Purcell Simplied: Magnetism, Radiation, and Relativity
Anaheim, CA, 14 January 1999
Dan Schroeder, Weber State University, http:/physics.weber.edu/schroeder
Introductory Comments
Theres almost nothing original in this talk; Purcell gets all the credit.
ELECTRODYNAMICS
PROBLEM SET 13 THE LAST ONE
due May4th , before class
I.
SCATTERING OF LONG WAVES FROM A DIELECTRIC SPHERE
Compute the (dierential) scattering cross section of a dielectric sphere with dielectric constant and radius R.
Assume the waveleng
q d R 0 V i + Ri V 0
qd
Vi /V0 + Ri /R0
[
]=
[(R0 V0 )
]
R V d
RV
R V d
RV
Ri i
q d Ri i
q
Ri i
=
[
]=
[
(R R )]
R V d 1 R
R V (1 R ) (1 R )2
q
=
[( i + i R + (Ri i )R ) + (Ri Ri R + (Ri i )R )]
R V (1 R )2
Fi 0 =
i + i R + ( R i i )R = R (R )
ELECTRODYNAMICS
PROBLEM SET 10
due April 20th , before class
Rotating dipole
Consider an electric dipole p spinning around an axis forming an angle theta with p. Compute the power radiated
as a function of the direction and the total power radiated.
Two d
E 0 E0
E0
E
E0 E0 = E 0
E 0 + E0 = n E0
E0 =
R=
n + 1
E
n1 0
1 2
2 E0
12
2 E0
=
1n 2

1+n
1 2
( E ) + 2 2 D = 0
c t
2
( E ) + D = 0
k
k
2
c
B
= k
k
n
( E ) E +
nn
v2
D=0
c2
ij
2
[(ni nj ij ) + v 2 (ij /vj )]Ej = 0
2
det(ni nj ij )+v 2 (ij /vj )
ELECTRODYNAMICS
PROBLEM SET 9
due April 13th , before class
I.
REFLECTION WITH DISPERSION
A plane wave of frequency is incident normally from vacuum on a semiinnite slab of material with a complex
n( ).
a) Show that the ratio of reected power to incident
x
J ( )
F=
N=
Fi
=
jk
=
jk
ijk [Bk (0)
x
x
J ( ) B ( )d3 x
x
x
(J ( ) B ( )d3 x
x
Ji ( )d3 x +
x
Ji ( ) Bk (0)d3 x + .]
xx
ijk (m )j Bk  =(0,0,0) + .
x
F = ( m ) B = ( m B )
U =mB
N = m B (0)
qm
qm
)
(0, 0, d
qm
z<0
(0, 0, d)
qm
z>0
(0, 0, d)
1 (x,
ELECTRODYNAMICS
PROBLEM SET 8
due March 30th , before class
Problem 1: Energy, force and torque on a magnetic dipole
Calculate the energy, force and torque acting on a magnetic dipole immersed on a almost homogeneous magnetic
eld. By nearly homogeneous I
ELECTRODYNAMICS
PROBLEM SET 7
due March 16th , before class
Problem 1: Dielectric fun
Two concentric conducting spheres of radii a and b carry charges Q. The empty space between them is halflled
by a hemispherical shell of dielectric (with dielectric con
ELECTRODYNAMICS
PROBLEM SET 6
due March 9th , before class
Problem 1: Two conducting hemispheres
A conducting sphere is divided into two hemispheres. The bottom one is kept at potential V, the top one is
grounded.
a) Using separation of variables and matc
x = a
2
x=
a
2
a
0(x < )
2
= ex ( a < x < a )
E
0
2
2
a
0(x > )
2
a
0(x < )
2
a
a
= x( < x < )
0
2
2
a
0(x > )
2
=
a
20
2 1
1 2 2
+
+2
+
=0
2
2
z2
(, , z ) = R()Q()Z (z )
d2 Z
k2 z = 0
dz 2
d2 Q
+ 2Q = 0
d 2
d2 R 1 dR
2
+
+ (k 2 2 )R = 0
d2
d
(z
ELECTRODYNAMICS
PROBLEM SET 5
due March 2nd , before class
Problem 1: Relaxation method
Implement the relaxation algorithm described in class to nd the potential inside a region with the shape as in the
gure. The top edge is kept at = V and the other bord
y
x
1
N+ mv+
1
=
2
v+
c2
Ima
1
(
q
1
2
v+
c2
1
N mv
1
1
1
2
v
c2
)
N+ mv+ N mv
=0
Ima
1
(
q
1
2
v+
c2
1
1
2
v
c2
)
Ia 1
Ia 1
E =
(Ex Lq )
q c2
q c2
1
1
= 2 Ex (IaL) = 2 Ex 2
c
c
=
2
v
c2
x
E
Ex
1
(x, y, z ) =
40
L/2
0
1
1
dl
2 + y 2 + (l z )2
40
x
1
ELECTRODYNAMICS
PROBLEM SET 4
due February 23th , before class
Problem 1.: Hidden momentum
In the discussion of the energy ow in a coaxial cable in class we argue that the Poynting vector was nonvanishing
inside the cable and pointed from the battery to
1
T = F J
c
M = (x T x T )
= T T + x T x T
= x T x T
1
= (x F J x F J )
c
1
= (x J F x J F )
c
M
M = 0
j
0
d3 xj 0 =
d3 x i j i =
j
dS = 0
0
Q=
d3 xj 0
M
Q =
M
T
T
E
1 Sx
c
= 1
Sy
c
1
c Sz
E=
d3 xM 0
1
c Sx
xx
yx
zx
1
c Sy
xy
yy
zy
1
c Sz
xz
ELECTRODYNAMICS
PROBLEM SET 3
due February 16th , before class
Problem 1.: Angular momentum
One point that was not emphasized enough in class is that conservation laws are a consequence of symmetries of
Nature. For instance, translation symmetry leads to
ELECTRODYNAMICS
PROBLEM SET 2
due February 9, before class
Problem 1.: Field invariants
a) Write the Lorentz scalars F F and F F in terms of E and B .
b)Show that if E and B are seen as perpendicular in one reference frame, they are perpendicular in any o
ELECTRODYNAMICS
PROBLEM SET 1
due February 2nd, before class
Problem 1.: tensor (anti)symmetry
Show that if A = A is a symmetric tensor in one frame, itll be symmetric in any other frame. Is antisymmetry
(A = A ) also frame independent?
Show that if S i
ON THE ELECTRODYNAMICS OF MOVING
BODIES
By A. EINSTEIN
June 30, 1905
It is known that Maxwells electrodynamicsas usually understood at the
present timewhen applied to moving bodies, leads to asymmetries which do
not appear to be inherent in the phenomena.
o
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