Physics Ii
A.Y. 2024/2025
Learning objectives
Making judgements in the choice of the solutions of simple problems.
Communication skills logically explaining what has been learnt.
Learning skills at least the basics of Physics, how and why to face problems.
Knowledge and understanding of some basic optical and electromagnetic properties of Nature.
Applying knowledge and understanding to simple problems of electromagnetism and optics.
Communication skills logically explaining what has been learnt.
Learning skills at least the basics of Physics, how and why to face problems.
Knowledge and understanding of some basic optical and electromagnetic properties of Nature.
Applying knowledge and understanding to simple problems of electromagnetism and optics.
Expected learning outcomes
Knowledge and understanding of some basic optical and electromagnetic properties of Nature.
Applying knowledge and understanding to simple problems of electromagnetism and optics.
Applying knowledge and understanding to simple problems of electromagnetism and optics.
Lesson period: First semester
Assessment methods: Esame
Assessment result: voto verbalizzato in trentesimi
Single course
This course can be attended as a single course.
Course syllabus and organization
Single session
Responsible
Lesson period
First semester
No emergential phasa
Course syllabus
4,718 / 5,000
1. vectors, scalar product and vector product of two vectors.
2. Waves: Amplitude, wavelength, frequency, phase, and polarization of
waves. Three-dimensional case, definition of the wave vector.
-Examples. Acoustic waves and mechanical waves
(elastic waves): differences between solid, liquid or gas media, especially in
terms of possible polarizations.
-Relationship between propagation speed, period, and length
wave (i.e. between frequency and wave vector).
-Typical wavelengths and energies of the various regions of the spectrum
electromagnetic. Examples.
-Solutions of the Newton equation F=ma with
F=kx and negative and positive K: oscillating and damped solutions.
-Interference between waves.
-Diffraction of waves: general case (any incidence) and deduction of the law
\vec d [scalar] DeltaK = 2pi * m
-Single slit diffraction (qualitative description only e
implications for the resolution limit of optical microscopy).
-Diffraction from periodic gratings (outline).
3, geometric optics, laws of reflection and
Snell's law for refraction. Dispersive media (refractive index
frequency dependent). Prism and spectrum decomposition
visible. Rainbow.Examples.
-Following geometric optics: Limit angle and total reflection.
4. Forces and fields, usefulness of the field concept. Strength of
Coulomb, Electric field. definition of the flow through a surface, theorem of
Gauss. Comparison with the case of the gravitational force.
-Perfect conductors in electrostatic equilibrium.
-Surface charge.
-Review of the concept of potential energy (gravitational,
elastic). Application to the case of electric forces.
(Review of the link between Force and Field, analogy with Potential and Potential Energy. Force
as -derivative of potential energy and field as -derivative of
potential . )
-Writing forces and fields with the gradient operator. Definition of
potential up to a constant. Potential difference, surface
equipotential, spherical case and uniform case.
-relation:(Null field <=> constant potential), therefore the
potential is always defined unless a constant => has meaning
physical "potential difference". Superposition principle for the
potential (in the case of more charges, or more masses in the gravitational case).
-Ideal (perfect) conductors in equilibrium
Application of Gauss' theorem: field inside e
full charge inside; Surface charge density. Application to
shielding from electromagnetic fields (Faraday cage).
-Calculation of the external electric field near the surface as a function of the charge
superficial.
5. Capacitors and Resistors:
-Concept of electrical capacity. Unit'
of measurement. Case of the single spherical conductor. Case of the two plates
plane and parallel (flat condenser). Capacity as a function of
distance between the rebars. Connecting capacitors in parallel and in
series.
-Calculation of the energy accumulated in a capacitor. Ideal analogy.
-Definition of electric current as flow of charge. Resistance and resistivity.
Ohm's law. Origin of resistivity (mean free path of electrons, contribution of defects,
independent of T, and contributed by the thermal agitation of the nuclei, which instead increases with T).
- direct current circuits, in steady state (constant current:
Resistivity, Conductivity, Resistance, Admittance, and theirs
unit of measure.
-Joule effect: power dissipated in a resistor.
-Applications of Ohm's law to elementary circuits: series resistors
and in parallel. The case of the voltage divider.
-circuits in direct current, but not stationary (current varying over time):
-Law of *discharge* of the capacitor: analogies with other physical phenomena.
Graphs as a function of time. Characteristic time, and half-life.
-Case of the capacitor *charging* process. Charging trend Q,
current I and Potential Difference DeltaV as a function of time in
case of discharge and charge.
- Trend of accumulated energy as a function of time.
6. Magnetism: Differences between electric field and magnetic field. Lorentz force.
-Consequences on the birth of
currents in moving conductors immersed in field B. Consequences on
birth of forces on conductors that are stationary but current-carrying and immersed in
an external B field.
-Magnetic effects of currents
in the case of constant fields and currents (not varying over time):
-Ampere's theorem
Deduction formulas for the value of the B generated by
straight wire, in the center of a single circular coil, and within a
"infinite" solenoid.
Case of time-varying electric fields: example of the charging and discharging of a capacitor,
inconsistency of Ampere's theorem (example of the charge of el
inconsistency of Ampere's theorem (example of the charge of el
inconsistenza del teorema di Ampere (esempio della carica di el
inconsistency of Ampere's theorem (example of the charge of the element
incoerenza del teorema di Ampere (esempio della carica dell'elemento
capacitor using "glass" type surface having the same line
border lock that goes around the conductor leading to the armature
of the capacitor). Displacement current and generalized Ampere theorem.
-Effects of a time-varying magnetic field B:
principle of the electromagnetic seismograph and the current generator.
-Definition of inductance L as muzero*N/l. Comparison
with Ohm's law. Permanent magnets (outline).
1. vectors, scalar product and vector product of two vectors.
2. Waves: Amplitude, wavelength, frequency, phase, and polarization of
waves. Three-dimensional case, definition of the wave vector.
-Examples. Acoustic waves and mechanical waves
(elastic waves): differences between solid, liquid or gas media, especially in
terms of possible polarizations.
-Relationship between propagation speed, period, and length
wave (i.e. between frequency and wave vector).
-Typical wavelengths and energies of the various regions of the spectrum
electromagnetic. Examples.
-Solutions of the Newton equation F=ma with
F=kx and negative and positive K: oscillating and damped solutions.
-Interference between waves.
-Diffraction of waves: general case (any incidence) and deduction of the law
\vec d [scalar] DeltaK = 2pi * m
-Single slit diffraction (qualitative description only e
implications for the resolution limit of optical microscopy).
-Diffraction from periodic gratings (outline).
3, geometric optics, laws of reflection and
Snell's law for refraction. Dispersive media (refractive index
frequency dependent). Prism and spectrum decomposition
visible. Rainbow.Examples.
-Following geometric optics: Limit angle and total reflection.
4. Forces and fields, usefulness of the field concept. Strength of
Coulomb, Electric field. definition of the flow through a surface, theorem of
Gauss. Comparison with the case of the gravitational force.
-Perfect conductors in electrostatic equilibrium.
-Surface charge.
-Review of the concept of potential energy (gravitational,
elastic). Application to the case of electric forces.
(Review of the link between Force and Field, analogy with Potential and Potential Energy. Force
as -derivative of potential energy and field as -derivative of
potential . )
-Writing forces and fields with the gradient operator. Definition of
potential up to a constant. Potential difference, surface
equipotential, spherical case and uniform case.
-relation:(Null field <=> constant potential), therefore the
potential is always defined unless a constant => has meaning
physical "potential difference". Superposition principle for the
potential (in the case of more charges, or more masses in the gravitational case).
-Ideal (perfect) conductors in equilibrium
Application of Gauss' theorem: field inside e
full charge inside; Surface charge density. Application to
shielding from electromagnetic fields (Faraday cage).
-Calculation of the external electric field near the surface as a function of the charge
superficial.
5. Capacitors and Resistors:
-Concept of electrical capacity. Unit'
of measurement. Case of the single spherical conductor. Case of the two plates
plane and parallel (flat condenser). Capacity as a function of
distance between the rebars. Connecting capacitors in parallel and in
series.
-Calculation of the energy accumulated in a capacitor. Ideal analogy.
-Definition of electric current as flow of charge. Resistance and resistivity.
Ohm's law. Origin of resistivity (mean free path of electrons, contribution of defects,
independent of T, and contributed by the thermal agitation of the nuclei, which instead increases with T).
- direct current circuits, in steady state (constant current:
Resistivity, Conductivity, Resistance, Admittance, and theirs
unit of measure.
-Joule effect: power dissipated in a resistor.
-Applications of Ohm's law to elementary circuits: series resistors
and in parallel. The case of the voltage divider.
-circuits in direct current, but not stationary (current varying over time):
-Law of *discharge* of the capacitor: analogies with other physical phenomena.
Graphs as a function of time. Characteristic time, and half-life.
-Case of the capacitor *charging* process. Charging trend Q,
current I and Potential Difference DeltaV as a function of time in
case of discharge and charge.
- Trend of accumulated energy as a function of time.
6. Magnetism: Differences between electric field and magnetic field. Lorentz force.
-Consequences on the birth of
currents in moving conductors immersed in field B. Consequences on
birth of forces on conductors that are stationary but current-carrying and immersed in
an external B field.
-Magnetic effects of currents
in the case of constant fields and currents (not varying over time):
-Ampere's theorem
Deduction formulas for the value of the B generated by
straight wire, in the center of a single circular coil, and within a
"infinite" solenoid.
Case of time-varying electric fields: example of the charging and discharging of a capacitor,
inconsistency of Ampere's theorem (example of the charge of el
inconsistency of Ampere's theorem (example of the charge of el
inconsistenza del teorema di Ampere (esempio della carica di el
inconsistency of Ampere's theorem (example of the charge of the element
incoerenza del teorema di Ampere (esempio della carica dell'elemento
capacitor using "glass" type surface having the same line
border lock that goes around the conductor leading to the armature
of the capacitor). Displacement current and generalized Ampere theorem.
-Effects of a time-varying magnetic field B:
principle of the electromagnetic seismograph and the current generator.
-Definition of inductance L as muzero*N/l. Comparison
with Ohm's law. Permanent magnets (outline).
Prerequisites for admission
Elementary Mathematics
- fractions, percent, decimal numbers
- 1° e 2° degree equations
- powers and their properties
- elementary geometry:
perimeter, area
main geometricas shapes
(square, triangle, circle, sphere, cube, cone, )
- angols (90, 180, 360 degrees, )
- basic trigonometry: sinus, cosinus, tangent
- elementary analytic functions:
, parabolic, iperbolic functions and their graphical representation
( y=ax+b, y=ax^2+bx+c, y=a/x, )
- elementary derivatives and integrals:
x, x^n, sin(x), cos(x), ln(x)
Physical dimensions:
length, surface, volume, mass, time, ..
- units of misure, prefixes and conversions:
length: 1 m = 100 cm = 1000 mm = 0.001 km
mass: 1 kg = 1000 g
time: 1 h = 60 min = 3600 s
- orders of magnitude:
Physically reasonable mumerical values
- algebraic operations with physical values:
sum, product.
- fractions, percent, decimal numbers
- 1° e 2° degree equations
- powers and their properties
- elementary geometry:
perimeter, area
main geometricas shapes
(square, triangle, circle, sphere, cube, cone, )
- angols (90, 180, 360 degrees, )
- basic trigonometry: sinus, cosinus, tangent
- elementary analytic functions:
, parabolic, iperbolic functions and their graphical representation
( y=ax+b, y=ax^2+bx+c, y=a/x, )
- elementary derivatives and integrals:
x, x^n, sin(x), cos(x), ln(x)
Physical dimensions:
length, surface, volume, mass, time, ..
- units of misure, prefixes and conversions:
length: 1 m = 100 cm = 1000 mm = 0.001 km
mass: 1 kg = 1000 g
time: 1 h = 60 min = 3600 s
- orders of magnitude:
Physically reasonable mumerical values
- algebraic operations with physical values:
sum, product.
Teaching methods
Frontal lectures and exercises
Teaching Resources
-Serway "Principi di Fisica", published by EdiSes.
-Teacher's slides
-Teacher's slides
Assessment methods and Criteria
The ordinary exam consists of a written and an oral test. The written test is always mandatory.
The written exam is considered passed if the score is at least 18/30. It is always possible to ask for the vote to be recorded directly, without an oral exam (you must still register for the first registration session).
Anyone who wishes to have a chance to raise (or lower) the grade of the paper can request to be heard orally.
The possibility of requesting this oral exam is extended to students who have achieved a grade of at least 16/30 in the written exam. In this case the oral test is therefore mandatory to pass the exam.
Students with a score lower than 16/30 will necessarily have to re-apply for a written appeal
following.
You are also given the opportunity to pass the exam by taking two "ongoing" tests (approximately the first at the end of November/beginning of December, the second at the end of January/beginning of February).
Anyone who passes the two ongoing tests or the written test and accepts the proposed grade has passed the exam without further tests and the result is recorded.
The ongoing tests consist of a written exam with quizzes, theory questions and simple exercises.
The written exam is considered passed if the score is at least 18/30. It is always possible to ask for the vote to be recorded directly, without an oral exam (you must still register for the first registration session).
Anyone who wishes to have a chance to raise (or lower) the grade of the paper can request to be heard orally.
The possibility of requesting this oral exam is extended to students who have achieved a grade of at least 16/30 in the written exam. In this case the oral test is therefore mandatory to pass the exam.
Students with a score lower than 16/30 will necessarily have to re-apply for a written appeal
following.
You are also given the opportunity to pass the exam by taking two "ongoing" tests (approximately the first at the end of November/beginning of December, the second at the end of January/beginning of February).
Anyone who passes the two ongoing tests or the written test and accepts the proposed grade has passed the exam without further tests and the result is recorded.
The ongoing tests consist of a written exam with quizzes, theory questions and simple exercises.
FIS/01 - EXPERIMENTAL PHYSICS - University credits: 6
Practicals: 24 hours
Lessons: 32 hours
Lessons: 32 hours
Professors:
Castelli Fabrizio, Facchini Stefano
Educational website(s)
Professor(s)
Reception:
tuesday 14:30 - 19:00
Department of Physics, via Celoria 16 Milan (fifth floor, room A/5/C3)
Reception:
By appointment
Office 1.1.10, first floor, Department of Physics, via Celoria 16