Chapter 2
Electrostatics II. Potential Boundary
Value Problems
2.1
Introduction
In Chapter 1, a general formulation was developed to nd the scalar potential
electric eld E =
r
(r) and consequent
for a given static charge distribution (r): In a system invo
Chapter 7
Diraction: Boundary Value Problems of Electromagnetic Waves
7.1 Introduction
In electrostatics, a prescribed potential distribution on a closed surface uniquely determines the potential elsewhere according to the Dirichlet' formulation, s (r) =
Chapter 10
Electromagnetism and Relativity
10.1 Introduction
If I am moving at a large velocity along a light wave, what propagation velocity should I measure? This was a question young Einstein asked himself and in 1905, he published a monumental paper o
Chapter 8
Radiation by Moving Charges
8.1 Introduction
The problem of radiation of electromagnetic waves by a single charged particle moving at an arbitrary velocity had correctly been formulated independently by Lienard and Wiechert before the advent of
P812 Solution No. 3
1. In the limit k ! 0; does the Green function for the Helmholtz equation
s
0
1
l
X X
eikjr r j
G r; r =
= ik
Rl r; r0 Ylm ( ; ) Ylm ( 0 ;
4 jr r0 j
0
0
);
l=0 m= l
reduce to an expected form? Here
Rl r; r0 =
and note that for small x
Chapter 9
Conned and Guided Waves
9.1 Introduction
Electromagnetic waves can be conned in a volume surrounded by a conductor wall as in microwave cavities and also guided to propagate in conducting tubes and dielectric bers. Parallel wire transmission lin
Chapter 5
Radiation from Macroscopic Sources (Antennas and Apertures)
5.1 Introduction
Strictly speaking, radiation of electromagnetic waves from antennas and apertures should be analyzed as a boundary value problem incorporating the boundary conditions f
P812 Solution No. 3
1. In the limit k ! 0; does the Green function for the Helmholtz equation
s
0
1
l
X X
eikjr r j
G r; r =
= ik
Rl r; r0 Ylm ( ; ) Ylm ( 0 ;
4 jr r0 j
0
0
);
l=0 m= l
reduce to an expected form? Here
Rl r; r0 =
and note that for small x
Chapter 3
Magnetostatics
3.1 Introduction
Magnetostatics is a branch of electromagnetic studies involving magnetic elds produced by steady non-time varying currents. Evidently currents are produced by moving charges undergoing translational motion. An eec
P812 Assignment No. 1
1. The potential due to a ring charge (charge q; radius a) placed on the x
q
(r; ) =
where K
k2
2
2
0
p
r2
+
a2
y plane is
1
K (k 2 )
+ 2ar sin
is the complete elliptic integral of the rst kind de ned by
K (k 2 ) =
Z =2
0
The argumen
P812 Solution No. 1
1. The potential due to a ring charge (charge q; radius a) placed on the x
(r; ) =
q
2
2
0
p
r2
+
a2
y plane is
1
K (k 2 )
+ 2ar sin
where K k 2 is the complete elliptic integral of the rst kind de ned by
K (k 2 ) =
Z =2
The argument k
Chapter 4
Time Varying Fields, Simple Waves
4.1 Introduction
and current density J are generalized to be varying with time. @ + r J = 0; @t (4.1)
In this Chapter, the charge density The charge conservation law
imposes a constraint between the two quantiti
P812 (2010-11) Assignment No. 2
1. The upper half (0 < < =2) of a spherical shell of radius a carries a uniform surface charge
(C m 2 ) and the lower half ( =2 < < ) carries a surface charge of opposite sign
:
(a) Find the potential along the z axis
(b) F
Chapter 6
Harmonic Expansion of
Electromagnetic Fields
6.1
Introduction
For a given current source J(r; t); the vector potential can in principle be found by solving the
inhomogeneous vector wave equation,
r2
1 @2
c2 @t2
A (r; t) =
0 J (r; t) ;
provided t
Chapter 1
Electrostatics I. Potential due to Prescribed Charge Distribution, Dielectric Properties, Electric Energy and Force
1.1 Introduction
In electrostatics, charges are assumed to be stationary. Electric charges exert force on other charges through C
P812 (2010-11) Solutions No. 2
1. The upper half (0 < < =2) of a spherical shell of radius a carries a uniform surface charge
(C m 2 ) and the lower half ( =2 < < ) carries a surface charge of opposite sign
:
(a) Find the potential along the z axis
(b) Fr