electrodynamics lecture
DESCRIPTION
A lecture on electrodynamics. This lecture is part of a course of Physics during the 2nd Semester at The LNMIIT, Jaipur.TRANSCRIPT
Classical Electrodynamics
Physics II
Reference Books
1. Introduction to Electrodynamics by David. J. Griffiths
2. Classical Electrodynamics by John David Jackson
3. Electricity and Magnetism by Edward M. Purcell
%
45
10
45
Final exam
quizzes
Mid term exam.
� Electrostatics
�Special techniques
�Concepts of Dipole
�Electric Field in Materials
� Magnetostatics
�Magnetic Field in Materials
�Electrodynamics
�Maxwell’s Equation
� Review of Mathematical Tools 4 lectures
1 lectures
1 lectures
1 lectures
1 lectures
2 lectures
2 lectures
3 lectures
2 lectures
(x,y,z)
(x′,y ′,z ′)
θcosABAr)r
=•
Vector Field / Vector Function
Vector Calculus
jxiyF ˆsinˆsin +=r
A vector field describing the velocity of a flow in a pipe
Velocity vector field of a flow around a aircraft wing
Circular flow in a tub
kzyxFjzyxFizyxFzyxF ˆ),,(ˆ),,(ˆ),,(),,( 321 ++=r
kxjzxixyzzyxF ˆˆˆ),,( 42 +−=r
dx
dfh
xfhxfh
)()(lim
0
−+→
Scalar field),,( zyxTT =
h
zyxfzyhxfzyxf
hx
),,(),,(lim),,(
0
−+=→
h
zyxfzhyxfzyxf
hy
),,(),,(lim),,(
0
−+=→
h
zyxfhzyxfzyxf
hz
),,(),,(lim),,(
0
−+=→
Scalar Field
Vector Field
T(x,y)
Ty
Yx
XT
∂∂+
∂∂=∇ ˆˆ
∇⋅≠⋅∇ VVrr
In many cases, the divergence of a vector function at point P may be predicted by considering a closed surface surrounding P and analyzing the flow over the boundary, keeping in mind that at P:
=⋅∇ Fr
outflow – inflow
Paddle wheel analysis
0ˆ)],([ 00 <⋅×∇ kyxFr
jxiyyxF ˆˆ),( +−=r
2=×∇ Fr
iyyxF ˆ),( =r
1−=×∇ Fr
jxiyyxF ˆˆ),( +=r
jyixyxF ˆˆ),( +=r
0=×∇ Fr
Laplacian oparator
Vector Line Integration
http://upload.wikimedia.org/wikipedia/commons/d/d8/Line-Integral.gif
Vector surface Integral
Volume Integral
Difference of function’s value at b and a
The integral of a derivative over a region is equal to the value of the function at the boundary
0=∇×∇ Trr
0=×∇ Frr
F conservative field
=⋅∇ Vr
outflow – inflow +ve (source)-ve (sink)
The integral of a derivative over a region is equal to the value of the function at the boundary
The integral of a derivative over a region is equal to the value of the function at the boundary
Stokes’ theorem
rotational force field / non-conservative force field
Cylindrical and spherical co-ordinate system
φρ
φr
(ρ,φ,z)
z
Y
X
zz
y
x
aa
aaa
aaa
=
+=
−=
φφφφ
φρ
φρ
cossin
sincos
zz
yx
yx
aa
aaa
aaa
=
+−=
+=
φφφφ
φ
ρ
cossin
sincos
−=
zz
y
x
a
a
a
a
a
a
ϕ
ρ
φφφφ
100
0cossin
0sincos
−=
z
y
x
z a
a
a
a
a
a
100
0cossin
0sincos
φφφφ
φ
ρ
zayaxaA zyx ˆˆˆ ++=r
zaaaA z ˆˆˆ ++= φρ φρ
r
ρρρρφφφφρρρρρρρρφφφφ ˆˆ3 dzddIdIda z ==
zddzdIdIda ˆˆ2 ρρρρφφφφρρρρρρρρφφφφ ==
φφφφρρρρφφφφρρρρˆˆ
1 dzddIdIda z ==
The infinitesimal surface elements
dφ
dρρ
ρdφdz
dφ
dρρ
ρdφdz
Volume element in cylindrical coordinate system
dz
dρ
y
x
φ
φ
z
dz
dρ
y
x
φ
φ
z
φφφφρρρρφφφφρρρρˆˆ
1 dzddIdIda z ==
dρ
ρdφy
x
φ
dρ
ρdφy
x
φ
zddzdIdIda ˆˆ2 ρρρρφφφφρρρρρρρρφφφφ ==
dz
ρdφ
y
x
φ
φ
z
dz
ρdφ
y
x
φ
φ
z
ρρρρφφφφρρρρρρρρφφφφ ˆˆ3 dzddIdIda z ==
(r,θ,φ)
r
θ
φ
θθφφθφθφφθφθ
θ
φθ
φθ
sincos
cossincossinsin
sincoscoscossin
aaa
aaaa
aaaa
rz
ry
rx
−=
++=
−+=
−
−=
φ
θ
θθφφθφθφφθφθ
a
a
a
a
a
a r
z
y
x
0sincos
cossincossinsin
sincoscoscossin
−−=
z
y
xr
a
a
a
a
a
a
0cossin
sinsincoscoscos
cossinsincossin
φφθφθφθ
θφθφθ
φ
θ
zayaxaA zyx ˆˆˆ ++=r
φθ φθˆˆˆ aaraA r ++=
r
r
z
y
x
dr
rdθ
rsinθdφ
dφφ
θ
The infinitesimal surface elements
φφφφθθθθφφφφθθθθˆˆ
3 rdrddIdIda r ==