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

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##### Course info
Number of course hours
60
Number of hours of lecturers of reference
60
Number of hours of supplementary teaching
0
CFU 9
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## Type of exam

Written and oral exam

## Lecturer

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## Lecturer

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## Prerequisites

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

## Programme

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 multibody systems
• Lagrangian formalism
• conservation laws
• single and coupled oscillators (using complex exponential techniques)

Second module

• central forces
• rigid body dynamic
• 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).

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.

## Educational aims

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)