal with the changing pressure, volume, and temperature in a gas with a constant number of molecules (and a constant number of moles). In such problems, it is often easiest to write the ideal gas law as follows: PV nr = = T PV T Slide 49

50 Under what conditions do real gases approximate the behavior of an ideal gas? A. high temperature and low pressure B. low temperature and low pressure C. low temperature and high pressure D. high temperature and high pressure