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georgina-henderson
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Physics
Mechanics Thermal properties Electromagnetism Optics Atoms & particles
• Electrostatic• Electric current• Magnetism
• Geometrical optics• Wave optics
Condensed Mater High energy Biophysics
Classical physics Quantum physics
Relativistic physics Quantum relativistic physics
1
Electromagnetism(electric and magnetic phenomena)
I. Electrostatics
This is about: electric charges, electromagnetic forces, and electromagnetic fields
This is about: non-moving electric charges, electrostatic forces, and electrostatic fields.
(With very good approximation, electrostatics could be applied to slow moving charges. Slow means that the speed of the considered charge is much smaller then speed of light: v<<c)
2
1b. Elementary charge (smallest isolated charge found in nature)•Electron has negative charge: -e
•Electric charge is quantized in units of e
•Quarks have 1/3e or 2/3e but cannot be isolated
Ce 19106.1
1. Electric charge
1a. Qualitative description•There are two and only two types of electric charges
•Charges of the same type repel, and charges of different type attract (this is already qualitative description of electrostatic forces)
•These two types are referred to as positive and negative (+q and –q)
•Charges can be treated algebraically, and the net amount of electric charges in an isolated system is conserved (is not changed in any process). This is the law of conservation of electric charges
3
4
1c. Electric charge and the structure of matter (atom) (very brief, qualitative description)
•The particles of the atom are the negative electron, the positive proton, and the uncharged neutron.
•Protons and neutrons make up the tiny dense nucleus which is surrounded by electrons
•The electric attraction between protons and electrons holds the atom together.
•A neutral atom has the same number of protons as electrons.
•A positive ion is an atom with one or more electrons removed. A negative ion has gained one or more electrons.
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1d. Electric properties of different materials (classification)
(very brief, qualitative description)
•Conductors - charges can move easily•Insulators - charges cannot move easily•Semiconductors - intermediate between good conductors and good insulators•Superconductors - charges can move without resistance
There are no perfect conductors or perfect insulatorsExamples •Good conductors: most metals, solutions of salts (like tap water)…•Good insulators: plastics, rubber, glass, wood, air, pure water…
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•Although the word comes from the Greek for "rubbing", τρίβω (τριβή: friction), the two materials only need to come into contact and then separate for electrons to be exchanged.
•After coming into contact, a chemical bond is formed between some parts of the two surfaces, called adhesion, and charges move from one material to the other to equalize their electrochemical potential. This is what creates the net charge imbalance between the objects.
•When separated, some of the bonded atoms have a tendency to keep extra electrons, and some a tendency to give them away.
•In addition, some materials may exchange ions of differing mobility, or exchange charged fragments of larger molecules.
1e. Charging by contact. Triboelectric effect + most positiveAirHuman skinLeatherRabbit's furGlassQuartzMicaHuman hairNylonWoolCat's furSilkAluminiumPaper (Small positive charge)Cotton (No charge)0Steel (No charge)AcrylicPolystyreneRubber balloonBrass, SilverGold, PlatinumPolyesterPolyurethaneVinyl (PVC)SiliconTeflonSilicone rubberEbonite− most negative
Stronger repulsion
Charged rod (closer)
Repulsion
Charged rod
Inducted charge
Inducted charge
disk
Gold leaves (or vane)
The electroscope(Charging by contact and by induction)
PositiveNegativeNeutral
7
If we ground the electroscope while the rod is there, the charges in the electroscope that were “escaping” from the rod flow to the ground.
No repulsion
No repulsion
Then we cut the grounding…
Repulsion
Electroscope charged by induction
And remove the rod…
The electroscope is now charged.The charge spreads now all over the object.
8
2. Electrostatic forces (Coulomb’s law)
221
r
QQkF
Q1 Q2r constantty permittivi
1085.8
/1099.84
1
0
22120
229
0
mNC
CmNk
Units:
Example:
?
10.0
100.3
100.26
2
61
F
mr
CQ
CQ
NF
m
CCCNmF
4.5
1.0
100.3100.2/100.9 2
66
229
9
AI
sACQ
1][
111][
IdtdQdt
dQI
Q1 Q2r
Q1 and Q2 have the same sign Q1Q2 >0
21F
12F Q1 Q2r 21F
12F
2a. Coulomb’s law in vector form
2b. Principle of superposition: ...21 FFFnet
Q1 and Q2 have opposite signs Q1Q2 <0
10
r
r
r
QQkFF 12
221
2112
N
CC
m
CCNm
r
Qk
r
QQk
r
QQkF
9.04
100.12100.2
1.0
100.1/100.9
42
66
2
6
229
322
1231
221
1
Example:Q1 Q3r
13F
12F
Q2 r
13121
13121
FFF
FFF
?
10.0
0.12
0.2
0.1
1
3
2
1
F
mr
CQ
CQ
CQ
NNNFFF
Nm
CCCNm
r
QQkF
Nm
CCCNm
r
QQkF
9.07.28.1
7.21.02
100.12100.1/100.9
2
8.11.0
100.2100.1/100.9
13121
2
66
2292
3113
2
66
2292
2112
11
Example:
Q
Q Q
Q
a
321
2
2
3
2
2
21
2
FFFF
a
QkF
a
QkFF
tot
1F
2F
3F
Nm
CCNmF
a
Qk
a
Qk
a
QkFFF
tot
tot
7.110.0
101.0 /1099.8
2
12
2
12
222
2
26-229
2
2
2
2
2
2
31
?
10.0
0.1
F
ma
CQ
12
Example: A 4.7μC and a -3.5μC charge are placed 18.5 cm apart. Where can a third charge be placed so that it experiences no net force?
x
–
Q
d
To experience no net force, the third charge Q must be closer to the smaller magnitude charge (the negative charge). The third charge cannot be between the charges, because it would experience a force from each charge in the same direction, and so the net force could not be zero. And the third charge must be on the line joining the other two charges, so that the two forces on the third charge are along the same line. Equate the magnitudes of the two forces on the third charge, and solve for x > 0.
CQ 7.41 CQ 5.32
cmcm
dx
xdxQ
Qxdx
Q
Q
x
QQk
xd
QQkFF
11615.3/7.4
5.18
1/ 21
2
122
2
12
2
2
121
13
Example: Compare the gravitational attraction and the electric repulsion of two electrons
19
31
1.6 10 C
9.1 10 kg
e
m
2
2
r
ekFE
2
2
r
mGFG
422312211
219229
2
2
102.4101.9107.6
106.1100.9
kgkgNm
CCNm
Gm
ke
F
F
G
E Big!
Example: A student can resist a force of 100 lb (450 N) with his arms apart. You give him two charged balls with charges Q and Q to hold on each hand. How large a charge Q can he hold outstretched?
Q -Q
r ~ 1.5 m
2
2
r
QkF
2-4
max max 3.35 10e
rQ F C
k
-314 -15
-19
1 9.1 103.35 10 2 10
1 1.6 10
electron kgC kg
electronC
Less than a cell in your body!14