Physics II A - L

Academic Year 2023/2024 - Teacher: IVANO LOMBARDO

Expected Learning Outcomes

After having successfully followed the course, students must be able to independently solve a large class of problems related to electromagnetism and optics, and must have learned and internalized the conceptual foundations and the main experimental results related to the historical development of electromagnetism.

Course Structure

Frontal teaching accompanied by numerous exercises

Required Prerequisites

Physics I. It would be better to have a good knowledge of Differential Calculus and Linear Algebra.

Attendance of Lessons

The participation to the lectures is mandatorily requires.

Detailed Course Content

1.1 - Electrostatic force. Electrostatic field.
The composition of matter and the presence of electrical interactions between its charged constituents. Quantization and conservation of the electric charge. Insulating and conducting materials. Electrifying processes. Force between electric charges. Coulomb's law. The electrostatic field. Calculation of electrostatic fields for discrete and continuous distributions. The lines of force. Motion of a charge in an electrostatic field.
1.2 - Electrical work. Electrostatic potential.
The work of the electric force. The electrical voltage between two points. The electromotive force of the electric field. The electrostatic potential. The electrostatic potential energy. Calculation of the potential and electrostatic potential energy for a point charge and for discrete and continuous charge distributions. Potential energy of a system of charges. Motion of a charge in an electrostatic field. The electrostatic field as a gradient of the potential. Calculation of electrostatic fields from the potential for continuous charge distributions. The rotor of the electric field. Equipotential surfaces. Electric field and potential generated by a dipole. Potential energy of a dipole placed in a field.
1.3 - Gauss's law.
Flux of the electrostatic field vector. Proof of Gauss's theorem. Applications of Gauss's theorem: spherical shell, sphere, wire and plane uniformly charged. Gauss law in local form.
1.4 - Conductors. Dielectrics. Electrostatic energy.
Conductors in equilibrium. Electrostatic induction. Hollow conductor. Electrostatic screen. Capacitors in a vacuum. Connection of capacitors. Electrostatic energy. Dielectrics. Relative, absolute dielectric constant, electrical susceptibility. Polarization of dielectrics. Definition of the vector D (dielectric induction).
2.1 - Electricity.
Electric conduction. Average current, instantaneous current, current density. Ohm's law for ohmic conductors. Conductivity and resistivity. Classic model of management. Electrical resistance. Dependence on temperature. Superconductors. Electricity and absorbed power. EMF generators Resistors in series and in parallel. Kirchhoff's laws. Charge and discharge of an RC circuit.
2.2 - Magnetic field.
Properties of magnets. Magnetic field. Lorentz force. Magnetic force on a current-carrying wire: Laplace's second elementary law. Torque acting on a current-carrying coil immersed in a uniform magnetic field. Magnetic moment of a coil traversed by a stationary current. Hall effect. Motion of a particle in a uniform magnetic field.
2.3 - Sources of the magnetic field. Ampère's law. Magnetic properties of matter.
Magnetic field produced by an element of current - Laplace's first elementary law. Magnetic permeability of vacuum. Ampère-Laplace law for the magnetic field generated by a closed circuit carried by current. Magnetic field produced by a straight wire (Biot-Savart law), by a circular coil, by an ideal solenoid. Forces acting on parallel wires carried by current. Ampère's law. Gauss's law for the magnetic field - Magnetic properties of matter. Permeability and magnetic susceptibility. Mechanisms of magnetization and amperian currents.
3.1 - Electric and magnetic fields varying over time.
Faraday's law. Lenz's law. Current generators. Foucault currents. Self-induction. RL circuits. Magnetic energy. Magnetic energy density. Mutual induction. Displacement current. Ampère-Maxwell's law. 
4.1 - Electromagnetic waves.
Solution of the Maxwell equations in vacuum - Lorenz and Coulomb gauges - Plane electromagnetic waves. Harmonic plane electromagnetic waves. Linear polarization. Poynting vector. Intensity of an e.m. wave Radiation pressure. Electromagnetic spectrum. Spherical waves.
5.1 - Reflection and refraction of light and geometric optics
Measurements of the speed of light. Refractive index. Reflection and refraction. Limiting angle. Total reflection. Construction of images in geometric optics.

Textbook Information

1 - R. A. Serway, Physics, Saunders
2 - D. Halliday, R. Resnick, K.S. Krane, Physics, 2nd vol., J. Wiley & Sons

3 - F.W. Sears, M.W. Zemansky, University Physics, vol II,  Pearson

4 - D. Giancoli, Physics, vol. 2, Pearson

Course Planning

 SubjectsText References
1Serway, Halliday, Giancoli
2Serway, Halliday, Giancoli
3Serway, Sears
4Sears, Giancoli
5Serway, Sears
6Serway. Halliday, Sears, Giancoli
7Serway, Giancoli, Sears
8Serway, Roller-Blum
10Serway, Sears

Learning Assessment

Learning Assessment Procedures

The exam consists of a written examination followed by an oral test. The written test (duration 2 hours) consists in the resolution, justified and clearly commented, of four exercises. Students who pass the written test (minimum score: 15/30) can take the subsequent oral test within the SAME exam session. the oral test consists, starting from a discussion of the written examination, in the discussion of the topics in the program.

Examples of frequently asked questions and / or exercises

Gauss's law - examples of electrostatic effects due to the 1 / r2 dependence of the field - capacitance of a conductor - examples of capacitance calculation - definition of electrostatic potential energy - rotor and divergence theorems (without proof) - properties of operators differential - polarization mechanisms - dipoles in external fields - analogies between electric and magnetic dipoles - Ohm's laws - Kirchhoff's laws - RC circuits - Biot Savart's law - magnetic field calculations - Ampere's law - displacement current - Faraday's law - self-induction and RL circuits - mutual induction - Poynting vector - radiation pressure - c measurements - Snell's laws - construction of optical images for a mirror and a lens .