Download final_review1

Electrostatics
1. Charge  force:
•
•
Like sign charges repel, unlike sign
charges attract.
Coulomb’s Law: direction and magnitude of
force between two point charges.
2. Force  electric field:
•
•
•
Introduced to explain interaction over a
distance.
Field lines: start from positive charge, end
at negative charge.
More often used as:
q1q2
F  k0 2
r


F
E
qtest


F  qE
3. Force  charge:
•
•
Force moves charge, does work on charge.
Electric potential.
4. Electric field  charge:
•
•
A
Electric flux:
Electric field originated from charge: Gauss’
Law.
E 
 
U (A  B)    F  dr
B

enclosed surface
 
 E   E  dS
  q
E  dS 
0
1
Direct Current
1. Moving charge  current:
•
•
Electric field inside a conductor keeps the
charges moving.
Current direction is defined as the electric
field direction.
I
dq
dt
2. Charge  electric potential:
•
•
•
Accumulated charge generates potential: C  Q C   A
0
capacitance.
V
d
Parallel plate capacitor.
1
1 Q2
2
Energy stored in a capacitor.
PE  CV 
2
3. Current  resistance:
•
•
•
Ohm’s law defines resistance.
Resistance as a function of the wire.
Resistance as a linear function of
temperature.
4. Power
•
•
2 C
L
V  IR R  
A
R(T2 )  R(T1 )  1   (T2  T1 )
General formula.
With a resistor only (combined with Ohm’s
law).
P  VI
V2
P  VI 
 I 2R
R
2
Circuits
1. Resistors network:
•
•
•
Connection in series, current the same,
voltage divided.
Connection in parallel, voltage the same,
current divided.
Questions with power: nominal power v.s.
actual power.
2. Capacitors network:
•
•
Connection in series, the same charge,
voltage divided.
Connection in parallel, the same voltage,
charge divided.
3. Kirchhoff’s rules
•
•
•
Loop:
Junction:
Follow the steps.
4. RC circuit
•
•
•
Charging.
Discharging.
The time constant.
V
loop
I
0
t
emf 
I
e
R
Reff  R1  R2  ...  Rn
1
1
1
1
 
 ... 
Reff R1 R2
Rn
1
1
1
1
 
 ... 
Ceff C1 C2
Cn
Ceff  C1  C2  ...  Cn
junction
0
t
Q 
I
e
RC
  RC
3
Magnetism and Induction
1. Current (moving charge) generates
magnetic field.
•
•
The Biot-Savart law and Ampere’s law.
B-field of a straight wire, at the center of a
wire loop, inside a solenoid and the righthand rules.
2. Force on a charge from the E and B fields:
•
The Lorentz force law.
0 I
0 I
B
B
B  0 In
2R
2R


 
F  qE  qv  B
3. Induction of emf from changing magnetic
flux.
•
•
 
d B
emf  LvB emf   E  ds  
dt
Motion emf.
Faraday’s law, Lenz law.
4. Self-induction and the inductor
•
•
•
•
Self-induction
Magnetic energy in an inductor
Inductor and the LR circuit.
The LC circuit.
I  I MAX sin( t )  2 
1
LC
emf self
dI
 L
dt
1 2
PE  LI
2
t

emf
I
(1  e  )
R
I  I 0e

t


L
R
4
Alternating Current and the circuits
1. AC
•
•
AC voltage power supply.
Average voltage, current and power.
VMAX  2Vrms
V  VMAX sin( t )
PMAX  2 Prms
I MAX  2I rms
2. R, C and L in AC circuit
•
•
•
R, Ohm’s law applies.
C, current leads voltage by 90o
L, voltage leads current by 90o
3. RLC in AC circuit
•
•
Impedance Z
Phase angle φ
I  I MAX sin( t   ) 
VMAX
sin( t   )
Z
Z  R 2  ( X L  X C )2 tan  
•
Resonance frequency
1
X L  XC ,  
LC
•
Power consumed in an AC circuit.
2
prms  I rms
R  I rmsVrmscos
X L  XC
R
2
0
5
Optics -- reflection
1. The law of reflection
•
 r  i
Angles in optics are always measured with
respect to the normal of the interface.
2. Planary mirror
•
•
The virtual image has the same distance to
the mirror as the object does.
The magnification is 1.
3. Spherical mirors
•
•
•
•
•
•
R
f  ( )
2
Converging and diverging mirrors.
Focal length and the radius.
Mirror equation and the sign conventions.
h
d
The magnification.
m i  i
ho
do
The 3-ray diagram.
Multi-mirror problems.
1 1 1
 
do di
f
6
Spherical mirror
 The 3-ray diagram:
Magnification M

Ray 3 begins as an
incident ray that
passes through the
center of curvature,
strikes the mirror
perpendicularly, and
reflects back,
moving along the
same line as the
incident ray.
hi
d
 i
ho
do
h
o
hi
Ray 2 starts as an
incident ray that passes
through the focal point
and then reflects parallel
to the principal axis.
Ray 1 starts as an incident
ray that is parallel to the
principal axis. It reflects off
the mirror and passes
through the focal point after
it reflects.
Image up-side-down,
smaller, real
7
Spherical mirror
 The 3-ray diagram, convex mirror:
Image always upright, smaller, virtual
8
Optics -- refraction
1. Index of refraction
•
Light travels slower in medium than in
vacuum.
2. refraction
•
•
Snell’s law
Total internal reflection.
n
n1sin 1  n2sin 2
n1sin c  n2 so n1  n2
3. Lens
•
•
•
•
•
c
v
Focal length and the radius, lens maker’s
equation.
lens equation and the sign conventions.
The magnification.
The 3-ray diagram.
Multi-lens problems.
1 1 
1
 ( n  1 )  
f
 R1 R2 
1 1 
nlens
1
(
 1 )  
f
nmedium
 R1 R2 
1 1 1
 
do di
f
m
hi
d
 i
ho
do
9
Find image with a thin lens
 Converging lens
h
o
F
d
o
Object
F
hi
di
magnificat ion : m   
ho
do
f
di
hi
Real image,
inverted,
smaller
10
Find image with a thin lens
 Diverging lens
h
o
d
o
Object
hi
F
F
di
Virtual image,
upright,
smaller
f
hi
di
magnificat ion : m   
ho
do
11