Examination procedure
<p>written + oral</p>
Prerequisites
second year Biology students
Syllabus
First module
- Cartesian and polar space coordinate systems vector algebra, scalar and vector product, properties of vectors under orthogonal coordinate transformations.
- dynamics of material points and of multibodysystems
- Lagrangian formalism
- conservation laws single and coupled oscillators (using complex exponential techniques)
Second module
- central forces
- rigid body dynamics
- Coulomb's Law, electrostatic force and electricfield; Gauss Law (integral and differential formulation); circulation of the electric field and definition of electric potential. Dipole field. The unicity theorem. Electrostatic energy.
- Conductors, equipotential surfaces. Method of images for the infinite conducting plane and for the conducting sphere. Capacitors. Electrostatic energy of a capacitor and energy density of the electric field. Dielectrics (hints).
Third module
- Electric current, continuity law. Simplified Drude model explaining local formulation of Ohm's law.
- Charge/discharge of a capacitor, Kirchhoff's laws for electric circuits.
- Magnetostatics: Lorentz force on a point charge and on a circuit segment. Biot-Savart law. Static Maxwell laws for the magnetic field. Magnetic field as a pseudo-vector; difference wrt the electric field for highly symmetric configurations.
- Faraday's law, inductance. LC and RLC circuits. Energy density of the magnetic field.
- Ampère-Maxwell's law, displacement current,wave equation for fields. Poynting vector. Plane waves.
Bibliographical references
Morin (Classical Mechanics)
Morin-Purcell, Griffiths (Electrodynamics)
Halliday-Resnick (Mechanics + Electrodynamics)