Principi e Metodi della Fisica

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Principi e Metodi della Fisica
Elettromagnetismo dalla carica elettrica, ai
campi, alle equazioni di Maxwell ed alle onde
elettromagnetiche
Relatività dal mistero della velocità della
luce, allo spazio-tempo, alla equivalenza di
massa ed energia. La gravitazione come geometria
Meccanica Quantistica la crisi della Fisica
Classica, comportamenti corpuscolari ed
ondulatori di materia e radiazione, i quanti di
energia. Principio di indeterminazione.
Statistiche quantistiche e struttura atomica
della materia
Bibliografia Robert H. March, Fisica per Poeti,
Ed. Dedalo, 1994
Website http//hyperphysics.phy-astr.gsu.edu/hbas
e/hframe.html
LT in Comunicazione Scientifica, a.a. 2004-05
Mauro Anselmino
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Electric Charge The unit of electric charge is
the coulomb. Ordinary matter is made up of atoms
which have positively charged nuclei and
negatively charged electrons surrounding them.
Charge is quantized as a multiple of the electron
or proton charge
The influence of charges is characterized in
terms of the forces between them (Coulomb's law)
and the electric field and voltage produced by
them. One coulomb of charge is the charge which
would flow through a 120 watt lightbulb (120
volts AC) in one second. Two charges of one
coulomb each separated by a meter would repel
each other with a force of about a million
tons! The rate of flow of electric charge is
called electric current and is measured in
ampères.
In introducing one of the fundamental properties
of matter, it is perhaps appropriate to point out
that we use simplified sketches and constructs to
introduce concepts, and there is inevitably much
more to the story. No significance should be
attached to the circles representing the proton
and electron, in the sense of implying a relative
size, or even that they are hard sphere objects,
although that's a useful first construct. The
most important opening idea, electrically, is
that they have a property called "charge" which
is the same size, but opposite in polarity for
the proton and electron. The proton has 1836
times the mass of the electron, but exactly the
same size charge, only positive rather than
negative. Even the terms "positive" and
"negative" are arbitrary, but well-entrenched
historical labels. The essential implication of
that is that the proton and electron will
strongly attract each other, the historical
archtype of the cliche "opposites attract". Two
protons or two electrons would strongly repel
each other. Once you have established those basic
ideas about electricity, "like charges repel and
unlike charges attract", then you have the
foundation for electricity and can build from
there. From the precise electrical neutrality of
bulk matter as well as from detailed microscopic
experiments, we know that the proton and electron
have the same magnitude of charge. All charges
observed in nature are multiples of these
fundamental charges. Although the standard model
of the proton depicts it as being made up of
fractionally charged particles called quarks,
those fractional charges are not observed in
isolation -- always in combinations which produce
/- the electron charge.
One of the fundamental symmetries of nature is
the conservation of electric charge. No known
physical process produces a net change in
electric charge.
3
Coulomb's Law Like charges repel, unlike charges
attract. The electric force acting on a point
charge q1 as a result of the presence of a second
point charge q2 is given by Coulomb's Law
Where e0 permittivity of spaceNote that this
satisfies Newton's third law because it implies
that exactly the same magnitude of force acts on
q2 . Coulomb's law is a vector equation and
includes the fact that the force acts along the
line joining the charges. Like charges repel and
unlike charges attract. Coulomb's law describes a
force of infinite range which obeys the inverse
square law, and is of the same form as the
gravity force.
Electric Force Example
(1 Kg-peso 9.8 N)
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How many electrons in matter?
If such enormous forces would result from our
hypothetical charge arrangement, then why don't
we see more dramatic displays of electrical
force? The general answer is that at a given
point in a wire, there is never very much
departure from electrical neutrality. Nature
never collects a Coulomb of charge at one point.
It might be instructive to examine the amount of
charge in a sphere of copper of volume one cubic
centimeter. Copper has one valence electron
outside of closed shells in its atom, and that
electron is fairly free to move about in solid
copper material (that's what makes copper a good
electrical conductor). The density of metallic
copper is about 9 grams/cm3 and one mole of
copper is 63.5 grams so the cubic centimeter of
copper contains about 1/7th of a mole or about
8.5 x 1022 copper atoms. With one mobile electron
per atom, and with the electron charge of 1.6 x
10-19 Coulombs, this means there are about 13,600
Coulombs of potentially mobile charge in one cm3
of copper.
A mole (abbreviated mol) of a pure substance is a
mass of the material in grams that is numerically
equal to the molecular mass in atomic mass units
(amu). A mole of any material will contain
Avogadro's number of molecules.
1 mole contains 6 1023 molecules, Avogadros
number
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Fundamental Forces
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Electromagnetic forces bind atoms in molecules
Strong forces bind protons and neutrons
(nucleons) in nuclei
u,d are quarks
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Nucleus contains protons with charge e and
uncharged neutrons
10-10 m
10-14 m
8
Empty atomic matter
Nuclear matter
Composite nucleons
No evidence yet for further structure of
electrons and quarks
9
Electric field is defined as the electric force
per unit charge. The direction of the field is
taken to be the direction of the force it would
exert on a positive test charge. The electric
field is radially outward from a positive charge
and radially in toward a negative point charge.
The electric field of a point charge can be
obtained from Coulomb's law
The electric field from any number of point charges can be obtained from a vector sum of the individual fields. A positive number is taken to be an outward field the field of a negative charge is toward it.                               
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Electric Potential Energy and Electric
Potential Potential energy can be defined as the
capacity for doing work which arises from
position or configuration. In the electrical
case, a charge will exert a force on any other
charge and potential energy arises from any
collection of charges. For example, if a positive
charge Q is fixed at some point in space, any
other positive charge which is brought close to
it will experience a repulsive force and will
therefore have potential energy. The potential
energy of a test charge q in the vicinity of this
source charge will be
where k is Coulomb's constant
The potential energy of a point charge can be
evaluated by calculating the work necessary to
bring a test charge q in from an infinite
distance to some distance r.
The zero of potential is chosen at infinity. From
the knowledge of the electric potential energy
one can compute the electric force.
In electricity, it is usually more convenient to
use the electric potential energy per unit
charge, just called electric potential or
voltage.
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Magnetic Fields Magnetic fields are produced by
electric currents, which can be macroscopic
currents in wires, or microscopic currents
associated with electrons in atomic orbits. The
magnetic field B is defined in terms of force on
moving charge in the Lorentz force law. The
interaction of magnetic field with charge leads
to many practical applications. Magnetic field
sources are essentially dipolar in nature, having
a north and south magnetic pole.
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Electric and Magnetic Monopoles
The magnetic field of a bar magnet
The electric field of a point charge is radially
outward from a positive charge
Magnetic sources are inherently dipole sources -
you can't isolate North or South "monopoles".
Electric sources are inherently "monopole" or
point charge sources.
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Magnetic Force The magnetic field B is defined
from the Lorentz Force Law, and specifically from
the magnetic force on a moving charge
The implications of this expression include 1.
The force is perpendicular to both the velocity v
of the charge q and the magnetic field B. 2. The
magnitude of the force is F qvB sin? where ? is
the angle lt 180 degrees between the velocity and
the magnetic field. This implies that the
magnetic force on a stationary charge or a charge
moving parallel to the magnetic field is zero. 3.
The direction of the force is given by the right
hand rule. The force relationship above is in the
form of a vector product. From the force
relationship above it can be deduced that the
units of magnetic field are Newton seconds
/(Coulomb meter) or Newtons per Ampere meter.
This unit is named the Tesla. It is a large unit,
and the smaller unit Gauss is used for small
fields like the Earth's magnetic field. A Tesla
is 10,000 Gauss. The Earth's magnetic field is on
the order of half a Gauss.

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Lorentz Force Law Both the electric field and
magnetic field can be defined from the Lorentz
force law
The electric force is straightforward, being in
the direction of the electric field if the charge
q is positive, but the direction of the magnetic
part of the force is given by the right hand
rule.
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Magnetic Field of Current The magnetic field
lines around a long wire which carries an
electric current form concentric circles around
the wire. The direction of the magnetic field is
perpendicular to the wire and is in the direction
the fingers of your right hand would curl if you
wrapped them around the wire with your thumb in
the direction of the current.
An electric current acts with a force on a test
small magnet (Oersted)
The magnetic field of an infinitely long straight
wire can be obtained by applying Ampere's law.
The expression for the magnetic field is
µ0 permeability of free space
r distance from wire
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Magnetic Field of (Atomic) Current Loop
Electric current in a circular loop creates a
magnetic field which is more concentrated in the
center of the loop than outside the loop.
at center of loop
Magnetic Dipole Moment
B (µoi) / (2r)
(Notice µ of dipole is not the same as the
permeability µ0 )

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Magnetic Force on a Current (Faraday)
F i L x B
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Magnetic Force Between Wires
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Energy in Electric and
Magnetic Fields Both electric fields and
magnetic fields store energy. For the electric
field the energy density is
This energy density can be used to calculate the
energy stored in a capacitor. For the magnetic
field the energy density is



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Electric Field Energy in Capacitor
The energy stored on a capacitor is in the form
of energy density of an electric field and is
given by

This can be shown to be consistent with the
energy stored on a charged parallel plate
capacitor

E V/d
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Capacitance of Parallel Plates
The electric field between two large parallel
plates is given by
                               
The voltage difference between the two plates can
be expressed in terms of the work done on a
positive test charge q when it moves from the
positive to the negative plate.
it then follows from the definition of
capacitance C Q/V
The Farad, F, is the SI unit for capacitance,
equal to a Coulomb/Volt.
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Storing Energy in a Capacitor
The energy stored on a capacitor can be expressed
in terms of the work done by the battery. Voltage
represents energy per unit charge, so the work to
move a charge element dq from the negative plate
to the positive plate is equal to V dq, where V
is the voltage on the capacitor. The voltage V is
proportional to the amount of charge which is
already on the capacitor.
If Q is the amount of charge stored when the
whole battery voltage appears across the
capacitor, then the stored energy is obtained
from the integral
Element of energy stored
This energy expression can be put in three
equivalent forms by just permutations based on
the definition of capacitance C Q/V
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Magnetic Interactions with Moving Charge
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Applications - Voltage Generated in a Moving Wire
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Motional EMF
The magnetic force exerted on the charges in a
moving conductor will generate a voltage (a
motional emf). This motional emf is one of many
settings in which the generated emf is described
by the Faradays law.
The motional emf expression is an application of
Faraday's Law, as can be seen from
F BA is the flux of magnetic field it is given
by B times the perpendicular area that it
penetrates. ?F/?t gives the variation with time
of the flux.
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Faraday's Law
Any change in the magnetic environment of a coil
of wire will cause a voltage (emf) to be
"induced" in the coil. No matter how the change
is produced, the voltage will be generated. The
change could be produced by changing the magnetic
field strength, moving a magnet toward or away
from the coil, moving the coil into or out of the
magnetic field, rotating the coil relative to the
magnet, etc.
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AC Generator The turning of a coil in a magnetic
field produces motional emfs in both sides of the
coil which add. Since the component of the
velocity perpendicular to the magnetic field
changes sinusoidally with the rotation, the
generated voltage is sinusoidal or AC. This
process can be described in terms of Faraday's
law when you see that the rotation of the coil
continually changes the magnetic flux through the
coil and therefore generates a voltage.
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Magnetic Force on Moving Charge
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Circular Path from Magnetic Field If a charge
moves into a magnetic field with direction
perpendicular to the field, it will follow a
circular path. The magnetic force, being
perpendicular to the velocity, provides the
centripetal force.
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DC Motor Operation
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Electric Shock
The primary variable for determining the severity
of electric shock is the electric current which
passes through the body. This current is of
course dependent upon the voltage and the
resistance of the path it follows through the
body. An approximate general framework for shock
effects is as follows
Electric Current (1 second contact) Physiological Effect
1 mA Threshold of feeling, tingling sensation.
10-20 mA "Can't let go!" current - onset of sustainedmuscular contraction.
100-300 mA Ventricular fibrillation, fatal if continued.
One instructive example of the nature of voltage
is the fact that a bird can sit on a high-voltage
wire without harm, since both of its feet are at
the same voltage. You can also see that the bird
is not "grounded" -- you will not be shocked by
touching a high voltage if there is no path for
the current to reach the Earth or a different
voltage point. Typically if you touch a 120 volt
circuit with one hand, you can escape serious
shock if you have insulating shoes which prevent
a low-resistance path to ground. This fact has
led to the common "hand-in-the-pocket" practice
for engineers and electrical workers. If you keep
one hand in your pocket when touching a circuit
which might provide a shock, you are less likely
to have the kind of path to ground which will
result in a serious shock.
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Will the bird on the high voltage wire be shocked?
Electric current flow is proportional to voltage
difference according to Ohm's law, and both the
bird's feet are at the same voltage. Since
current flow is necessary for electric shock, the
bird is quite safe unless it simultaneously
touches another wire with a different voltage.
Want a scary job? Maintenance on high voltage
transmission lines is sometimes done with the
voltage "live" by working from a platform on a
helicopter, sitting on a metal platform! The
helicopter must make sure it doesn't touch
neighboring wires which are at a different
voltage.
Power P VI RI2
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Maxwell's Equations Maxwell's equations
represent one of the most elegant and concise
ways to state the fundamentals of electricity and
magnetism. From them one can develop most of the
working relationships in the field. Because of
their concise statement, they embody a high level
of mathematical sophistication and are therefore
not generally introduced in an introductory
treatment of the subject, except perhaps as
summary relationships.
I. Gauss' law for electricity
II. Gauss' law for magnetism                 
III. Faraday's law of induction                      
IV. Ampere's law                                       
?, J charge, current density
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The Wave Equation
Maxwell's Equations contain the wave equation for
electromagnetic waves
In 1-dimension
with the same form applying to the magnetic field
wave in a plane perpendicular the electric field.
The wave equation for electromagnetic waves
arises from Maxwell's equations. The forms of a
plane wave solution for the electric and the
magnetic fields are
To be consistent with Maxwell's equations, these
solutions must be related by
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Electromagnetic waves carry energy as they travel
through empty space. There is an energy density
associated with both the electric and magnetic
fields. The rate of energy transport per unit
area is described by the vector
which is called the Poynting vector. This
expression is a vector product, and since the
magnetic field is perpendicular to the electric
field, the magnitude can be written
(B E/c)
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Traveling Wave Relationships
A single frequency traveling wave will take the
form of a sine wave. A snapshot of the wave in
space at an instant of time can be used to show
the relationship of the wave properties
frequency, wavelength and propagation velocity.
The motion relationship "distance velocity x
time" is the key to the basic wave relationship.
With the wavelength as distance, this
relationship becomes ? vT. Then using f 1/T
gives the standard wave relationship v f ?
Waves change periodically in space and time
k 2p/? ? 2p/T
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Transverse Waves
For transverse waves the displacement of the
medium is perpendicular to the direction of
propagation of the wave. A ripple on a pond and a
wave on a string are easily visualized transverse
waves. Electromagnetic waves are transverse waves.
Longitudinal Waves
In longitudinal waves the displacement of the
medium is parallel to the propagation of the
wave. Sound waves in air are longitudinal waves.
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Sound Waves in Air
A single-frequency sound wave traveling through
air will cause a sinusoidal pressure variation in
the air. The air motion which accompanies the
passage of the sound wave will be back and forth
in the direction of the propagation of the
sound, a charateristic of longitudinal waves.
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Interference and Phase
If a mass on a rod is rotated at constant speed
and the resulting circular path illuminated from
the edge, its shadow will trace out simple
harmonic motion. If the shadow vertical position
is traced as a function of time, it will trace
out a sine wave. A full period of the sine wave
will correspond to a complete circle or 360
degrees. The idea of phase follows this parallel,
with any fraction of a period related to the
corresponding fraction of a circle in degrees.

                               
waves add with their phases
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Diffraction
This is an attempt to more clearly visualize the
nature of single slit diffraction. The phenomenon
of diffraction involves the spreading out of
waves past openings which are on the order of the
wavelength of the wave. The spreading of the
waves into the area of the geometrical shadow can
be modeled by considering small elements of the
wavefront in the slit and treating them like
point sources.
If light from symmetric elements near each edge
of the slit travels to the centerline of the
slit, as indicated by rays 1 and 2 above, their
light arrives in phase and experiences
constructive interference. Light from other
element pairs symmetric to the centerline also
arrive in phase. Although there is a progressive
change in phase as you choose element pairs
closer to the centerline, this center position is
nevertheless the most favorable location for
constructive interference of light from the
entire slit and has the highest light intensity
The first minimum in intensity for the light
through a single slit can be visualized in terms
of rays 3 and 4. An element at one edge of the
slit and one just past the centerline are chosen,
and the condition for minimum light intensity is
that light from these two elements arrive 180
out of phase, or a half wavelength different in
pathlength. If those two elements suffer
destructive interference, then choosing
additional pairs of identical spacing which
progress downward across the slit will give
destructive interference for all those pairs and
therefore an overal minimum in light intensity.
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Double Slit Interference
42
Double Slit Diffraction
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Speed of light                                  
                    
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AM Radio Band
The Amplitude Modulated (AM) radio carrier
frequencies are in the frequency range 535-1605
kHz. The frequencies 30-535 kHz are used for
maritime communication and navigation and for
aircraft navigation. Carrier frequencies of 540
to 1600 kHz are assigned at 10 kHz intervals.
f 500 kHz 5 105 s-1
Frequencies 500-1500 kHz
Wavelengths 600 - 200 m
Quantum energies 2 - 6 x 10-9 eV
T 1/f 2 10-6 s
? cT 3 108 m/s 2 10-6 s 600 m
E h f 6.6 10-34 J s 5 105 s-1 33 10-29 J
33 10-29 6.25 1018 eV 2 10-9 eV
TV and FM Radio Band
Frequencies 54-1600 MHz
Wavelengths 5.55 m - 0.187 m
Quantum energies 0.22 x 10-6 - 0.66 x 10-5 eV

h Planck constant 6.6 10-34 J s 1 eV
1.6 10-19 J
Rays with quantum energy of 1 eV correspond to ?
12 10-7 m, E hc/?
45
Visible Light
                                                  
  The narrow visible part of the electromagnetic
spectrum corresponds to the wavelengths near the
maximum of the Sun's radiation curve. White light
may be separated into its spectral colors by
dispersion in a prism.


Frequencies 4 - 7.5 x 1014 Hz
Wavelengths 750 - 400 nm
Quantum energies 1.65 - 3.1 eV
1 nm 10 Å
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X-rays and gamma-rays
X-ray was the name given to the highly
penetrating rays which emanated when high energy
electrons struck a metal target. Within a short
time of their discovery, they were being used in
medical facilities to image broken bones. We now
know that they are high frequency electromagnetic
rays which are produced when the electrons are
suddenly decelerated - these rays are called
bremsstrahlung radiation, or "braking radiation".
X-rays are also produced when electrons make
transitions between lower atomic energy levels in
heavy elements. X-rays produced in this way have
definite energies just like other line spectra
from atomic electrons. They are called
characteristic x-rays since they have energies
determined by the atomic energy levels The term
gamma ray is used to denote electromagnetic
radiation from the nucleus as a part of a
radioactive process. The energy of nuclear
radiation is extremely high because such
radiation is born in the intense conflict between
the nuclear strong force and the electromagnetic
force, the two strongest basic forces. The gamma
ray photon may in fact be identical to an x-ray,
since both are electromagnetic rays the terms
x-ray and gamma rays are statements about origin
rather than implying different kinds of
radiation. In interactions with matter, both X
and gamma rays are ionizing radiation and produce
physiological effects which are not observed with
any exposure of non-ionizing radiation, such as
the risk of mutations or cancer in tissue.

Frequencies typically gt1020 Hz
Wavelengths typically lt 10-12 m
Quantum energies typically gt1 MeV
Frequencies 7.5 x 1014 - 3 x 1016 Hz
Wavelengths 400 nm - 10 nm
Quantum energies 3.1 - 124 eV

X-rays
gamma-rays
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Gamma radioactivity is composed of
electromagnetic rays. It is distinguished from
x-rays only by the fact that it comes from the
nucleus. Most gamma rays are somewhat higher in
energy than x-rays and therefore are very
penetrating. It is the most useful type of
radiation for medical purposes, but at the same
time it is the most dangerous because of its
ability to penetrate large thicknesses of
material.
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Radiation and the Human Body
49
(No Transcript)
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Microwave Interactions
The quantum energy of microwave photons is in the
range 0.00001 to 0.001 eV which is in the range
of energies separating the quantum states of
molecular rotation and torsion. The interaction
of microwaves with matter other than metallic
conductors will be to rotate molecules and
produce heat as result of that molecular motion.
Conductors will strongly absorb microwaves and
any lower frequencies because they will cause
electric currents which will heat the material.
Most matter, including the human body, is largely
transparent to microwaves. High intensity
microwaves, as in a microwave oven where they
pass back and forth through the food millions of
times, will heat the material by producing
molecular rotations and torsions. Since the
quantum energies are a million times lower than
those of x-rays, they cannot produce ionization
and the characteristic types of radiation damage
associated with ionizing radiation.
E (10-5 10-3) eV ? ? (12 0.12 ) cm
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Visible Light Interactions
The primary mechanism for the absorption of
visible light photons is the elevation of
electrons to higher energy levels. There are many
available states, so visible light is absorbed
strongly. With a strong light source, red light
can be transmitted through the hand or a fold of
skin, showing that the red end of the spectrum is
not absorbed as strongly as the violet end.
While exposure to visible light causes heating,
it does not cause ionization with its risks. You
may be heated by the sun through a car
windshield, but you will not be sunburned - that
is an effect of the higher frequency UV part of
sunlight which is blocked by the glass of the
windshield.
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Ultraviolet Interactions
The near ultraviolet is absorbed very strongly in
the surface layer of the skin by electron
transitions. As you go to higher energies, the
ionization energies for many molecules are
reached and the more dangerous photoionization
processes take place. Sunburn is primarily an
effect of UV, and ionization produces the risk of
skin cancer. The ozone layer in the upper
atmosphere is important for human health because
it absorbs most of the harmful ultraviolet
radiation from the sun before it reaches the
surface. The higher frequencies in the
ultraviolet are ionizing radiation and can
produce harmful physiological effects ranging
from sunburn to skin cancer. Health concerns for
UV exposure are mostly for the range 290-330 nm
in wavelength, the range called UVB. According to
Scotto, et al, the most effective biological
wavelength for producing skin burns is 297 nm.
Their research indicates that the biological
effects increase logarithmically within the UVB
range, with 330 nm being only 0.1 as effective
as 297 nm for biological effects. So it is
clearly important to control exposure to UVB.
53
Since the quantum energies of x-ray photons are
much too high to be absorbed in electron
transitions between states for most atoms, they
can interact with an electron only by knocking it
completely out of the atom. That is, all x-rays
are classified as ionizing radiation. This can
occur by giving all of the energy to an electron
(photoionization) or by giving part of the energy
to the photon and the remainder to a lower energy
photon (Compton scattering). At sufficiently high
energies, the x-ray photon can create an electron
positron pair.
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Heart Electrical Phenomena
The rhythmic contractions of the heart which pump
the life-giving blood occur in response to
periodic electrical control pulse sequences. The
natural pacemaker is a specialized bundle of
nerve fibers called the sinoatrial node (SA
node). Nerve cells are capable of producing
electrical impulses called action potentials. The
bundle of active cells in the SA node trigger a
sequence of electrical events in the heart which
controls the orderly pattern of muscle
contractions that pumps the blood out of the
heart.
The electrical potentials (voltages) that are
generated in the body have their origin in
membrane potentials where differences in the
concentrations of positive and negative ions give
a localized separation of charges. This charge
separation is called polarization. Changes in
voltage occur when some event triggers a
depolarization of a membrane, and also upon the
repolarization of the membrane. The
depolarization and repolarization of the SA node
and the other elements of the heart's electical
system produce a strong pattern of voltage change
which can be measured with electrodes on the
skin. Voltage measurements on the skin of the
chest are caled an electrocradiogram or ECG.
The heart's electrical control system must
properly synchronize the pumping functions
illustrated above.