PH2200
Formula Sheet
a   q / m E
Electric Charges and Forces
F1 on 2  F2 on 1 
q   Np  Ne  e
U elect  U 0  qEs (parallel-plate capacitor)
Gauss’s Law
e 
Fon B  qB E

E  dA
q
rˆ point charge
4 0 r 2
e 
Qin
 E  dA  
0
E at surface of a charged conductor:
The Electric Field
Esurface
Enet   Ei
i
Current and Conductivity
s
p   qs, from negative to positive 
1 2p
4 0 r 3
Field in bisecting plane E  
i  nAvd
1
p
4 0 r 3
Uniform infinite line of charge:
 1 2

E 
, perpendicular to line 
 4 0 r

Uniform infinite plane of charge:
 

E 
, perpendicular to plane 
 2 0

Uniformly charged sphere:
E
Q
rˆ
4 0 r 2
for r  R
Parallel-plate capacitor:


E   , from positive to negative 
 0

 Ering  z  41 2 zQ2 3/ 2
0 z  R 
 Edisk  z 

 
z
1  2

2
2 0 
z R 
Electron current:
i  rate of electron flow
N e  i t
e
vd  E
m
Conventional current:
I  rate of charge flow  ei
Q  I t
Current density:
J I/A
J  nevd   E

I
in
ne 2 1

m

  I out
i j
1 qi q j
4 0 rij
V
U q  sources
q
 inside a parallel-plate capacitor 
V  Es
Vcapacitor  Ed (parallel plates)
1 q
4 0 r
V
V 
i
Electric dipole:
p
-q + +q
Field on axis E 


 0
perpendicular to surface

U elect  
U dipole   p  E   pE cos
U q  sources  qV
surface
1
1 q1q2
4 0 r
U q1  q2 
 e  E  A = EAcos constant field
E  Fon q / q
E
The Electric Potential
  pE sin
K q1 q2
r2
Knight
point charge
1 qi
4 0 ri
Potential and Field
sf
V  V ( sf )  V ( si )    Es ds
si
 the negative of the area under the Es graph
dV
ds
   V i  0
Es  
Vloop
i
Wchem
 E (ideal battery)
q
V
Ewire  wire
L
Vwire
L
R
I
A
R
Q
C
VC
Vbat 
C
0 A
(parallel-plate capacitor)
d
Ceq  C1  C2  C3  ... (parallel capacitors)
1
 1

1
1
Ceq   

 ...  (series capacitors)
 C1 C2 C3

2
Q
1
2
UC 
 C  VC 
2C 2
uE 
0
2
E2
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
V
R
junction law :
d  per coil
EN
I
Useful Geometry
dt
Circle
Area =  r 2
Circumference = 2 r
Ecoil   ABN sin t
I
in
  I out
Vloop    V i  0
loop law :
V2 
N2
V1
N1
i
Electromagnetic Fields and Waves
Pbat  I E
PR  I VR  I 2 R 
 VR 
2
R
Req  R1  R2  R3  ...  RN (series)
1
 1
1
1
1 
Req   

 ... 
 (parallel)
RN 
 R1 R2 R3
Q  Q0 e  t /  I  I 0 e  t /    RC
 E  dA 
Qin
0
 E  ds  
dm
dt
 B  ds   I
0 through

F  q E v B

 qv  rˆ  0 q v sin 
B 0

, RHR 
2
2
4 r
 4 r

I disp   0
Blong straight wire 
0 I
2 d
Bcoil center 
 0 NI
2 R
   AI , from south pole to north pole 
0 2
(on axis of dipole)
4 z 3
 B  ds  o I through
Bdipole 
Bsolenoid 
Fon q
o NI
L
 qv  B   q vB sin  , RHR 
f cyc 
qB
2 m
rcyc 
mv
qB
Fwire  IL  B =  ILB sin  , RHR 
 LI I
Fparallel wires  0 1 2
2 d
    B    B sin  , RHR 
Electromagnetic Induction
E  vlB
Cylinder
Lateral surface
area = 2 rL
Volume =  r 2 L
 B  dA  0
The Magnetic Field

 I s  rˆ  0 I  s  sin 
B 0

, RHR 
2
2
4 r
4 r


vem
  0 0

de
dt
de
dt
 c  1/  0 0
E  cB
1
EB
S
0

PH2100 in Brief
Fnet   Fi  ma
i
FA on B   FB on A
Constant Acceleration :

c
P
 Savg  0 E 2
2
A
F I
(perfect absorber)
prad  
A c
I  I 0 cos 2 
I
I transmitted 
Sphere
Surface area = 4 r 2
Volume = 43  r 3
1
I 0 (incident light unpolarized)
2
xf  xi  vix t + 12 ax  t 
2
yf  yi  viy t  12 a y  t 
2
vfx  vix +ax t
vfy  viy  a y t
vf2x  vi2x  2ax  xf  xi 
vf2y  vi2y  2a y  yf  yi 
Uniform Circular Motion :
2 r
2 rad

T
T
 f   i   t
v
Physical Constants
K  8.99  109 N  m 2 /C 2
 0  8.85  1012 C2 /N  m 2
ar 
v2
  2r
r
e  1.60  1019 C
me  9.11  1031 kg
mp  1.67  1027 kg
0  1.26  106 T  m/A
c  3.00  108 m/s
Energy Conservation
K  12 mv 2
Emech  K  U
Kf  U f  Ki  U i
 m  A  B  AB cos  (uniform B-field)
m 

B  dA
area of loop
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.
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.