LEARNING OUTCOMES

The course provides the fundamental concepts and laws of mechanics and electromagnetism highlighting the modeling used and the limits of validity,  and aiming to develop the ability to model and make conceptual schemes.

AIMS AND LEARNING OUTCOMES

The course provides the fundamentals of classical mechanics and electromagnetism. Applications to these topics aim to develop in the student the ability to develop conecptual schemes and simple models to solve simple problems, using the tools learned in the parallel mathematics courses.

PREREQUISITES

There are no pre-requisites on prior physics knowledge. A good preparation of physics at high school level is certainly useful. It is necessary a good knowledge of elementary algebra and trigonometry as well as the elementary notions of mathematical analysis. 

TEACHING METHODS

Lectures and frontal exercises. Guided exercises are conducted. The AULAWEB portal and the TEAMS platform are used for distribution of additional teaching materials. 

SYLLABUS/CONTENT

1. Kinematics of the particle

Reference systems. Trajectory. Degrees of freedom. Parametric equations of motion.

Rectilinear motions.  Average and instantaneous velocity and acceleration. From acceleration to velocity and position.  Bodies in free fall.

Motions in the plane and in space. Kinematic vectors in Cartesian and polar coordinates. From acceleration to velocity and position. Plane motions: projectile motion, circular motions. Radial and tangential acceleration. Tangential acceleration and normal to the trajectory in any plane motion.

Relativity of kinematic quantities. Transformation of kinematic quantities between reference systems in relative rectilinear uniform motion, Galileo transformations. Relative rectilinear uniformly accelerated motion. Relative circular motion. Relative roto-translatory motion.

2- Particle dynamics

Principle of relativity.  Newton's first law and inertial reference systems. Second law of Newton. Action and reaction. Applications: weight force; normal plane reaction; static and dynamic friction forces; viscous friction; tension in strings. Elastic forces and simple harmonic oscillator.    Newton's law of universal gravitation and fundamental forces. Inertial mass and gravitational mass.  Dynamics in non-inertial reference systems. Impulse and momentum theorem. Conservation of q.d.m. Theorem of angular momentum. Conservation of angular momentum. Case of central forces. Second law of Kepler. Work. Theorem of work and kinetic energy. Power. Conservative forces and potential energy. Conservation of mechanical energy. Potential energy associated with central forces. Motion of satellites. General discussion of 1D conservative systems from knowledge of U(x) and total energy E: equilibrium conditions.

3-Dynamics of systems

Discrete and continuous systems. External and internal forces in the system. Center of mass (c.m.). Simple examples of calculating the position of the c.m. .   Quantity of motion of a system.  First cardinal equation and motion of the m.o.s.  Conservation of momentum. Angular momentum of a system. Moments of internal and external forces. Second cardinal equation. Conservation of angular momentum.  Isolated systems and third principle of dynamics.  Kinetic energy.  Reference system of c.m..  Koenig theorems for kinetic energy and angular momentum.  Collision processes between material points; elastic and inelastic collisions; collisions in the m.c. reference system. Variable mass systems.

Simple rigid systems. Parallel forces: center of gravity. Rotation around axes of symmetry: moment of inertia, axial moment and second law for rotational motion. Calculation of moment of inertia for simple bodies. Theorem of parallel axes. Rotation of non-symmetric rigid bodies around an axis passing through the c.m..  Precession. Role of constraint reactions. Kinetic energy and work in rotational motion. Rototranslational motions: pure rolling.  Simple impact processes for rigid bodies.  Rigid body statics: role of constrained reactions.

4- Electrostatics

Electrization phenomena. Electric charge. Elementary charge. Charge distributions.  Conservation of charge.  Electric force.  Electrostatic field.  Field lines.  Electric field generated by simple charge distributions. Gauss theorem and its applications to symmetrical charge distributions. Layer and double layer.  Conservation properties of the electrostatic field: potential; calculation of potential in the case of simple charge distributions.  Equipotential surfaces. Relationship between field lines and equipotential surfaces. Gradient of potential.  Electric field and gravitational field.  Mechanical actions of an electric field on an electric dipole. Motion of charges in an electrostatic field.

5- Electrostatic field in homogeneous and isotropic media.

Conductors

Charge, electrostatic field and potential in conductors. Electric field in the vicinity of a charged conductor. Relationship between surface charge density and radius of curvature in conductors. Electrostatic screen. Electrical capacity. Capacitors. Capacitance of spherical, flat and cylindrical capacitors. Capacitors in parallel and in series. Potential energy and energy density of a configuration of charges. Case of a system of conductors.  Example: plane capacitor. Force between the armatures of a plane capacitor.

Dielectrics

Capacitance of a capacitor filled with uniform dielectric medium: static dielectric constant. Introduction to the microscopic structure of dielectrics.  Polarization and electrical susceptibility. Vector D. Energy density associated with the electric field in dielectrics.

6-Stationary electric currents

Electromotive force. Charge carriers. Current intensity and density. Ohm's law.  Resistivity. Temperature coefficient. Orders of magnitude (conductors, semiconductors, insulators). Joule effect.  Superconductivity (briefly).

Microscopic aspects. Drift velocity: relationship with current density. Evaluation of the order of magnitude of the drift velocity in the case of a good conductor and comparison with thermal velocities. Relationship between drift velocity and electric field (Drude Lorentz model).  Conservation of charge and continuity equation in integral form.

Circuit applications. Nodes and meshes. Resistors equivalent to series and parallel resistors. Internal resistance of generators. Kirchhoff's laws. Quasi-stationary currents; charging and discharging of a capacitor.

7- Magnetostatics

Permanent magnets and electrical circuits as sources of magnetic phenomena. Operational definition of magnetic field. First Laplace's formula, calculation of magnetic field generated by current-carrying circuits: undefined straight wire (Biot-Savart's law) and circular loop.  Magnetic actions on current-carrying wires: Laplace's second law.  Lorentz force.  Magnetic actions between circuits traversed by currents: general formula. Case of two parallel wires and definition of the unit of measurement of electric current. Magnetic field properties in integral form: circuitation and flux through closed surfaces. Field inside an ideal solenoid. Field generated by moving charges. Magnetic field and relativity.  Motion of a charged particle in a uniform magnetic field. Applications: velocity selector, mass spectrometer, particle accelerators, magnetic confinement, Hall effect. Equivalence between a current loop and a magnetic needle.  Magnetic dipole moment. Mechanical actions on a dipole in a uniform magnetic field. Introduction to magnetic materials. Diamagnetism, paramagnetism and ferromagnetism.  M and H fields. Ferromagnetism and hysteresis loop.

8- Electromagnetic induction and Maxwell's equations

Faraday-Neumann-Lenz law. Induction by motion. Origin of electromotive force in various situations. Slowly varying magnetic fields and electric field circuitry. Examples of application of induction. Mutual induction effects in close circuits. Self-induction.  Energy and magnetic energy density.  Displacement current.  Maxwell's equations in integral form.

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RECOMMENDED READING/BIBLIOGRAPHY

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