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Choice-based Credit-based B Sc (Physics) courses – Electromagnetism – Bhas Bapat Physical Research Laboratory, Ahmedabad 31 October 2011 Choice-based Credit Courses – Electromagnetism
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31 October 2011 1 Outline1. Introduction2. Credit Modules3. Remarks on Methodology4. Suggestions for Module Contents5. Electrostatics : A viewpointChoice-based Credit Courses – Electromagnetism Bhas Bapat, PRL
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31 October 2011 2 1a. Electromagnetism : What is it?Description of the eﬀects of charged particles on each other.Various “ﬂavours”: electrostatics, magnetostatics, electricity and magnetism,electromagnetism, electrodynamics. Do not mean the same thing.Electromagnetism covers electricity and magnetism, but not radiation (acceleratedcharged particles radiate) – electrostatics, magnetostatics, electricity and magnetismare sub-domains.Electrodynamics is the all-encompassing term – study of uniform and acceleratedmotion of charged particles – includes the phenomena of electricity, magnetism andradiation.At the B Sc level we restrict ourselves to Electromagnetism.Choice-based Credit Courses – Electromagnetism Bhas Bapat, PRL
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31 October 2011 3 1b. Role of Electromagnetism in the development of PhysicsAbility to describe the eﬀect of electric and magnetic ﬁelds on matter.Understanding the structure of atoms and molecules (Quantum Mechanics andElectrodynamics).One of the pillars of the special theory of relativity (Maxwell’s equations areinvariant under Lorentz transformation).Clearly, a fundamental component of physics, must be studied by all Physicsstudents.Choice-based Credit Courses – Electromagnetism Bhas Bapat, PRL
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31 October 2011 4 2a. Suggested Credit Modules1. Electrostatics (in vacuum and in continuous media) [Compulsory]2. Magnetostatics (in vacuum and in continuous media) [Compulsory]3. Time varying ﬁelds, ﬁelds of moving charges [Compulsory]4. Maxwell’s Equations, Electromagnetic waves [Elective]5. Current Electricity, circuits, theorems, AC and DC, capacitive and inductive circuits, devices [Elective]6. Applications of electromagnetism in Physics Research [Elective]Some of the above could be divided or re-organised, if needed, for proper teaching.Choice-based Credit Courses – Electromagnetism Bhas Bapat, PRL
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31 October 2011 5 2b. Books1. Introduction To Electrodynamics, 3/E D J Griﬃths Publisher: Ubs-Bangalore, Price Approx Rs 250.2. Foundations of Electromagnetic Theory , 3/E J. R. Reitz, F. J. Milford, R. W. Christy Publisher: Narosa, Price Approx Rs 250. 4/E, Publisher: Pearson Educational, Price Approx Rs 400.Choice-based Credit Courses – Electromagnetism Bhas Bapat, PRL
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31 October 2011 6 3a. Remarks on Methodology• Need to lay greater stress on problem solving than merely proving laws/theorems and covering standard situations.• Use of graphical teaching aids (accurate, well-drawn, and imaginative diagrams) will enormously beneﬁt students in the early sessions.• Necessary mathematics should be introduced as need arises; if introduced as a pre-requisite, it becomes too abstract and uninteresting for most students.• Also keep in mind that analogies helpful only up to a point; misleading when taken too far.• Historical perspective is often helpful. Should be given to improve clarity, not to present the chronology of the development of the subject.Choice-based Credit Courses – Electromagnetism Bhas Bapat, PRL
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31 October 2011 7 3b. Diﬃculties faced in studying EMVector nature of the EM ﬁelds make the equations and mathematics diﬃcult(requires substantial leap of imagination and mathematical skill on part of thestudent).Most student are ill-equipped to appreciate the nuances of vectors and symmetries.Need to stress symmetries in a problem/situation and exploiting the symmetries tosimplify problems.The concept of a ﬁeld takes time to digest.Choice-based Credit Courses – Electromagnetism Bhas Bapat, PRL
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31 October 2011 8 4a. Electrostatics (vacuum, free charges)Coulomb’s Law, Force between several particles – vector addition.Concept of a source charge and a test charge, electric ﬁeld, vector nature of theelectric ﬁeld (discuss scalar and vector ﬁelds with examples), spherical symmetry,breaking of a spherical symmetry.Calculation of electric ﬁeld due to simple charge distributions (integral method,exploiting symmetries)Work done by a moving charge, path independence, concept of a gradient, potentialenergy, conservative and non-conservative ﬁeld.Divergence of a vector ﬁeld, Line integral, Surface integral, Gauss divergencetheorem, rotational vector ﬁelds, curl of a vector, Stokes theorem.Charge distributions and application of Gauss’ Law to calculate ﬁelds.Force and Torque between dipole/monopole and dipole/dipole.Choice-based Credit Courses – Electromagnetism Bhas Bapat, PRL
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31 October 2011 9 4a. Electrostatics (in continuous media)Capacitance and dielectric constant, conductors and insulators, microscopic view ofdielectrics, dipole moment, polarization.Gausss law in dielectric media, electric displacement, the three electric vectorsE , D, P .Boundary conditions at a dielectric surface, polarizability and susceptibility.Choice-based Credit Courses – Electromagnetism Bhas Bapat, PRL
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31 October 2011 10 4b. MagnetostaticsOrigin of B (naturally occurring magnetism).Magnetic eﬀects of steady current: Lorentz force, magnetic force on a currentcarrying conductor.Amperes circuital law, application of the law, the Biot-Savart Law and itsapplications.Magnetic properties of a small current loop, current loop in an external magneticﬁeld.Magnetization, Magnetic pole density, magnetic intensity, the relation betweenH, B, M.Magnetic properties of materials, types of magnets, hysteresis in ferromagneticmaterials, permeability, remnance.Choice-based Credit Courses – Electromagnetism Bhas Bapat, PRL
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31 October 2011 11 4c. Electromagnetic Fields of moving chargesLorentz force on a charge moving in combined E and B ﬁelds.Force in a co-moving reference frame.Interchangeability of forces due to E and B separately in diﬀerent frames ofreference.Relativistic TransformationTime varying ﬁelds – Faraday’s Law, Charge conservation and Displacement Current.Choice-based Credit Courses – Electromagnetism Bhas Bapat, PRL
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31 October 2011 12 4d. Maxwell’s Equations and Electromagnetic WavesMaxwell’s Equations.Propagation of time varying electromagnetic ﬁelds, wave equation.Boundary conditions and their implications to wave propagations – refraction,diﬀractionThis course will have pre-requisitesChoice-based Credit Courses – Electromagnetism Bhas Bapat, PRL
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31 October 2011 13 4e. Current Electricity and CircuitsSimple circuits, concepts of currents, potential drop, resistance, capacitance andinductance.Circuit theorems.DC and AC circuits, inductive, capacitive and resistive loads. Losses in circuits.Mechanical eﬀects of current: heat and motion, electromotive applications (motorsand genertors).Generation and transmission of electric power.This course will have pre-requisitesChoice-based Credit Courses – Electromagnetism Bhas Bapat, PRL
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31 October 2011 14 4f. Application of electromagnetism in Physics ResearchCreation and manipulation of charged particles (ion and electron sources)Creation of electric and magnetic ﬁeldsAcceleration of charged particles (DC and RF accelerator designs)Generation and conﬁnement of plasmasAtmospheric Physics: Ionospheric processes, probing of the atmosphere by radiowaves, propagation of radio waves in the atmosphere etc.Radio Communication: “windows” in the atmosphere, design of antennas, andradars, communication using EM wavesElectron Microscopy, Hall Probes, NMRThis course will have pre-requisitesChoice-based Credit Courses – Electromagnetism Bhas Bapat, PRL
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31 October 2011 15 5. Electrostatics : A viewpointCoulomb’s Law – 1/r 2 behaviour, stress on the direction of the force.Concept of a source charge and a test charge – convey that the force is alwaysradial – idea of a ﬁeld – vector nature of the ﬁeld. Lines of force.Various coordinate systems – usefulness of diﬀerent systems in diﬀerent situations.Go over from the ﬁeld due to a point charge to that due to two charges, due to aline charge etc.Underline the symmetry of the problem and hence the eﬃcacy of a particularcoordinate system – link between a symmetry and redundancy of one or morecoordinates in the description of the ﬁeld.Calculation of the electric ﬁeld for simple charge distributions.Choice-based Credit Courses – Electromagnetism Bhas Bapat, PRL
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31 October 2011 16 5. Electrostatics : A viewpointVector integration – introduce diﬀerential length, area, volume elements in variouscoordinate systems.Stress the diﬀerence between ﬁeld point and source point, e.g. r ˆ ρ(r ) (ˆ − r ) d 3r E= V |r − r |2Simpliﬁcation of the ﬁeld calculation – introduce the electric potential (ﬁrst for apoint charge then for a collection of charges) – either from the point of view ofwork done in moving a test charge, or merely as a mathematical device.Equipotential surface, ﬁeld lines, concept of a gradient (to be showngeometrically/pictorially)Choice-based Credit Courses – Electromagnetism Bhas Bapat, PRL
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31 October 2011 17 5. Electrostatics : A viewpoint(Mathematical) properties of vectors ﬁelds, signiﬁcance of 1/r 2 nature of theelectrostatic force.Gauss’ Law, Laplace Equation, Poisson Equation.Application of Gauss’ Law to calculation of electric ﬁeld and to obtain boundaryconditions.Choice-based Credit Courses – Electromagnetism Bhas Bapat, PRL
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31 October 2011 18 SummaryBreak-up the electromagnetic theory topics into a few mandatory and few electivemodules.Elective modules will have pre-requisites, including some from other topics (Q.Mech,Solid State, Mechanics).Build up mathematics concurrently with the mandatory modules as per need.Stress on the vector nature, symmetries etc.Employ graphical/visual aids to teach vector analysis and properties of EM ﬁelds.Include problem solving in all mandatory modules.Choice-based Credit Courses – Electromagnetism Bhas Bapat, PRL
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