1. Choice-based Credit-based B Sc (Physics) courses
– Electromagnetism –
Bhas Bapat
Physical Research Laboratory, Ahmedabad
31 October 2011
Choice-based Credit Courses – Electromagnetism

2. 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

3. 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 (accelerated
charged particles radiate) – electrostatics, magnetostatics, electricity and magnetism
are sub-domains.
Electrodynamics is the all-encompassing term – study of uniform and accelerated
motion of charged particles – includes the phenomena of electricity, magnetism and
radiation.
At the B Sc level we restrict ourselves to Electromagnetism.
Choice-based Credit Courses – Electromagnetism Bhas Bapat, PRL

4. 31 October 2011 3
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 and
Electrodynamics).
One of the pillars of the special theory of relativity (Maxwell’s equations are
invariant under Lorentz transformation).
Clearly, a fundamental component of physics, must be studied by all Physics
students.
Choice-based Credit Courses – Electromagnetism Bhas Bapat, PRL

5. 31 October 2011 4
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 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

6. 31 October 2011 5
2b. Books
1. 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

7. 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

8. 31 October 2011 7
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 the
student).
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 to
simplify problems.
The concept of a field takes time to digest.
Choice-based Credit Courses – Electromagnetism Bhas Bapat, PRL

9. 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 the
electric 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, potential
energy, conservative and non-conservative field.
Divergence of a vector field, Line integral, Surface integral, Gauss divergence
theorem, 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

10. 31 October 2011 9
4a. Electrostatics (in continuous media)
Capacitance and dielectric constant, conductors and insulators, microscopic view of
dielectrics, 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.
Choice-based Credit Courses – Electromagnetism Bhas Bapat, PRL

11. 31 October 2011 10
4b. Magnetostatics
Origin of B (naturally occurring magnetism).
Magnetic effects of steady current: Lorentz force, magnetic force on a current
carrying conductor.
Amperes circuital law, application of the law, the Biot-Savart Law and its
applications.
Magnetic properties of a small current loop, current loop in an external magnetic
field.
Magnetization, Magnetic pole density, magnetic intensity, the relation between
H, B, M.
Magnetic properties of materials, types of magnets, hysteresis in ferromagnetic
materials, permeability, remnance.
Choice-based Credit Courses – Electromagnetism Bhas Bapat, PRL

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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 of
reference.
Relativistic Transformation
Time varying fields – Faraday’s Law, Charge conservation and Displacement Current.
Choice-based Credit Courses – Electromagnetism Bhas Bapat, PRL

13. 31 October 2011 12
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
Choice-based Credit Courses – Electromagnetism Bhas Bapat, PRL

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4e. Current Electricity and Circuits
Simple circuits, concepts of currents, potential drop, resistance, capacitance and
inductance.
Circuit theorems.
DC and AC circuits, inductive, capacitive and resistive loads. Losses in circuits.
Mechanical effects of current: heat and motion, electromotive applications (motors
and genertors).
Generation and transmission of electric power.
This course will have pre-requisites
Choice-based Credit Courses – Electromagnetism Bhas Bapat, PRL

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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 radio
waves, propagation of radio waves in the atmosphere etc.
Radio Communication: “windows” in the atmosphere, design of antennas, and
radars, communication using EM waves
Electron Microscopy, Hall Probes, NMR
This course will have pre-requisites
Choice-based Credit Courses – Electromagnetism Bhas Bapat, PRL

16. 31 October 2011 15
5. Electrostatics : A viewpoint
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 always
radial – 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 a
line charge etc.
Underline the symmetry of the problem and hence the efficacy of a particular
coordinate system – link between a symmetry and redundancy of one or more
coordinates in the description of the field.
Calculation of the electric field for simple charge distributions.
Choice-based Credit Courses – Electromagnetism Bhas Bapat, PRL

17. 31 October 2011 16
5. Electrostatics : A viewpoint
Vector integration – introduce differential length, area, volume elements in various
coordinate systems.
Stress the difference between field point and source point, e.g.
r ˆ
ρ(r ) (ˆ − r ) d 3r
E=
V |r − r |2
Simplification of the field calculation – introduce the electric potential (first for a
point charge then for a collection of charges) – either from the point of view of
work done in moving a test charge, or merely as a mathematical device.
Equipotential surface, field lines, concept of a gradient (to be shown
geometrically/pictorially)
Choice-based Credit Courses – Electromagnetism Bhas Bapat, PRL

18. 31 October 2011 17
5. Electrostatics : A viewpoint
(Mathematical) properties of vectors fields, significance of 1/r 2 nature of the
electrostatic force.
Gauss’ Law, Laplace Equation, Poisson Equation.
Application of Gauss’ Law to calculation of electric field and to obtain boundary
conditions.
Choice-based Credit Courses – Electromagnetism Bhas Bapat, PRL

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Summary
Break-up the electromagnetic theory topics into a few mandatory and few elective
modules.
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