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NPTEL Syllabus

Electrodynamics - Web course

COURSE OUTLINE

The course is a one semester advanced course onElectrodynamics at the M.Sc. Level.

It will start by revising the behaviour of electric and magneticfields, in vacuum as well as matter, and casting it in thelanguage of scalar and vector potentials.

Writing Maxwell equations in the same language will lead to theanalysis of electromagnetic waves, their propagation, scatteringand radiation.

Special relativity will be introduced, which will allow thecovariant formulation of Maxwell's equations and theLagrangian formulation of electrodynamics.

Relativistic motion of charges in electromagnetic fields, and themotion of electromagnetic fields through matter will be covered,

with plenty of examples.

COURSE DETAIL

Lectures Topics

Module I: Electromagnetic waves

Lecture 1:Maxwell'sequations: areview

Maxwell's equations in vacuum,Maxwell's equations inside matter

Lecture 2: Solvingstatic boundaryvalue problems

Uniqueness theorems, Separation ofvariables for Poisson's equation

Lecture 3: Time-dependentelectromagnetic

Relaxation to a stationary state,Propagating plane electromagnetic (EM)

wave, Decaying plane EM wave

NPTELhttp://nptel.iitm.ac.in

Physics

Pre-requisites:

1. Introductory course onElectricity andMagnetism at the level

of D. J. Griffiths,Introduction toElectrodynamics.

Additional Reading:

1. W. Greiner, ClassicalElectrodynamics,Springer (2009).

2. R. Resnick, Introductionto Special Relativity,Wiley (1992).

Coordinators:

Prof. Amol DigheTheoretical PhysicsTIFR

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fields

Lecture 4: Energyin electric andmagnetic fields

Energy in static electric field, Energy instatic magnetic field, Energy stored andtransported by EM waves

Lecture 5: EMwaves withboundaries

EM waves at dielectric boundaries:reflection, refraction, EM waves inconductors: inside and at the boundary

Lectures 6-7: EMwaves in confinedspaces

Rectangular waveguides, Circularcylindrical waveguides, Coaxial cable,Cavities

Lecture 8: EMwave equationswith sources

Wave equation for scalar and vectorpotentials with sources, Solving the waveequation with sources

Lecture 9: EMradiation

Electric and magnetic fields: radiationcomponents, Radiation energy loss,Radiation from antennas

Lectures 10-11:Multipole radiation

Multipole expansion, Electric dipoleradiation, Magnetic dipole and electricquadrupole radiation

Lecture 12:Problems

Module II: Relativity and electrodynamics

Lecture 1: Fromelectrodynamicsto SpecialRelativity

Faraday's law and Lorentz force,Motivations for Special Relativity, Lorentztransformations

Lecture 2: Lorentztransformations ofobservables

Length, time, velocity, acceleration, EMwave: aberration and Doppler effect,Transformations of electric and magneticfields

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Lecture 3:Relativistic energyand momentum

Defining momentum in Special Relativity,Defining relativistic energy

Lecture 4:

Covariant andcontravariant 4-vectors

Covariance and contravariance,

Examples of 4-vectors: x, del, p, J, A, u, A

Lecture 5: Metricand higher-rank4-tensors

Metric and invariant scalar products,Second rank 4-tensors: symmetric andantisymmetric, Higher-rank 4-tensors

Lecture 6: Tensorcalculus

Length, area, 3-volume and 4-volume in4-d, Gauss's law and Stokes' theorem in4-d

Lecture 7:Relativistickinematics

Two-body scattering, Decay of a particle

Lecture 8: EM fieldtensor 'andMaxwell'sequations

The electromagnetic field tensor F,Maxwell's equations in terms of F and F-tilde

Lectures 9-10:Lagrangianformulation ofrelativistic

mechanics

Lagrangian, Hamiltonian, energy,equations of motion, Non-relativisticparticle in a potential, Relativistic freeparticle, Relativistic particle in EM fields

Lecture 11:Lagrangianformulation ofrelativisticelectrodynamics

Volume distribution of changes in EMfields, Field-field interaction andMaxwell's equations

Lecture 12:Problems

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Module III: Relativistic electrodynamics: applications

Lectures 1-2:Motion of chargesin E and B fields

Relativistic equations of motion, Particlein a unifrm electric field, Particle in auniform magnetic field, Particle incombinations of electric and magneticfields

Lecture 3: EMpotentials from amoving charge

Lienard-Wiechert potentials: withoutrelativity and using relativity

Lectures 4-5: EMfields from auniformly movingcharge

E and B fields from Lienard-Wiechertpotentials, E and B fields from Lorentztransformations, Force between twouniformly moving charges

Lectures 6-7:Cherenkovradiation

Cherenkov: intuitive understanding andapplications, Cherenkov radiation: formalcalculations

Lecture 8:

Radiation from anacceleratingcharge

From Lienard-Wiechert potentials to EM

fields, Calculating relevant derivatives,Calculating E and B fields including theirradiative components

Lecture 9:Radiation fromlinear motion:Bremsstrahlung

Radiated power from an acceleratingcharge, Bremsstrahlung radiation: largevelocities

Lectures 10-11:Radiation fromcircular orbits:Synchrotron

Radiation from a circular orbit, Timevariation of the radiation signal,Instantaneous pattern of radiated power,Synchrotron radiation for producing X-rays

Lectures 12-13:radiation reactionforce

Force of an accelerating charge on itself:small acceleration, Radiation damping inultra-relativistic case

Lectures 14-15:EM radiation

Interactions of EM fields with electrons,Scattering of EM wave by a free electron,

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passing throughmatter

Scattering of EM wave by a boundelectron, Absorption by a bound electron,Refractive index: collective polarizationby electrons

Lecture 16:Problems

Total lectures: 12 (module I) + 12 (module II) + 16 (moduleIII) = 40

References:

1. Panofsky and Phillips, Classical Electricity and

Magnetism, 2nd Ed., Dover (2005) .

2. Landau and Lifshitz, The Classical Theory of Fields, 4thEd., Pergamon (1989).

3. J. D. Jackson, Classical Electrodynamics, 3rd Ed., Wiley(2007).

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