 # Electromagnetisms in materials and waveguides - classical mechanics

## Presentation

Programme (detailed contents):

Electromagnetisms in materials : Electromagnetism fundamental equations in dielectric, metallic and magnetic materials. EM wave propagation in linear, homogeneous and isotropic materials. Continuity equations. Application to reflection and the refraction. Propagation in rectangular metallic and optical waveguides.

Mechanics : Fundamental knowledge for the study of movements of mechanical systems and forces and momentums appearing. Short recall of mathematical basics: vectors, linear operators, points, fields vectors and twist/wrench theory.

Organisation:

Electromagnetisms in materials : The student will be given supports for lectures, tutorials and lab work. The lectures focus on the new concepts, their illustration and the demonstrations of some mathematical expressions related to the physical phenomena. The tutorials, as well as the lab-work, directly relate to the lectures through practical examples.

Mechanics : The course is divided in three parts. Kinematics: velocities, accelerations and their composition formulas; Kinetics: kinetic and dynamic twist and wrench; particular case of a solid: inertia operator and inertia elements. Dynamics: notion of Galilean space, theorems of Newton and Euler, power, energy, kinetic energy.

Main difficulties for students:

Difficulties with intrinsic reasoning and tendency to begin with extrinsic quantities with respect to a particular frame (generally the fixed one). Difficulties with analytical calculations.

## Objectives

At the end of this module, the student will have understood and be able to explain (main concepts):

Electromagnetisms in materials : the concepts related to the propagation of electromagnetic waves in simple materials (linear, homogeneous and isotropic, dielectric, magnetic or conductive), the reflection and the refraction at one interface, the principle of metallic and dielectric (optical fibres) waveguides and the related electromagnetic energy transport.

Classical Mechanics : the notions of twist and wrench which are at the heart of the course, the theorems of Newton and Euler which describe the movements of mechanical systems and the forces and momentums appearing.

The student will be able to:

Electromagnetisms in materials : use Maxwell's equations to determine the nature of the electromagnetic waves in a simple system (L.H.I. material, interface between two materials, confined space between two planes of conductive material). They will be able to determine the conditions and the characteristics of electromagnetic wave propagation in metallic and optical-fibre waveguides

Classical Mechanics : solve an elementary problem of classical mechanics. He should be able to handle the notions of power and energy.

## Needed prerequisite

Electromagnetism in vacuum (I2MAPH21)

## Form of assessment

The evaluation of outcome prior learning is made as a continuous training during the semester. According ot the teaching, the assessment will be different: as a written exam, an oral exam, a record, a written report, peers review...

## Bibliography

Supports de cours : Propagation des ondes, A. Balocchi, I. Gerber, S. Lachaize, 2007

Livres : M. Hulin, Equation de Maxwell, Ondes électromagnétiques, Dunod, 1993, ISBN : 2-10-001657-1 ; J.-P. Pérez, Electromagnétisme, Masson, 1996, ISBN : 2-225-85236-7

Mécanique classique tomes 1 et 2, J.J. Moreau, Masson, 1968

Cours de mécanique, P. Brousse, A. Colin, 1973 (le plus proche de ce cours)