PHYSICS 198-142
Electromagnetism:
12
221
12 ˆ
r
r
qqk
F=
, EqF
=, r
r
qk
rE eˆ
)( 2
=
, r
r
dq
krE eˆ
)( 2
∫
=
, y
k
echlineE e
λ
2
)arg( =
∞,
2
3
22 )(
),( ax
Qxk
axisringE e
+
=, 0
2
)(
ε
σ
=∞ planeE , ,, 12
21
r
qqk
Ue
=
,.
∫
−=
Δ
=Δ f
isdE
q
U
V
∫
== r
dq
kV
r
qk
Ve
e, , 0
κ
ε
ε
=
,
)/ln(
2)(,)(,/,),( 0
0
22 ab
L
cylinderC
d
A
plateparallelCVQC
ax
Qk
axisringV e
κπε
κε
===
+
=,
⎟
⎠
⎞
⎜
⎝
⎛
−
=abab
sphereC
κπε
0
4)( , 2
2
1CVU =, RIIVP 2
== , IRV
=
, d
nqv
A
I
J== , dt
dQ
I=, JE
ρ
=,
A
L
R
ρ
=, ∑=
=n
iieq CC 1, ∑=
=n
iieq CC 111 ,
∑
=
=n
iieq RR 1, ∑=
=n
iieq RR 111 , AdEd E
.=Φ ,
∫=
0
.
ε
in
q
AdE
, RC=
τ
, )1()( 0
τ
t
eQtQ −
−= ,
τ
t
eQtQ −
=0
)( , 2
0
2
1EuE
ε
=, BvqF
×= ,
B
I
F
×
=
,
∫×=
b
a
BsdIF
BANI
×=
τ
, ∫×
=2
0ˆ
4
r
rsd
I
B
π
μ
, a
I
wirelongB
π
μ
2
)( 0
=
)sin(sin
4
)( 21
0
θθ
π
μ
+= a
I
segmentB ,
θ
π
μ
R
I
arcB 4
)( 0
=, 2
3
22
2
0
)(2
)( Rx
IR
loopofaxisB +
=
μ
,
nIsolenoidB 0
)(
μ
=, in
IsdB
∫=0
.
μ
,
∫
=Φ AdB
B
., ∫Φ
−== dt
d
sdE B
.
ε
, vB=
ε
,
)sin( tNBA
ω
ω
ε
=, dt
dI
L
L−=
ε
, I
N
LB
Φ
=, RL/
=
τ
, )1()( 0
τ
t
eItI −
−= ,
τ
t
eItI −
=0
)( ,
2
2
1LIU =, AnsolenoidL 2
0
)(
μ
=, 0
2
2
μ
B
uB=, )sin(
0tII
ω
=
, 2/
0
IIrms =, 2/
0
VVrms =,
LXL
ω
=, )/(1 CXC
ω
=, ZIV rmsrms =, 22 )( CL XXRZ −+= ,
φ
cos
rmsrms IVP
=
,
ZR/cos =
φ
, RXX CL /)(tan −=
φ
Optics:
λ
fv =, v
c
n=, 2211 sinsin
θ
θ
nn =, 2211 nn
λ
λ
=
, fqp 111 =+ , p
q
M−= ,
λ
θ
md =sin ,
λ
θ
ma =sin , dLm
ym
λ
=, d
L
mym
λ
)2/1( += ,
λ
mnt
=
2,
λ
)2/1(2
+
=
mnt , NmR avg =
Δ
=
λ
λ
,
D
λ
θ
22.1
min =,
π
φ
λ
δ
2// =