# Physics complements (Classical Mechanics and Electrodynamics) for Biology students

## Schedule

Friday, 4 October 2019 to Friday, 29 May 2020
Total hours: 60
Hours of lectures: 40
Hours of supplementary teaching: 20

• Written test
• oral exam

## Prerequisites

basic calculus, integrals and derivatives. Basic mechanics (Newton's laws)

## Syllabus

First part: Complements of Mechanics

Cartesian and polar space coordinate systems

vector algebra, scalar and vector product, properties of vectors under orthogonal coordinate transformations.

review of the dynamics of material points and of multibody systems, with particular focus on

- conservation laws

- central forces

- single and coupled oscillators (using complex exponential techniques)

- rigid body dynamics

Second part: Elettrodynamics

- Coulomb's Law, electrostatic force and electric field; 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).

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.

Educational Goals:

Integration of general education in basic classical physics for biology students, as propedeutical to third year courses in statistical and quantum mechanics, and in general aimed at providing useful physical and mathematical tools (i.e. the solution of differential equations applied to physics problems)

## Bibliographical references

Morin (Classical Mechanics)

Morin-Purcell, Griffiths (Electrodynamics)

Halliday-Resnick (Mechanics + Electrodynamics)