Radiation
Lecture40: Electromagnetic Theory
Professor D. K. Ghosh, Physics Department, I.I.T., Bombay
Radiation Zone Approximation
We had seen that the expression for the vector potential for a localized current distribution is given by
,
( ) =
0
3

Dielectrics - II
Lecture 21: Electromagnetic Theory
Professor D. K. Ghosh, Physics Department, I.I.T., Bombay
In the previous lecture we obtained a multipole expansion of the potential due to a continuous charge
distribution. We discussed in some detail,

Lecture 17: Electromagnetic Theory
Professor D. K. Ghosh, Physics Department, I.I.T., Bombay
SPECIAL TECHNIQUES-I
Method of Images
The uniqueness theorem for Poissions or Laplaces equations, which we studied
in the last couple of lectures, has some intere

Dielectrics
Lecture 20: Electromagnetic Theory
Professor D. K. Ghosh, Physics Department, I.I.T., Bombay
What are dielectrics?
So far we have been discussing electrostatics in either vacuum or in a conductor. Conductors, as we
know are substances which ha

Solutions to Laplaces Equations- II
Lecture 15: Electromagnetic Theory
Professor D. K. Ghosh, Physics Department, I.I.T., Bombay
Laplaces Equation in Spherical Coordinates :
In spherical coordinates the equation can be written as
Note that we are using th

Solutions to Laplaces Equations
Lecture 14: Electromagnetic Theory
Professor D. K. Ghosh, Physics Department, I.I.T., Bombay
We have seen that in the region of space where there are no sources of charge, Laplaces equation gives
the potential. In this lect

Gausss Law & Potential
Lecture 7: Electromagnetic Theory
Professor D. K. Ghosh, Physics Department, I.I.T., Bombay
Flux of an Electric Field :
In this lecture we introduce Gausss law which happens to be equivalent to Coulombs law. However,
under certain c

Coefficient of Potential and Capacitance
Lecture 12: Electromagnetic Theory
Professor D. K. Ghosh, Physics Department, I.I.T., Bombay
We know that inside a conductor there is no electric field and that the surface of a metal is an
equipotential surface. F

Lecture 8: Electromagnetic Theory
Professor D. K. Ghosh, Physics Department, I.I.T., Bombay
Electrostatics : Electric Field & Potential
We continue with our discussion of electric field and potential by giving more
examples.
Example 1: Two intersecting an

Lecture 13: Electromagnetic Theory
Professor D. K. Ghosh, Physics Department, I.I.T., Bombay
Poissons and Laplaces Equations
We will spend some time in looking at the mathematical foundations of
electrostatics. For a charge distribution defined by a charg

Potential & Potential Energy : Potential of a Charge Distribution
Lecture 9 : Electromagnetic Theory
Professor D. K. Ghosh, Physics Department, I.I.T., Bombay
In the last lecture we introduced the concept of electric potential. The electric field being a

Potential & Potential Energy
Lecture 10: Electromagnetic Theory
Professor D. K. Ghosh, Physics Department, I.I.T., Bombay
Electrostatic Boundary Conditions :
We had seen that electric field has a discontinuity at a charged boundary between two media. Let

Elements of Vector Calculus :Laplacian
Lecture 5: Electromagnetic Theory
Professor D. K. Ghosh, Physics Department, I.I.T., Bombay
Till now we have talked about operators such as gradient, divergence and curl which act on scalar or
vector fields. These op

Electrostatics : Electric Field & Potential
Lecture 6: Electromagnetic Theory
Professor D. K. Ghosh, Physics Department, I.I.T., Bombay
In the present module of Electrostatics, we will deal with properties of charges that are not in motion. In
this lectur

Elements of Vector Calculus : Divergence and Curl of a Vector Field
Lecture 3: Electromagnetic Theory
Professor D. K. Ghosh, Physics Department, I.I.T., Bombay
In the last lecture we had defined divergence of a vector field and had obtained an expression

Elements of Vector Calculus : Scalar Field & its Gradient
Lecture 1 : Electromagnetic Theory
Professor D. K. Ghosh, Physics Department, I.I.T., Bombay
Introduction : In this set of approximately 40 lectures covering a course of one semester, I would take

Elements of Vector Calculus : Conservative Field, Stokes Theorem
Lecture 4: Electromagnetic Theory
Professor D. K. Ghosh, Physics Department, I.I.T., Bombay
In the last lecture we defined the curl of a vector field as a ratio of the line integral over the

Elements of Vector Calculus : Line and Surface Integrals
Lecture 2: Electromagnetic Theory
Professor D. K. Ghosh, Physics Department, I.I.T., Bombay
In this lecture we will talk about special functions of vector fields and about operators which act
on vec

Lecture 15: Electromagnetic Theory
Professor D. K. Ghosh, Physics Department, I.I.T., Bombay
Solutions to Laplaces Equations- III
Laplaces Equation in Spherical Coordinates :
We continue with our discussion of solutions of Laplaces equation in spherical
c

Magnetostatics II
Lecture 24: Electromagnetic Theory
Professor D. K. Ghosh, Physics Department, I.I.T., Bombay
Magnetic field due to a solenoid and a toroid
A solenoid is essentially a long current loop with closely packed circular turns. The length of th

Magnetostatics
Lecture 23: Electromagnetic Theory
Professor D. K. Ghosh, Physics Department, I.I.T., Bombay
Magnetostatics
Up until now, we have been discussing electrostatics, which deals with physics of the electric field
created by static charges. We w

Wave Guides and Resonating Cavities
Lecture38: Electromagnetic Theory
Professor D. K. Ghosh, Physics Department, I.I.T., Bombay
Resonating Cavity (contd.)
We have shown in the last lecture that the electric field components for , , are given by
= 0 cos(

Radiation
Lecture 39: Electromagnetic Theory
Professor D. K. Ghosh, Physics Department, I.I.T., Bombay
So far we have discussed propagation of electromagnetic waves both in free space and in waveguides
without worrying about how they are produced. In the

Wave Guides
Lecture37: Electromagnetic Theory
Professor D. K. Ghosh, Physics Department, I.I.T., Bombay
Rectangular Waveguide
In the last lecture, we have coonsidered the case of guided wave between a pair of infinite conducting
planes. In this lecture, w

Electromagnetic Waves
Lecture34: Electromagnetic Theory
Professor D. K. Ghosh, Physics Department, I.I.T., Bombay
Electromagnetic wave at the interface between two dielectric media
We have so far discussed the propagation of electromagnetic wave in an iso

Electromagnetic Induction
Lecture 29: Electromagnetic Theory
Professor D. K. Ghosh, Physics Department, I.I.T., Bombay
Mutual Inductance
In the last lecture, we enunciated the Faradays law according to which if there is a changing magnetic
flux in a circu

Angular Momentum, Electromagnetic Waves
Lecture33: Electromagnetic Theory
Professor D. K. Ghosh, Physics Department, I.I.T., Bombay
=
0
= 0
=
= +
As before, we keep in view the four Maxwells equations for all our discussions.
=
In the last lectur

Electromagnetic Waves
Lecture 35: Electromagnetic Theory
Professor D. K. Ghosh, Physics Department, I.I.T., Bombay
Propagation of Electromagnetic Waves in a Conducting Medium
We will consider a plane electromagnetic wave travelling in a linear dielectric

Wave Guides
Lecture 36: Electromagnetic Theory
Professor D. K. Ghosh, Physics Department, I.I.T., Bombay
We have seen that electromagnetic waves carry both energy and momentum. It should therefore be
possible to transmit energy contained in the wave from

Magnetized Material (contd.) and Electromagnetic Induction
Lecture 28: Electromagnetic Theory
Professor D. K. Ghosh, Physics Department, I.I.T., Bombay
In the first half of this lecture we will continue with our discussion of magnetized material and in th