FormulaSheet - Physics

blockmindlessUrban and Civil

Nov 16, 2013 (3 years and 9 months ago)

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Need additional help? Then visit the Physics Learning Center located in 228 Fisher. Walk
-
in hours are Monday
through Thursday 3:00
-

5:00 p.m. and 7:00
-

9:00 p.m. and Sunday 7:00
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9:00 p.m.




Electric Charges and Forces




1 2
1 on 2 2 on 1
2
p e
on q
on B B
2
0
/
1
ˆ
point charge
4
K q q
F F
r
q N N e
E F q
F q E
q
E r
r

 
 






The Electric Field




3
0
3
0
0
Electric dipole:
, from negative to positive
1 2
Field on axis
4
1
Field in bisecting plane
4
Uniform infinite line of charge:
1 2
, perpendicular to l
4
net i
i
E E
p qs
p
E
r
p
E
r
E
r







 


0
2
0
0
ine
Uniform infinite plane of charge:
, perpendicular to plane
2
Uniformly charged sphere:
ˆ
for
4
Parallel-plate capacitor:
, from positive to negative
E
Q
E r r R
r
E





 
 
 
 

 
 
 
 









ring
3/2
2 2
0
disk
2 2
0
1
4
1
2
z
z
zQ
E
z R
z
E
z R







 
 
 

 




/
sin
a q m E
pE
 






Gauss’s Law


e
e
surface
in
e
0
0
surface
= cos constant field
at surface of a charged conductor:

perpendicular to surface

E A EA
E dA
Q
E dA
E
E




  
  
   











Current and Conductivity


e
d
d
d
2
in out
Electron current:
rate of electron flow



Conventional current:
rate of charge flow

Current density:
/

1

i
N i t
i nAv
e
v E
m
I ei
Q I t
J I A
J nev E
ne
m
I I






 


 
 

 
 

 













The Electric Potential




1 2
elect 0
1 2
elect
0 0
dipole
sources
sources
capacitor
(parallel-plate capacitor)
1 1

4 4
cos

inside a parallel-plate capacitor
(paral
i j
q q
i j
ij
q
q
U U qEs
q q
q q
U U
r r
U p E pE
U
U qV V
q
V Es
V Ed
 





 
 
    
 

 

0
0
lel plates)
1
point charge
4
1
4
i
i
i
q
V
r
q
V
r








Potential and Field




f
i
f i
loop
chem
bat
wire
wire
wire
C
0
( ) ( )
the negative of the area under the grap
h
0
(ideal battery)

(parallel-plate capacitor)
s
s
s
s
s
i
i
V V s V s E ds
E
dV
E
ds
V V
W
V
q
V
E
L
V
L
R I
A R
Q
C
V
A
C
d


    

 
   
  



 





E


eq 1 2 3
1
eq
1 2 3
2
2
C C
2
0
E
... (parallel capacitors)
1 1 1
...(series capacitors)
1
2 2
2
C C C C
C
C C C
Q
U C V
C
u E


   
 
   
 
 
  


PH2200
Formula Sheet Knight


-
q

+
q

p

-

+

s

Need additional help? Then visit the Physics Learning Center located in 228 Fisher. Walk
-
in hours are Monday
through Thursday 3:00
-

5:00 p.m. and 7:00
-

9:00 p.m. and Sunday 7:00
-

9:00 p.m.

Fundamentals of Circuits






in out
bat
2
R
2
R R
eq 1 2 3 N
1
eq
1 2 3 N
//
0 0
junction law:
loop law: 0
... (series)
1 1 1 1
... (parallel)

loop
i
i
t t
V
I
R
I I
V V
P I
V
P I V I R
R
R R R R R
R
R R R R
Q Q e I I e RC
 


 



   


   
    
 
    
 
 
  
 

E


The Magnetic Field






0
0
2 2
0
0
2 2
0 0
long straight wire coil center
0
dipole
3
sin
ˆ
, RHR
4 4
sin
ˆ
, RHR
4 4

2 2
, from south pole to north pole
2
(on axis of dip
4
q v
qv r
B
r r
I s
I s r
B
r r
I NI
B B
d R
AI
B
z
 

 
 

 
 





 

 
 
 
  
 
 
 
 
 








through
solenoid
on q
cyc cyc
wire
0 1 2
parallel wires
ole)
sin, RHR

2
= sin, RHR
2
sin, RHR
o
o
B ds I
NI
B
L
F qv B q vB
qB mv
f r
m qB
F IL B ILB
LI I
F
d
B B







   
 

  
 
 

  



Electromagnetic Induction


m
m
area of loop
cos (uniform -field)
vlB
A B AB B
B dA


   
  

E

per coil
coil
2
2 1
1
sin
d
N
dt
ABN t
N
V V
N
 


 

E
E


Electromagnetic Fields and Waves






in
0
m
e
0 through 0 0
e
disp 0
em 0 0
0
2
0
avg
rad
2
0
transmitted 0
0
1/
1
2
(perfect absorber)
cos
1
(incid
2
Q
E dA
B dA
d
E ds
dt
d
B ds I
dt
F q E v B
d
I
dt
v c
E cB
S E B
P c
I S E
A
F I
p
A c
I I
I I

 





 
 

  

  
  


 

 
  
 






ent light unpolarized)



Physical Constants


9 2 2
12 2 2
0
19
31
e
27
p
6
0
8
8.99 10 N m/C
8.85 10 C/N m
1.60 10 C
9.11 10 kg
1.67 10 kg
1.26 10 T m/A
3.00 10 m/s
K
e
m
m
c







  
  
 
 
 
  
 





Useful Geometry


Circle


Area =
2
r



Circumference =
2
r



Sphere


Surface area =
2
4
r



Volume =
3
4
3
r



Cylinder


Lateral surface


area =
2
rL



Volume =
2
r L




PH2100 in Brief










net
A on B B on A
2
1
f i i
2
2
1
f i i
2
f i
f i
2 2
f i f i
2 2
f i f i
Constant Acceleration:
+

+

2
2
U
i
i
x x
y y
x x x
y y y
x x x
y y y
F F ma
F F
x x v t a t
y y v t a t
v v a t
v v a t
v v a x x
v v a y y
 
 
   
    
 
  
  
  

f i
2
2
2
1
2
mech
f f i i
niform Circular Motion:
2 2 rad



Energy Conservation



r
r
v
T T
t
v
a r
r
K mv
E K U
K U K U
 

  

 
  
 

 
  


Need additional help? Then visit the Physics Learning Center located in 228 Fisher. Walk
-
in hours are
Monday through Thursday 3:00
-

5:00 p.m. and 7:00
-

9:00 p.m. and Sunday 7:00
-

9:00 p.m.