Equations
C=
!0 A
2π!0 L
ab
P arallel P late, C =
Cylindrical, C = 4π!0
Spherical
d
ln(b/a)
a−b
1
1 Q2
,
U = CV 2 =
2
2 C
Q = CV,
dq
I= ,
dt
I=
!
−
→ −
→
J · dA ,
V = IR,
t
Q = Q0 (1 − e− RC ),
(charging)
t
Q = Q0 e− RC ,
−
→
−
→
→
F = q−
v × B,
−
→ −
−
→
→
F = I l × B,
−
→
dB =
ρl
,
A
qvB =
µ0 I
(center of whole loop),
2R
−
→
−
→
E = F /qtest =
1 q
2 r̂12 ,
4π!0 r12
1
σ
ρ=
mv 2
,
r
I=
Q0 − t
e RC ,
RC
! = κ!0
m
,
e2 nτ
P = IV
−
→
−
→
→
τ =−
µ × B,
$
V − t
e RC
R
1
KE = mv 2
2
ω = 2πf,
→
" µ # I−
" µ # q−
→
dl × r̂ −
v × r̂
→
0
0
,
B
=
,
2
4π
r
4π
r2
µ0 I
2πr
ρ=
τ = RC,
I=−
−
→ −
−
→
→
dF = I dl × B ,
B=
B=
R=
E0
,
κ
E=
1
1
1
1
=
+
+
+ ...
R
R1 R2 R3
R = R1 + R2 + R3 ... ,
(discharging)
C = κC0 ,
ω=
v
r
−
→
−
→
→
τ =−
r ×F
→
−
→ −
B · ds = µ0 Ienclosed
(inf inite wire)
B = µ0 nI (solenoid),
Φ=
$
−
→ −
→
E · dA =
$
B=
µ0 N I
(toroid)
2πr
qenclosed
−
→
E · n̂dA =
!0
Constants
µ0 = 4π × 10−7 TAm
= 3.0 × 108 m/s
c
e = 1.60 × 10−19 C
2
!0 = 8.85 × 10−12 NCm2
g = 9.8 m/s2
Mproton = 1.67 × 10−27 kg
Equations
!
dq
−
→ −
→
I = , I = J · dA ,
dt
!
dφB
−
→ −
→
φB = B · dA ,
ε=−
,
dt
(Increasing)
I = I0 (1 − e−t/τ ),
−
→ −
−
→
→
F = I l × B,
"
dφB
→
−
→ −
,
E · ds = −
dt
"
B = µ0 nI
UL = (1/2) LI 2 ,
µ0 =
dI
dt
ε = −L
τ = L/R,
I = I0 e−t/τ
(decreasing)
φE =
dφE
→
−
→ −
B · ds = µ0 $0
+ µ0 Ienclosed ,
dt
L = µ0 n2 Al
(solenoid),
UC = (1/2) CV 2 ,
Pavg = 0.5Vmax Imax cos(φ),
−
→
→
F = m−
a
P = IV,
φB = BA (sometimes),
−
→ −
−
→
→
dF = I dl × B ,
XC = 1/(wC), XL = wL, Z =
4π ×10−7 TAm ,
V = IR,
!
−
→ −
→
E · dA
IDisplacement = $0
dφE
dt
(solenoid)
uB = B 2 /(2µ0 ),
uE = $0 E 2 /2
#
wL − 1/(wC)
R2 + (XL − XC )2 , tan(φ) =
R
V = IZ,
VC = IXC ,
Constants
2
$0 = 8.85×10−12 NCm2 ,
VL = IXL ,
cos(φ) =
R
Z
c = 3.0×108 m/s, g = 9.8 m/s2
Equations
UL = (1/2) LI 2 ,
UC = (1/2) CV 2 ,
c = E/B, P ressure = S/c,
−
→ −
→
E = E0 sin (kx − ωt),
na sin θa = nb sin θb ,
E = E0 cos θpolarizer ,
sin θc =
a sin (θ) = mλ
nb
,
na
tan θp =
W ork =
M =−
!
φ = π, 3π, 5π...
φ = Kn ∆x,
P ower =
dW
= Fv
dt
1
1
1
= (n − 1)(
−
)
f
R1 R2
2d sin (θ) = mλ
θres =
λ
(slit),
a
θres = 1.22
Bragg
λ
D
(hole)
Resolving P ower, R = mN =
Destructive Interf erence
2π
,
λ/n
n a λa = n b λb
transmission
θpolarizer = θE − θaxis
Constructive Interf erence
Kn =
c
n= ,
v
Moverall = M1 · M2 · M3 ...
Double slit,
d sin (θ) = mλ Dif f raction grating,
φ = 0, 2π, 4π, 6π...
nb
,
na
n1 n2
n2 − n1
+ ! =
,
s
s
R
Single slit,
Sav = Emax Bmax /(2µ0 )
→
−
→ −
F · d l = F l,
s!
h!
= ,
s
h
uE = !0 E 2 /2
√
cvacuum = λf = 1/ !0 µ0
ω = 2πf,
I = I0 cos2 θpolarizer ,
|f | = |R/2| (mirror),
d sin (θ) = mλ
−
→
−
→ −
→
S = (1/µ0 ) E × B ,
k = 2π/λ,
Iunpolarized → Iunpolarized /2,
1
1
1
+ ! = ,
s s
f
uB = B 2 /(2µ0 ),
λ
∆λ
∆x = 0, λ, 2λ, 3λ...
∆x = λ/2, 3λ/2, 5λ/2...
φ = π (if n1 < n2 ) ∆x = λ/2
Constants
µ0 =
4π×10−7 TAm ,
!0 = 8.85×10−12
C2
N m2 ,
c = 3.0×108 m/s, g = 9.8 m/s2
Equations
!
γ = 1/ 1 − (v 2 /c2 ), β = v/c, ∆t = γ∆t0 , L0 = γL
!
f = (c + v)/(c − v)f0 , u = (u! + v)/(1 + u! v/c2 )
E = KE + mc2 ,
E 2 = p2 c2 + m2 c4 ,
λmax T = 0.2898 × 10−2 m K,
KEmax = Ephoton − Φ,
E = γmc2 ,
E = hc/λ (photons!)
KEmax = eVstop ,
Ethreshold = Φ (W ork F unction)
λscattered − λincident = (h/(me c))(1 − cos (θ)),
∆x∆px ≥
h
4π ,
2
En = − Ke
2ao
∆E∆t ≥
1
n2 ,
ao =
h
4π ,
h2
(2π)2 m
λ=
2
e Ke
h
p
=
KE = p2 /(2m)
h
mv (DeBroglie),
En = − 13.6eV
n2 ,
,
β = pc/E
1
λ
=
L=
13.6eV
hc
nh
2π (Bohr)
( n12 −
f
1
)
n2i
1/(2m)(h/2π)2 ∂ 2 Ψ(x)/∂x2 + U (x)Ψ(x) = EΨ(x)
En = h2 n2 /(8mL2 )
!
(T unnelling) T = Ge−2κL , G = 16(E/U0 )(1 − (E/U0 )), κ = 2π 2m(U0 − E)/h
(Inf inite Square W ell)
r = ro A1/3 ,
dN
dt
= −λN,
A = Z + N,
λn = 2L/n,
A X,
Z
Ebind = [Z · M (H) + N · Mn − M (A
Z X)]
N = No e−λt ,
R = λN,
R = Ro e−λt ,
T1/2 = ln (2)/λ
Useful Masses of Particles and Isotopes(Example!!!!)
Quantity
Mass (u)
Quantity
Mass (u)
proton
1.007276
12.000000
neutron
1.008665
electron
5.486 × 10−4
12 C
6
94 Zr
40
140 Ce
58
236 U
92
1H
1
1.007825
93.906450
139.90532
236.045637
Constants
6.626 × 10−34 J
h =
s
Melectron = 9.11 × 10−31 kg
me c2 = 0.511 × 106 eV
ao = 0.0528 nm
1Ci = 3.7 × 1010 decays/s
hc = 1239.8 eV nm
1 eV = 1.6022 × 10−19 J
1u = 931.494 M eV /c2
1Bq = 1 decay/s