Download PHYSICS 2B EQUATION SUMMARY

PHYSICS 2B EQUATION SUMMARY
Permeability of free
space
μ0 = 4π E-7 H/m
Permittivity of free
space
ε0 = 8.8542 E-12 F/m
k = 8.99 E9 N m2/C2
Charge of the
electron
e = 1.602 E-19 C
Plank’s constant
h = 6.626 E-34 J s
Coulomb’s Law

1 q1 q2
F12 
(rˆ12 )
40 r122
F12  k
q1 q 2
r122
Definition of Electric
Field 
 F
E
q0
Electric field of a
point charge

1 q
E
(rˆ)
40 r 2
Ek
q
r
2
Definition of Electric
Flux


 E   E  dA
ΦE = E ΔA cos(θ)
summed over surface
area.
Gauss’ Law
Q

0
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Definition of Electric
Potential
PE
V 
q0
Force of magnetic
field on a charged
object

 
F  qv  B
F  qvB sin(  ) in
direction ┴ v & B
For any electric
field:


E  V
E s  
Ampere’s Law for
constant current
 
 B  d  0 I
V
in
s
direction of Δs
Law of Biot and
Savart
  0 i ds  rˆ
dB 
4 r 2
For a point charge
1 q
V 
40 r
Definition of
capacitance
q=CV
Ohm’s Law
V = IR
Power in Resistive
Circuit:
P = IV = I2R = V2/R
For a long straight
wire
Voltage across a
capacitor:
Vrms  I rms  C
0 I
2 r
BN
0 I
2R
For any capacitor:
q = CV
PE = ½ qV = ½ CV2
For a solenoid
For a parallel-plate
capacitor:
 qAˆ
 ˆ
E

A
0 A 0
(From Gauss’ Law)
 V
E  Aˆ
d
RC time constant:
  RC
  nIAB sin 
B   0 nI
Torque on a flat coil
Magnetic flux:


   B  dA
ΦB = B ΔA cos(θ)
summed over surface
area.
Faraday’s Law
Δ
E  N
Δt
1
From Faraday’s law:
ΔI
E  L
Δt
Capacitive
Reactance
1
XC 
2 f C
For a coil of wire
I peak  2 I rms
Self inductance
N
L
I
PE = ½ LI2
Force on a currentcarrying element

 
F  i LB
F = iLBsin(θ) in the
direction ┴ i and B
B
For a sinusoidal
voltage or current:
V peak  2 Vrms
Mutual inductance
N 
M  S S
IP
From Faraday’s law:
ΔI p
ES   M
Δt
Inductive Reactance
X L  2 f L
Voltage across an
inductor:
Vrms = Irms XL
Impedance of a
series RLC circuit:
Z  R 2  X L  X C 
2
 XL  XC 

R


  tan 1 
Resonance:
1
f0 
2 LC
Speed of light:
1
c
 0 0
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PHYSICS 2B EQUATION SUMMARY
Doppler Effect for
Electromagnetic
waves:
v
1
c
  0
v
1
c
for v<<c this can be
written:
 v
f O  f S 1  
 c
For a thin spherical
lens or a mirror:
1 1 1
 
p q f
For a spherical
mirror:
f=½R
Index of Refraction:
c
n
v
Snell’s Law
n1 sin( 1 )  n2 sin(  2 )
Double slit
diffraction:
Bright fringes:
sin(θ) = m λ/d
Dark fringes:
sin(θ) = (m+½) λ/d
Single slit
diffraction:
Dark fringes:
sin(θ) = m λ/w
Diffraction grating:
sin(θ) = m λ/d
Gamma
1
 
1
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Time dilation
T   T0
Momentum of a
photon
h
p

Lorentz contraction
L
L 0

De Broglie
wavelength
h

p
Relativistic
momentum
p   mv
Heisenberg
Uncertainty
Principle
h
p x x 
4
h
p y y 
4
h
p z z 
4
h
E t 
4
Relativistic total
energy
E  mc 2
Relativistic kinetic
energy
KE  (  1)mc 2
Relativistic addition
of velocities
V  VCB
V AB  AC
V V
1  AC 2 CB
c
Spectral
wavelengths of
hydrogen:
1
1 
 1
 R 2  2 

n 
m
m, n = 1, 2, 3, …
Lorentz
transformations
x    x  vt
y  y
z  z
 vx 
t    t  2 
 c 
Energy levels in
Bohr Model
me 4 Z 2
En   2 2 2
2h  0 n
hf = Ei-Ef
Energy levels of a
bound particle
E=nhf n=0,1,2,3,…
Quantum
Mechanical model of
Atoms
Principle quantum
number n = 1, 2, 3 …
Orbital quantum
number
  0,1,..., n  1
magnetic quantum
number
m  ,...,2,1,0,1,2,..., 
ms  1 / 2
L  (  1 
Lz  m 
where:
h

2
Nuclear Structure
A=Z+N
Binding Energy =
(Mass defect) c2
Radioactive half life
N  N0 e t
.693

T1 / 2
Hubble’s Law
v=Hr
Energy of a photon
E  hf
Photoelectric effect
hf = KEmax + W0
v2
c2
2
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PHYSICS 2B EQUATION SUMMARY
LEPTONS
Flavor
1
1
2
2
3
3
Particle
electron
electron neutrino
muon
muon neutrino
tauon
tauon neutrino
Sym. Q Mass*c2
Le
e
-1
.511 MeV 1
ν
0
<0.6 eV 1
μ-1
106 MeV 0
νμ
0
<0.6 eV 0
τ-1 1777 MeV 0
ντ
0
<0.6 eV 0
Lμ
0
0
1
1
0
0
Lτ
0
0
0
0
1
1
Q = charge (in units of 1 electron charge), L= Lepton number
QUARKS
Q = charge
c = charm
B = Baryon Number
t = topness
Generation
1
1
2
2
3
3
Name
Sym
Up
Down
Charm
Strange
Top
Bottom
u
d
c
s
t
b
S = strangeness
b = bottomness
Q
c
+⅔
-⅓
+⅔
-⅓
+⅔
-⅓
0
0
+1
0
0
0
S
0
0
0
-1
0
0
t
b
0
0
0
0
+1
0
0
0
0
0
0
-1
Mass
MeV/c2
5
10
1500
200
175000
43000
All Quarks have B = ⅓, All Leptons have B, c, S, t and b = 0. The masses of the quarks are in much
dispute; don’t take them too seriously.
SOME USEFUL MASSES:
Object
electron
proton
neutron
deuterium
earth
moon
sun
Kg
9.1093826E-31
1.67262171E-27
1.67492728E-27
u
5.4857990945 E-4
1.00727646688
1.00866491560
2.014102
MeV/c2
.511
938.3
939.6
5.98E24
7.35E22
1.99E30
Note:1 atomic mass unit = 1.66053886E-27 Kg = 931.494044 MeV/c2.
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