lecture1

lecture1 - Preprint typeset in JHEP style PAPER VERSION...

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Unformatted text preview: Preprint typeset in JHEP style - PAPER VERSION Lecture notes for General Physics 219 Martin Kruczenski Department of Physics, Purdue University, 525 Northwestern Avenue, W. Lafayette, IN 47907-2036. E-mail: [email protected] Abstract: These are the notes for the lectures. They contain what is explained in class and can be used to refresh your memory or to stay up to date if you miss a class. They do not replace the book since they have much less information. Also take into account that the actual lectures might run a little behind schedule. Keywords: Introductory physics. Contents 1. Lecture 1 1.1 Introduction 4 4 2. Lecture 2 2.1 Electric charge 2.2 Electric field 9 9 13 3. Lecture 3 3.1 Dipole and quadrupole 3.2 Electrostatic energy 3.3 Electrostatic potential 17 17 17 22 4. Lecture 4 4.1 More on electrostatic potential 4.2 Electric flux 4.3 Electric current 25 25 27 31 5. Lecture 5 5.1 Resistivity 5.2 Capacitors 36 36 37 6. Lecture 6 6.1 Energy contained in a capacitor 6.2 Dielectrics 6.3 RC circuits 40 40 40 42 7. Lecture 7 7.1 Capacitor charge and discharge 7.2 DC circuits 7.2.1 Resistors in series and parallel 7.2.2 Kirchhoff ’s laws 7.3 Example of circuit using charge and discharge of a capacitor 7.3.1 Oscillator using the 555 chip 7.3.2 Actual construction 46 46 46 46 48 50 51 51 –1– 8. Lecture 8 8.1 Capacitors in series and parallel 8.2 Magnetic field 55 55 56 9. Lecture 9 9.1 Magnetic forces on an electric current 9.2 Magnetic field created by a current 9.2.1 Ampere’s law 9.2.2 Displacement current 9.2.3 Magnetic field of a wire and a solenoid (coil) 62 62 62 62 64 66 10. Lecture 10 10.1 Force between currents 10.2 Magnetic induction 69 69 69 11. Lecture 11 11.1 Inductors 11.2 Transformers 76 76 77 12. Lecture 12 12.1 LR circuit, comparison with RC 12.2 Using the oscilloscope 12.3 Energy contained in a solenoid 80 80 81 82 13. Lecture 13 13.1 Electric generators and alternate current 13.2 AC resistor circuit 87 87 91 14. Lecture 14 14.1 AC circuits: capacitors and inductors 14.1.1 Capacitors 14.1.2 Inductors 92 92 92 93 15. Lecture 15 15.1 Demo: Sound transmission with (laser) light 15.2 Electromagnetic waves 15.3 Light as an electromagnetic wave 15.3.1 Index of refraction 15.3.2 Fermat’s principle –2– 98 98 98 101 102 103 16. Lecture 16 16.1 Refraction 16.2 Mirrors 16.2.1 Flat mirror 16.2.2 Concave mirror 106 106 107 107 108 17. Lecture 17 17.1 Concave mirror 17.2 Mirror equation 17.3 Convex mirror 17.4 Convergent lens 112 112 113 114 115 18. Lecture 18 18.1 Lens equation 18.2 Divergent Lens 18.3 Camera, microscope, telescope 18.4 Aberrations 118 118 118 119 120 19. Lecture 19 19.1 Interference 19.1.1 Interferometer 19.1.2 Thin films 19.1.3 Two slits 123 123 123 125 127 20. Lecture 20 20.0.4 Fresnel Equations 20.1 Gratings 20.2 Diffraction 131 131 133 135 21. Lecture 21 21.1 Diffraction and optical instruments 21.2 Light-matter interaction: Photoelectric effect 138 138 139 22. Lecture 22 22.1 Photons 22.2 Hydrogen spectrum and Bohr atomic theory 22.3 Uncertainty principle 142 142 142 143 –3– 23. Lecture 23 23.1 De Broglie waves 23.2 Other results and applications 148 148 149 24. Lecture 24 24.1 Nuclear Physics 24.1.1 Constituents and binding energy 24.1.2 Nuclear decays 24.1.3 Fission and Fusion 153 153 153 154 156 1. Lecture 1 1.1 Introduction One of the things that science does is to use the tools and ideas from our everyday experience and extrapolates them to other realms. If you look around you will see that one of the first things we notice and are able to determined about object is its size, perhaps inherited from our ancestor for whom a big or small animal meant the difference between predator or food. For that reason, when we explore a new area of science, from galaxies to atoms one of the first things we need to ask to get a grasp on the new subject is what is the typical size of the objects that we are going to deal with. We say that we determine the scale or order of magnitude of the systems we analyze. As a way to fix ideas then let us revise the size of some systems in figure 1. 10 −15 m 10 −10 −6 1m bacteria people m 10 m 7 10 m 10 21 m 10 27 m p+ galaxy proton atom Earth visible Universe Figure 1: When studying a new phenomenon the first question is at which length scale it occurs. Typical examples are shown. We see that in physics we have to deal with objects of very different size. For that reason it is convenient to use scientific notation where we write for example 103 for a –4– thousand (also we use the prefix kilo) and 10−3 for a thousandth (prefix milli). Some commonly used prefixes Factor prefix abbr. 10−15 10−12 10−9 10−6 10−3 1 103 106 109 1012 femto pico nano micro milli f p n µ m kilo mega giga tera K M G T Not all of them are always used, for example Megameter is not used although we are familiar with MegaByte or GigaByte. The other important thing to notice is what are the forces acting on objects at different scales. At the planetary scale and larger the dominant force is gravity. Not because it is particularly strong but because most macroscopic objects are neutral under the other forces. At our scale and down to the atomic scale electromagnetism (electricity and magnetism) is the most important one. When we think about electromagnetism we first think of light-bulbs, phones, computers etc. but we should remind ourselves that everything around us works through the electromagnetic force. Solids are solids because electric charges keep the atoms together, chemical reactions occurs as a consequence of transfer of charged electrons between atoms making and destroying molecular bonds. Only inside the atomic nucleus, namely scales of 10−15 m do we find new forces, the strong force that keep the nucleus together and the weak force that induces certain radioactive decays. So if we understand gravity and electromagnetism we pretty much understand everything that surrounds us, at least in principle!. A very notable exception is the Sun, only after the discovery of the strong force it became apparent that the source of energy for the Sun is nuclear reactions. Finally, once we understand the forces we need to know how they modify the objects that interact with them. At distances much larger that the atomic nucleus this is given by Newton’s famous third law: ￿ F = m￿ a (1.1) namely a force acting on an object produces an acceleration, a change in velocity, proportional to the force. If we explore distances of 10−10 meters an below (atomic –5– scale) then Newton’s law is replaced by quantum mechanics as we will find out later in the course. Furthermore, if objects move at speeds close to the speed of light then Einstein’s theory of relativity should be used. Before we start with electromagnetism we can make a quick review of gravity. Newton’s law of gravity is one of the greatest achievements of mankind and made clear what Galileo and others had expressed, namely that, through the use of reasoning and mathematics we can gain insight into Nature at a depth that was previously unimaginable. It is not clear why this is so but it has been proved right until now, the more we explore Nature the more amazing phenomena we discover and the more interesting the mathematical constructions that are needed to describe them. In any case, going back to the Law of Gravity, it simply states that two massive bodies attract each other with a force proportional to the mass and inversely proportional to the square of the distance separating them: M1 M2 ￿ |F | = G 2 (1.2) r Remember that the force is a vector, it has a magnitude that we just gave and a direction which is toward the other body. The constant G is called Newton’s constant. Its value is G = 6.67 × 10−11 m2 kg −1 s−2 = 6.67 × 10−11 N (m/kg )2 . Please take your time to see that you understand the units. Units are fundamental in physics since a number without a unit has no meaning. M1 M2 Figure 2: Two masses attract each other due to gravity. Problem 1: Using that the radius of the Earth is rE ￿ 6000Km, the acceleration of gravity on the surface g = 10m/s2 and the density five times that of water, give an estimate of G and compare with the value given. Solution: The gravitational force on an object of mass m at the surface of the Earth is given by ME m ￿ |F | = G 2 (1.3) RE where ME is the mass of the Earth and RE is its radius. According to Newton’s law the acceleration is ￿ |F | ME g= =G 2 (1.4) m RE –6– The mass of the Earth is given by 43 M E = π R E ρE 3 (1.5) with ρE = 5 × 103 Kg its density. Replacing in our previous equation and after m3 some algebra we find gR2 3g G = 4 3E = (1.6) 4 π R E ρE π RE ρE 3 replacing the values RE = 6, 000Km, g = 10m/s2 , ρE = 5 × 103 Kg we find m3 G ￿ 8 × 10−11 m3 Kgs2 (1.7) 2 a good estimate of the actual measured value G = 6.7×10−11 N m2 . Notice that the Kg units are the same since 1N = 1Kg m/s2 . A final observation is that historically this was done the other way around, namely by measuring G the density of the Earth was determined. Problem 2: Using that the period of the Moon orbit is around a month, estimate the distance of the Earth to the Moon. How can you use that to know the size of the Moon? Hint: Remember that the centripetal acceleration if ar = v 2 /r and v = ω r where ω is the angular velocity. Solution: Now we equate the gravitational force with the mass of the Moon times the 2 centripetal acceleration given by ar = vr . We have: ￿ |F | = G ME Mm v2 = Mm 2 R0 R0 (1.8) where R0 is the radius of the orbit. The velocity v is given by v = ω R0 where ω is the angular velocity given by ω = 2π , with T the period of the orbit. Furthermore T we can use that GME g= (1.9) 2 RE as we had before. This allows us to do the calculation without using G, we simple need g the acceleration of gravity on the surface of the Earth. Putting everything together we find T2 2 3 R0 = g 2 RE (1.10) 4π Replacing the numbers we find an estimate R0 = 4.5 × 108 m = 450, 000Km –7– (1.11) ...
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This note was uploaded on 12/07/2011 for the course PHY 219 taught by Professor Na during the Fall '11 term at Purdue.

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