Lecture 7 Notes: Magnetic Dipole
Diamagnetism
e
I = 2
=
e
2
, m = I R
2
_
_
e
2
R iz =
iz =
2
eR
2
2_
iz
Angular Momentum
_
L = m R ir v = m R
e
e
R
_
ir i
r p
_
= m R
e
=
2
_
iz
2me
e m
linear momentum
L is quantized in units of h ,
2
e L
m =
eh
2m
Lecture 5 Notes: Poissons Equation
I. MQS Governing Equations
Avector potential
i 0H 00HA
1
2
Ai A A 0 J
H A J
0
II. Uniqueness
If AA ,A is unchanged because
0
For iA to also remained unchanged requires
2
0
When, for EQS systems
2
r
' dV '
r
V ' 4
Lecture 4 Notes: Conservative Notions
I. Quasistatics
Electroquasistatics (EQS)
Magnetquasistatics (MQS)
0
E
0H
0
E
0 H
t
0
i E
H J
E
t
t
H J
i H 0
i Jt0
i J0
i E
II. Irrotational EQS Electric Field
1. Conservative Electric Field
0
E
Lecture 3 Notes: Parallel Electrodes
A. Order
of
Magnitude
Characteristic time ]
H E H
t
L
E
E
error
H
t
3
L
E
E
error
L
L
2
E
L
2
error
L
1 c
1
E
[Characteristic
L
E
L E
i E
E
Estimate
H
2
EL L
2
H L
2
L
c2
;
2
E
error
c
1
L
3
Length
L,
B. Esti
Lecture 2 Notes: Divergence Theorem
1. Divergence Operation
A i dS = div A dV
S
V
div A = lim
S
V0
Axx,y,z
A i dS
V
dydz Axx - x,y,z dydz
1
Ayx,y + y,z
1'
dxdz Ayx,y,z dxdz
2
2'
Azx, y,z + z dxdy Azx, y,z
3
A
xyz
+
V
A x
x
div A = lim
V0
+
x
A
z
A
Lecture 6 Notes: Bohr Magnets
Diamagnetism
I=
e
2
=
e
, m = I R
2
Angular Momentum
2
_
_
e
2
R iz =
iz =
2
_
L = m R ir v = m R
e
e
R
_
_
ir i
eR
= m R
=
iz
2
e
r p
2_
2
_
iz
2me
e m
linear momentum
L is quantized in units of h ,
2
e L
m =
2me
eh
=
Lecture 10 Notes: Hookes Law
I. Governing Equations
2
A x
1
t
2
t
T
11
2
11
2
11
x
x
1
1
T
11
x
F
1
A F A x
1
2
(F is body force density)
x1
E
Hookes Law (stress-strain relation)
x1
Youngs modulus (modulus of elasticity)
E F
2
2
x
1
2
T
T
t x1
2
2
Lecture 9 Notes: MQS Energy
I. MQS Energy Method of Forces
A. Circuit Approach
v=
d
= d L
dt
dt
i=L
di
2
dL
p = vi = L i dt i
d 1
= L
di i dL
dt
dt
dt
2
i i
2
dL
dt 2
dt
d1
2
= dt
2 L i 1 i2 dL
2
= d 1L i2 dt 2
1 i2 dL d
2
d
1
dWm
v i = dt f dt
Lecture 8 Notes: Laplaces Equation
=0
z
A. Product Solution
1
2
=
r
rr
r
r d
r
dr
dR
R dr
dr
R dr
2
2
1 d2F
F d
-m
dR
dr
2
1d F =m
2
F d
=m
2
2
d F
r
2
r
2
Rr
m
r d
r
0
2
=0
2
F
dr
dR
r
1
r
r, = R r
F d
2
2
2
Multiply through
2
d
=0
r
R r F
by
=0
2
Lecture 1 Notes: Faradays Law
1. Faradays Law
E
C
d
ids = - dt
Circulation
of E
0
S
H
i da
Magnetic Flux
0 = 4 10
-7
henries/meter
[magnetic permeability of
free space]
Eids = 0 (Kirchoffs Voltage Law, conservative electric
EQS form:
C
field)
MQS circuit