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 479072036. Email: [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 Lightmatter 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 lightbulbs, 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.
 Fall '11
 NA
 Physics

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