Electricity and Magnetism, Spring 2010


This course is being offered to students of the 2nd semester at IISER Pune. It is being taught by Dr Prasad Subramanian. We will also have some guest lectures by distinguished scientists.

Here is the timetable for semester 2 and here is the academic calendar for Spring 2010.

We will have guest lectures by Prof J. V. Narlikar (IUCAA) on March 11 and 12 2010, and by Prof K. Subramanian (IUCAA) on April 12 and 15 2010.

Prof Narlikar will talk on Electromagnetism and Gravitation: Comparison and Contrast. He will cover the following topics:

1. Coulomb's law and Newton's law: Why gravitation is non-linear
2. Why electromagnetism can be shielded but not gravitation
3. The experiment of Tweedledum and Tweedledee: tidal transfer of energy
4. The paradox of hot and cold stars: effect of negative energy in gravitation
5. The run-away effect of strong gravitation: gravitational collapse to a black hole
6. Radiation in elctromagnetism and gravitation

Prof K Subramanian will talk on Batteries and Dynamos in the universe. He will discuss:

1. Ohm's law in a conducting plasma and the Biermann battery
2. Homopolar dynamo
3. Zeldovich Rope dynamo
4. Turbulent dynamos

Here is the pdf file containing Prof K Subramanian's presentations.

Quiz on Feb 19 2010 .
Solutions to Quiz.

Mid-term exam on March 2 2010 .
Solutions to midterm exam.

Final exam on April 27 2010 .
Solutions to final exam.

Pre-requisites for the course:

You will need a high school level introduction to electricity and magnetism and some familiarity with basic vector calculus concepts such as gradient, divergence and curl. This course will be a prerequisite for Phy 312 (Electrodynamics)

Objectives of the course:

This course can be viewed as an introduction to electricity and magnetism as a unified whole, at a post-12th grade level. It will be useful to all science majors, especially so for those who plan to specialize in Physics. At the end of the course, students would be familiar with Maxwell's equations as a unified whole, and with the phenomenon of electromagnetic waves.

Course contents:

Section 1: Electrostatics and magnetostatics

Introduction to course

(Mostly chapter 1) Electrical forces (and comparison with gravitational forces). How "electrical" forces also depend upon the velocity of the charge, and how electricity and magnetism are intertwined. Superposition of fields, arising from linearity of underlying equations. Why/how the laws of electricity and magnetism are best expressed in terms of vector fields, and how this is related to the concept of action at a distance. Concepts of flux and circulation, and the laws of electromagnetism in terms of these quantities (flux and circulation).

(Chapter 2) Scalar and vector fields. Concept of gradient, the 'nabla' operator. Concept of divergence and curl.

(Chapter 3) Line integral, Flux of a vector field, the divergence theorem

(Chapter 3) Circulation of a vector field, Stokes' theorem. Potential fields, curl-free and divergence-free fields.

Review of vector calculus

Electrostatics (Chapter 4, parts of chapter 5): Gauss's law, relation between Coulomb's inverse square law and Gauss's law. Equipotential surfaces. Poisson's and Laplace's equations. Why/how the solution to Laplace's equation is a feature-less scalar field, impossibility of (purely) electrostatic confinement. Using Gauss's law to solve simple problems that exhibit symmetry, more about equipotential surfaces, electrostatic shielding. Method of images.

Chapter 8: Electrostatic energy; electrostatic energy of a charge distribution, energy stored in a capacitor, energy in the electrostatic "field", problem with infinities.

Magnetostatics: (elements of Chapters 13 and 15) The charge continuity equation, basic assumptions inherent in magnetostatics. Ampere's law, forces between currents. "Relativity" of electric and magnetic fields. The vector potential; derivation, and its role in specifying magnetic fields. Why the vector potential is useful at all: a very basic understanding. The Biot-Savart law.

Section 2: Electromagnetic induction and circuits

(Elements of chapters 16 and 17) Distinction between statics and dynamics: table in chapter 15. Qualtitative understanding of induced currents in various circumstances in chapter 16, and the concept of inductance. In particular, the importance of understanding the so-called "flux rule" both via Faraday's law and via Lorentz forces. Some paradoxes, such as the homopolar motor/generator. Forces on induced currents and some demonstrations of this effect, such as the "jumping ring". Eddy currents, and forces due to such currents. A basic understanding of an elementary AC generator.

Mid-term exam

Section 3: Maxwell's equations and electromagnetic waves

How the displacement current term is "derived"/how it makes Ampere's law consistent with the charge continuity equation. Maxwell's equations in free space, wave solutions. Some basic properties of the wave solution. Basic features of electromagnetic waves. (EM) wave interference, diffraction.

Evaluation

End-sem examination: 40%, mid-sem examination: 35%, one quiz: 15%, project presentations during tutorials: 10%

Primary text

Feynman's Lectures on Physics, vol II (Pearson Education)

Supplementary material (including problem set):

Here is a collection of problems (based on Feynman's lectures) that will be used in the course

For those unfamiliar with vector calculus,
here is a fairly friendly primer; here is another. There are several excellent books on it, of course.

Project presentations (10% of the overall grade)

We will have project presentations during the tutorial hour (11:25 - 12:25) every Friday, starting on Friday, Feb 26 2010. The presentation will be made by a group comprising of five students each, and will last for 20 minutes. There will be one grade assigned to all members of a group. Group 1 will comprise of students will roll numbers 20091001, 1002, 1003, 1004 and 1005. Group 2 will comprise of roll numbers 1006 - 1010 and so on. There will be 3 parallel sessions taking place in Raman Hall and the two physics labs, with a teaching assistant present in each session. There will be two 20 min presentations in each session. On each day, the first two groups will present their work in Raman Hall, the next two groups in Physics Lab 1 and the next two groups in Physics lab 2. For instance, on Friday, Feb 26, groups 1 and 2 will present their work in Raman Hall, groups 3 and 4 in Physics lab 1 and groups 5 and 6 in Physics lab 2.

The projects will be based on simple toys, such as those in the "Motors and Generators" and "Electricity and Magnetism" sections of Arvind Gupta's
website. We will be looking for a brief demonstration, and a quantitative analysis of measurements, along with a comparison with theoretical intrepretation. Here is some material that can be of (significant) help. The grades will be based on the novelty of the experiment, analysis of data, comparison with theory and overall presentation. You should need no more than a white/blackboard for your presentation. Please also note that the toys/experiments should be made of commonly available material, and should cost very little (in keeping with the philosophy of Arvind Gupta's toys). The measurements too, should use only commonly available instruments, like a multimeter, stopwatch or such.