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

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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)

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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

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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

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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.

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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

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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

QQ

r

Qk

r

QQk

r

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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

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mr

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CQ

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Nm

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7.21.02

100.12100.1/100.9

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2

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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

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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

QQ

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

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Example: electrostatic painting

Induced positive charge on the metal object attracts the negatively charged paint droplets.

Example: laser printer makes use of forces between charged bodies