B sc ama-emtheory

Choice-based Credit-based B Sc (Physics) courses

– Electromagnetism –

Bhas BapatPhysical Research Laboratory, Ahmedabad

31 October 2011

Choice-based Credit Courses – Electromagnetism

31 October 2011 1

Outline

1. Introduction

2. Credit Modules

3. Remarks on Methodology

4. Suggestions for Module Contents

5. Electrostatics : A viewpoint

Choice-based Credit Courses – Electromagnetism Bhas Bapat, PRL

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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.


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1b. Role of Electromagnetism in the development of Physics

Ability 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.


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2a. Suggested Credit Modules

1. 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 inductivecircuits, 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.


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2b. Books

1. Introduction To Electrodynamics, 3/ED J GriffithsPublisher: Ubs-Bangalore, Price Approx Rs 250.

2. Foundations of Electromagnetic Theory , 3/EJ. R. Reitz, F. J. Milford, R. W. ChristyPublisher: Narosa, Price Approx Rs 250.4/E, Publisher: Pearson Educational, Price Approx Rs 400.


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3a. Remarks on Methodology

• Need to lay greater stress on problem solving than merely proving laws/theoremsand 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 apre-requisite, it becomes too abstract and uninteresting for most students.

• Also keep in mind that analogies helpful only up to a point; misleading whentaken too far.

• Historical perspective is often helpful. Should be given to improve clarity, not topresent the chronology of the development of the subject.


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3b. Difficulties faced in studying EM

Vector 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.


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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.


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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 vectors~E , ~D, ~P .

Boundary conditions at a dielectric surface, polarizability and susceptibility.


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4b. Magnetostatics

Origin 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 between~H, ~B, ~M.

Magnetic properties of materials, types of magnets, hysteresis in ferromagneticmaterials, permeability, remnance.


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4c. Electromagnetic Fields of moving charges

Lorentz 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 Transformation

Time varying fields – Faraday’s Law, Charge conservation and Displacement Current.


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4d. Maxwell’s Equations and Electromagnetic Waves

Maxwell’s Equations.

Propagation of time varying electromagnetic fields, wave equation.

Boundary conditions and their implications to wave propagations – refraction,diffraction

This course will have pre-requisites


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4e. Current Electricity and Circuits

Simple 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.



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4f. Application of electromagnetism in Physics Research

Creation and manipulation of charged particles (ion and electron sources)

Creation of electric and magnetic fields

Acceleration of charged particles (DC and RF accelerator designs)

Generation and confinement of plasmas

Atmospheric 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 waves

Electron Microscopy, Hall Probes, NMR



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Coulomb’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.


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Vector integration – introduce differential length, area, volume elements in variouscoordinate systems.

Stress the difference between field point and source point, e.g.

~E =

∫V

ρ(~r ′) (r̂ − r̂ ′) d3~r ′

|~r − ~r ′|2

Simplification 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)


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(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.


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Summary

Break-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.


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