
q1q2
F12  ke 2 rˆ
r

q
E  ke 2 rˆ
r


Fe  qE
 
 E   E.dA
surface
Attractive/repulsive force
between charges
Every charge generates
an electric field
Electric Flux
  qin
 E   E.dA 
0
Gauss’ Law
Only charges within the Gaussian
surface contribute to the electric flux
through the surface
 
U  q0  E.d s
B
Electric Potential Energy
A
 
U
V 
   E.d s
q0
A
B
Potential Difference
In a Uniform Field
For a Point Charge
For a Charge Distribution
V   Ed
q
V  ke
r
V
Ex 
x
V
Ey 
y
dq
V  ke 
r
V
Ez 
z




There is no electric field inside a conductor.
The field on the surface is perpendicular to
the surface and proportional to the surface
charge density.
All charges reside on the surface.
Electric potential is constant throughout the
conductor.
Q
C
V
Parallel Plate
Capacitor
For series
capacitors
For parallel
capacitors
Q 0 A
C

V
d
n
1
1

Ceq j 1 C j
n
Ceq   C j
j 1
(C/V=F)
Stored Energy in a Capacitor
Q2 1
1
U
 QV  C (V ) 2
2C 2
2
Capacitor with a dielectric
C  C0
dQ
I (t ) 
dt


J  E
l
R
A
V
R
I

2



V
P  IV  I 2 R 
R
Kirchoff’s
Rules
 V  0  I
closed
loop
in
junction

I
out
junction
1

FB

 
FB  qv  B
B
q
+q
v

 
FB  IL  B
For a closed
loop of current
For a straight wire in
a uniform field
 

τ  IA  B

FB  0


μ  IA
  
τ  μB

U  μ.B
v2
FB  qvB  m
r
mv
r
qB

v qB

r m
T
2r 2 2m


v

qB
Cyclotron frequency
 0 I d s  rˆ
B
4  r 2
 
 B.ds  0 I
For r >= R
0 I
B
2a
For r < R
I 
B   0 02 r
 2R 
B  0 nI
Magnetic Flux
 
 B   B.dA
 
 B.dA  0
Faraday’s Law
d B
E  N
dt
 
d B
 E.ds   N dt
The polarity of the induced
emf is such that it tends to
produce a current that creates
a magnetic flux to oppose the
change in magnetic flux
through the area enclosed by
the current loop.
  Q
 E.dA 
0
Gauss’ Law
 
 B.dA  0
Gauss’ Law for Magnetism –
no magnetic monopoles
 
d B
 E.ds   dt
 
d E
 B.ds  0 I  0 0 dt


 
F  qE  qv  B
Faraday’s Law
Ampère-Maxwell Law
Lorentz Force Law
Displacement
Current
c
1
0 0
  2f

E  Emax coskx  t 
B  Bmax cos kx  t 
E Emax 

 c
B Bmax k
k
c
f
2

Speed of Light
Angular Frequency
Wavelength
Wavenumber
 1  
S
EB
0
I  Sav  cuav
 
2
Bmax
1
2
2
uav   0 E av   0 Emax 
2
20
Complete Absorption
Complete Reflection
Momentum
Pressure
U
p
c
F 1 dp S
P 

A A dt c
p
2U
c
P
2S
c
q1  q1
c
n
v
n1 sin q1  n2 sin q 2
n2
sin q c 
n1
pq
M 1
1 1 1
 
p q f
R
f 
2
h
q
M  
h
p
n1 n2 n2  n1 
 
p q
R
1 1 1
 
p q f
1
1
1 
 n  1  
f
 R1 R2 
M
h
q

h
p
The intensity observed at any point is proportional to
the time average of the sum of the fields incident on
that point.
 If the fields are coherent and monochromatic they can
interfere with each other, creating bright and dark
areas (fringes).
 Destructive or constructive interference depends on
the relative phase of the waves with each other.


  2

Path length difference
  d sin q
Double Slit
  2nt 
Thin Film

Reflection
n1 > n2 : no phase
n1 < n2 :  phase
n1
n2
Relative phase change on reflections
0

m
Const.
Dest.
(m+½)
Dest.
Const.



Rays going through obstacles or openings
can diffract around the edges.
The amount of diffraction depends on the
ratio of the wavelength of the wave to the
size of the opening/obstacle.
The diffracted beam interferes with itself to
create a pattern of bright and dark fringes on
a far away screen.
sin q 
ym 
m
a
m  1,2,3,...
L
m
a
q min 
For circular
apertures

a
q min  1.22

D
A device for spectrally analyzing light sources
d sin q  m




Polarization of a wave is the direction of its electric
field vector.
Ordinary light is unpolarized.
A polarizer passes light only with polarization along
its transmission axis.
If light is incident on a surface at Brewster’s angle, the
reflection is also polarized.
q p  q2  90
n  tan q p
I0
I0 / 2
(I0 / 2)cos2q