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1
Physics
v=
p
FT /µ
2
(1)
2
∂ y
1 ∂ y
= 2 2
(2)
∂x2
v ∂t
v = f λ = ω/k (3)
2π
k=
(4)
λ
y(x, t) = A sin (kx ± ωt) (5)
2π
ω = 2πf =
(6)
T
Pav
I=
(7)
A
v2 − v1
r=
(8)
v2 + v1
2v2
τ=
(9)
v2 + v1
v ± ur
fs (10)
fr =
v ± us
2π∆x
δ = k∆x =
(11)
λ
λn,f ix−f ix
L=n
(12)
2
nf ix−f ix = 1, 2, 3, . . .
(13)
λn,f ix−f ree
(14)
L=n
4
nf ixed−f ree = 1, 3, 5, . . .
(15)
v
fn =
(16)
λn
1
m2
k=
=8.99 × 109 N · 2
4π0
C
(17)
kq1 q2
F~12 = 2 r̂12 (18)
r12
~
~ = F
E
(19)
q0
~ iP = kqi r̂iP (20)
E
2
riP
X
~P =
~ iP (21)
E
E
En+ − En− =
~τ
~ =
E
Z
~
dE
φe
(22)
~
= p~ × E
(23)
Z
kr̂
=
dq (24)
r2
Z
~ · n̂dA
=
E
S
(25)
I
φe,net
Qinside
~
=
E·n̂dA
=
0
S
(26)
∆Q
(49)
∆t
I = qnAvd
(50)
J~ = qn~vd (51)
I=
(27)
σmetal
(28)
0
∆U
∆V =
(29)
q0
Z b
~ · d~`
∆V = −
E
En,nearmetal =
V
I
ρL
R=
A
P = IV = I 2 R
R=
a
(30)
kq
kq
V =
−
r
rref
(31)
U = q0 V
(32)
X kqi
V =
ri
i
(33)
Z
V =
V
kdq
r
(34)
~ = −∇V
~
E
(35)
dV
(36)
Ex = −
dx
dV
Er = −
(37)
dr
X
1
qi Vi
U=
2 i
(38)
U=
C=
C=
U=
ue =
i
~
p~ = q L
σinterf ace
0
1
QV (39)
2
Q
(40)
V
A0
(41)
d
1
CV 2 (42)
2
1 ~ 2
0 |E|
2
(43)
Ceq,par = C1 + C2 + . . .
(44)
1
Ceq,series
=
1
1
+
+ ...
C1
C2
(45)
E0
E=
(46)
κ
C = κC0
(47)
= κ0
(48)
(52)
(53)
(54)
Va − Vb = E − Ir
(55)
E = QE
(56)
Req,series = R1 + R2 + . . .
(57)
1
1
1
=
+
+ ...
Req,par
R1
R2
(58)
~
F~ = q~v × B
(59)
~
~
~
dF = Id` × B
(60)
µ
~ = N IAn̂
(61)
~ (62)
~τ = µ
~ ×B
VH = vd Bw =
~ = µ0 q~v × r̂
B
4π r2
~
~ = µ0 Id` × r̂
dB
4π Ir2
φm,net =
I
|I|
B (63)
nte
(64)
(65)
~
B·n̂dA
= 0 (66)
S
~ · d~` = µ0 IC (67)
B
Z
~
=
B·n̂dA
(68)
C
φm
S
φm = N BA cos θ
I
~ · d~`
E=
E
(69)
(70)
C
|E| = vB`
dI
E = −L
dt
dφm
E =−
dt
(71)
(72)
(73)
Irms
PR,avg
1
= √ Ipeak
2
= VR,rms IR,rms
XL = ωL
1
XC =
ωC
VR,rms
IR,rms =
R
VL,rms
IL,rms =
XL
VC,rms
IC,rms =
XC
dφe
Id = 0
dt
Z
dφe
d
=
En dA
dt
dt S
Z
d
dφm
=
Bn dA
dt
dt S
I
Qinside
En dA =
0
IS
Bn dA = 0
IS
~ · d~` = − dφm
E
dt
IC
~ · d~` = µ0 (IC + 0 dφe )
B
dt
C
2~
2~
∂ E
1 ∂ E
= 2 2
∂x2
c ∂t
~
~
∂2B
1 ∂2B
= 2 2
2
∂x
c ∂t
E = cB
c
n
θ1 = θ10
(91)
v=
(74)
(92)
(75)
n1 sin θ1 = n2 sin θ2
(93)
(76)
n1 sin θc = n2 sin 90◦
(94)
2
I = I0 cos θ
hc
E = hf =
λ
h
h̄ =
2π
1
1
1
+ 0 =
s s
f
s0
y0
=−
m=
y
s
2π∆r
δ=
λ
λ
αc = 1.22
D
E = hf
(77)
(78)
(79)
(80)
(81)
(82)
(83)
(96)
(97)
(98)
(99)
(100)
(101)
(102)
E = pc
h
p=
λ
P (x) = ψ 2 (x)
(84)
(85)
(86)
(95)
Z
(103)
(104)
(105)
∞
ψ 2 (x)dx = 1
(106)
−∞
(87)
(88)
(89)
(90)
1
h̄
2
c = 3.00 × 108 m/s
∆x∆px ≥
(107)
(108)
e = 1.60 × 10
−19
C
0 = 8.85 × 10
−12
F/m
(110)
2
(111)
µ0 = 4π × 10
−7
h = 6.63 × 10
N/A
−34
(109)
J ·s
(112)
These formulas and variables are copied from the summary sections of Tipler and Mosca, Physics for Scientists and Engineers,
6th edition. The relevant chapters are 15, 16, 21-34. The meaning of the variables and constants and the way of using these
equations is explained in the book and lectures.