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Physics 2020
Spring 2009
Stephan LeBohec
DATA SHEET - FINAL
SEAT #
Constants & mathematics:
N A =6.02×1023
Boltzmann's constant k =1.38×10−23 J⋅K −1
k=
R=8.31 J⋅mol−1⋅K −1
1
9
2
−2
=9.0×10 N⋅m ⋅C
4  0
−7
−1
0=4 ×10 T⋅m⋅A
1
2
Kinetic energy E K = m⋅v
2
cos 2  f t 
≈−2  f sin 2  f t 
t
−19
e=1.602×10 C
Q Proton =e & Q Electron=−e
c=
1
=299,792,458 m⋅s−1≈3×10 8 m⋅s−1
 0 0
Work, force & displacement relation
 ∣⋅ x⋅cos 
 W =∣F
sin 2 f t 
≈2  f cos 2  f t 
t
Thermodynamics:
T  K =T  C 273
P⋅V =N⋅k⋅T =n⋅R⋅T
n=
N
m
=
& R=N A⋅k
NA M
e Actual =
3
Ideal mono­atomic gas:  U = n⋅R⋅ T
2
Isobaric: W =P V f −V i 
Isochoric: W =0
Isothermal W =n⋅R⋅T ln 
First law of thermodynamics:  U =Q−W
Vf

Vi
W Cycle
QC
=1−
QH
QH
3
Adiabatic: W =− n⋅RT f −T i  &
2

P⋅V =Constant
5
with = for mono­atomic gases
3
e Carnot =1−
TC
TH
Waves:
=c⋅T =
c
1
as f =
f
T
In a gas c Sound =
Isotropic sound intensity: I =
c String =

5
P
with = for a mono­atomic ideal gas
3

P
2
4 ⋅r
Comparing intensities =10 log10
Doppler effect: f o= f s
Standing wave frequency (string or open pipe)
c
f n=n
with n=1,2,3,⋯
2L
Electric force, field and potential:
Force on a point charge in an electric field:
 =q E

F
Electric potential from a point charge: V r =k
q
r
q
V
R=
c±v o
c∓v s
Standing wave frequency in pipe open at one end
c
f n=n
with n=1,3,5,⋯
4L
Work by operator moving a charge in an electric potential: W =q⋅V f −V i 
Electric circuits:
Power in an electric circuit: P=V⋅I
Resistivity:
I1
in dB
I2
Electric field generated by a point charge:
 ∣=k q
∣E
r2
Force between two point charges:
q q
 ∣=k 1 2
∣F
2
r
Capacitance: C=

m
F
with =
L

L
A
Power from harmonic voltage and current:
I0
V0
P=I RMS⋅V RMS with I RMS =
and V RMS=
2
2
Equivalent resistance for resistors in parallel:
1
1 −1
R Parallel =  
R 1 R2
Equivalent capacitance for capacitors in series:
−1
1
1
C Series =  
C1 C 2
Electric field in a parallel plate capacitor:
 ∣=  V = 
∣E
d
0
Energy stored in a capacitor:
1
1
1 q2
2
U = q⋅ V = C⋅ V =
2
2
2C
Ohm's law: V =R⋅I
Temperature dependence of resistivity:
=0 1T −T 0
Equivalent resistance for resistors in series:
R Series= R1R 2
Kirchhoff's junction rule: ∑ I IN =∑ I OUT
and loop rule: ∑  V UP =∑  V DOWN
Equivalent capacitance for capacitors in parallel
C Parallel =C 1C 2
Magnetic force and field:
 ∣=∣q∣⋅∣v∣⋅∣ 
Magnetic force on a charge: ∣F
B∣sin 
Magnetic field produced by an infinitely long wire:
 r ∣= 0 I
∣B
2 r
Electromagnetic induction:
Magnetic flux: = A⋅∣
B∣cos 
Self inductance: L=
Transformers:
Magnetic field inside a solenoid:
∣
B∣=0 n I
Faraday's law: V =−
Induction in a moving wire
V =L⋅∣v∣⋅∣
B∣
Mutual inductance: M =
 ∣=I⋅L∣ 
Magnetic force on a current: ∣F
B∣sin 

t
Induction in a rotating set of coils
V =2  f N⋅A⋅∣
B∣sin 2  f t 
S
IP
Mutual induction: V =−M

I
Self induction: V =−L
I
t
I
t
VS NS IP
=
=
V P NP IS
Electromagnetic waves:
=c⋅T =c / f
Doppler effect: f o= f s
1±v o /c
≈ f s 1±v rel /c 
1∓v s /c
Reflection of light:
Law of reflection: R =I
Mirrors equation:
Spherical mirror: f =
1 1
1
= 
f dI dO
Magnification: M =
Snell's refraction law n1 sin 1 =n2 sin 2
Triangle geometry:
µ
E
b
c =a 2b2
cos =b/ c
sin =a /c
tan =a/b
R
2
hI
d
=− I
hO
dO
Brewster angle: tan  B=n 2 / n1
(ABD) and (ECD), similar triangles
AB DB AD
=
=
EC DC ED
c
a
Malus law: I T =I I cos 2 
D
C
2
A
B