handout lecture01 introduction and vector analysis

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FI 2201 Electromagnetism

Alexander A. Iskandar, Ph.D.Physics of Magnetism and Photonics Research Group

General Information• Lecture Schedule :

18 19 R120127 28 R????

• Tutorials57 58 R9132Teaching Assistant : Mr. Andika Putra.During the tutorial there will be several Quizes and average mark of the Quizes will be one of the component of the Final Mark

Electromagnetism

Mark

• Walk Out time : 20 minutes• Textbook :

Introduction to Electrodynamics, D. J. Griffiths, Prentice Hall, 1991.

2Alexander A. Iskandar

2

General Information• Evaluation :

2 Midterm Exams (15/3 and 10/5)A Re-evaluation Exam, if taken will replace the worst mark of Midterm Exam

• Expected Exam Answer :Answer should show good understanding of the physical phenomena considered in the problem, as evident by sound arguments and clear and correct steps in finding the solution.The use of correct formulas and notation (vector and scalar) and the right units

Electromagnetism

the right units.Final correct numerical value (if asked).


Introduction

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The Realm of Mechanics and Electromagnetism

Electromagnetism

• Electromagnetism is the ONLY theory that is well understood in all realm of mechanics.


Early Observation of ElectricityObservation from early Greeks time.If you rubbed a piece of amber, it will attract bits of straw.attract bits of straw.If you rubbed two pieces of amber, they will repels each other.Thus there are two results from one phenomena.There is a another force of nature aside gravity

Electromagnetism

aside gravity.

Alexander A. Iskandar 6

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Origin of Electricity : Electric ChargeNeeds a physical quantity to specify the property of a material with specific response of this phenomena.This physical quantity is called (electric) charge.Two types of charges: positive and negative

Like charges repel (unlike gravity)Opposite charges attract (like gravity)

Electromagnetism

Opp g ( g y)


Particles Discovered 1898 – 1964

ElectromagnetismAlexander A. Iskandar 8

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Particles Discovered since 1964


Interlude: The Strong Nuclear Force• In early 1960s there was a particle

explosion – in the time span of weeks new particles were discovered.

• The particles cannot be explained with the known theories at that time (electromagnetism).

• Need a new theory !! Hence new physical quantity that goes with this

Electromagnetism

p y q y gtheory !!

• The theory states that these particles were not elementary !!


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Interlude: The Strong Nuclear Force• These particles were build up from

smaller constituents called the QUARKS. Some particles consist of 3 quarks, others consist of 2 quarks.

• Interaction between the quarks cannot be seen from far away.

• Hence need a physical quantity like charge that has to be of three kinds

Electromagnetism

gand are invisible from far away →color charge.


Interlude: The Strong Nuclear Force3/22/2010

Mesons consist of a quark-antiquarkpair, while baryons consist of three

quarks.


The current view of how matter is composed of basic units.

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The Structure of an Atom


The Four Forces of Nature


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Fundamental Interactions of Nature


Comparison between the two Forces• Determine the electrostatic force and the gravitational

force between an electron and a proton that is separated 1 m apart

( )( )

mm

N

rQQkFC

28219

9

221

103.21106.1109 −

−

×=×

×=

=r

Gravity is 1040

times weaker


( )( )( ) N

rmmGFG

682731

11

221

10015.11

1067.11011.91067.6 −−−

− ×=××

×=

=r

than Electrostatic

force.

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Interaction Strength


The Ultimate Goal of Physics: Unification of All Forces

GRAVITATION

MAGNETISMELECTRICITY

WEAK

ELECTROWEAK

SINGLE FORCE?

GRAVITATION

ELECTROMAGNETISM


STRONG

GRANDUNIFICATION

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Unification : the Standard Model• Description of strong, weak, and electromagnetic

interactions• No known discrepancy with particle physics experimentsNo known discrepancy with particle physics experiments• Three types of fundamental particles

Stuff things are made of – spin ½Force carriers – spin 1Higgs field – spin 0


Fundamental Particles• There are only 12

fundamental particles of matter (also the antiparticles)


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Fundamental Particles


Interaction in Field Formulation• Action at a Distance – Electric Field• How do we explain the nature of non-contact force or

“force at a distance” between two charges?force at a distance between two charges?

• The concept of “Electric Field” - a charge creates an “electric field” in the space around it. Other charges interact with this field.

• The nature of an Electric Field - an electric field has a defined magnitude and direction at all points in space

Electromagnetism

defined magnitude and direction at all points in space. I.e. it is a vector field.


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Sources in Electromagnetism• Electric charge :

two typesconservedthe number of positive and negative charges exactly the same, compare gravity and electrostatic forces (if there are excess charges on the moon → the orbit won’t be like what is predicted by gravity alone)quantizedalthough there are fractional charges but there are not observed individually

Electromagnetism

y

• For accelerated charges, a portion of the field “detaches” and travel off at the speed of light – electromagnetic radiation.


Syllabus• Continuation and extension of classical electricity and

magnetism phenomena that have been introduced in the Fundamental Physics course. The aim of this course is to introduce a unified formulation of electric and magnetic phenomena as one of the fundamental interaction in nature. The main topics considered in this course are

Electrostatics, Techniques in solving Electric Potential, Electric field in matter,

Electromagnetism

Magnetostatics, Magnetic field in matter, Electrodynamics and an introduction to Electromagnetic wave.


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Vector Analysis

REVIEW ON VECTOR QUANTITIES

Vector Quantity• Graphical representation and transformation graphically.• A vector can be identified by specifying its three Cartesian

components:components:

zAyAxA zyx ˆˆˆ ++=A

Unit vectors

z axis

y axis

A

• Operations on Vectors :

Electromagnetism 26Alexander A. Iskandar

x axis

pTo add vectors, add like componentsTo multiply a vector by a scalar, multiply each components

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Operations between vectors• The dot product of two vectors is obtained by multiplying

like components and add:BABABA ++=⋅BA

• This operation is also called inner product and it yielded a scalar quantity, it is needed for finding distance.

zzyyxx BABABA ++=BA


Operations between vectors• The cross product of two vectors is obtained from the

determinant:

zyx ˆˆˆ

the Levi-Civita tensor

ikjijk

zyx

zyx eBABBBAAAzyx

ˆε==×BA

⎪

⎪⎨

⎧−+

=ε npermutatiooddanis)(if1npermutatioevenanis)(if1

ijkijk

ijk

Electromagnetism

• This operation yielded a vector quantity and it has anticommuting property as can be seen from the property of the Levi-Civita tensor.


⎪⎩ otherwise0

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Vector Transformation• The components of a vector

depend on the choice of the coordinate system.

• Different coordinate system will produce different components for the same vector.

• The choice of coordinate system being used can significantly change the complexity of

Electromagnetism

g p yproblems in electrodynamics.


Vector Transformation• The coordinates of vector in

coordinate system S are related to the coordinates of vector in

Ar

Ar

coordinate system S′ by

• The rotation considered here leaves the x axis untouched. Thex coordinate of vector will thus

⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛−

=⎟⎟⎠

⎞⎜⎜⎝

⎛

′

′

z

y

z

y

AA

AA

φφφφ

cossinsincos

Ar

Electromagnetism

x coordinate of vector will thus not change:


A

ARAAA

AAA

x

z

y

x

z

y

x rt⋅=

⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛

⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛

−=

⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛

′

′

′

φφφφ

cossin0sincos0001

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Vector Transformation• The 3 by 3 transformation matrix is the matrix

representation of the transformation tensor .• Coordinate transformation resulting from a rotation around

Rt

Coordinate transformation resulting from a rotation around an arbitrary axis can be written as:

or, more compactly,

⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛

++++++

=⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛

⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛

=⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛

′

′

′

zzzyzyxzx

zyzyyyxyx

zxzyxyxxx

z

y

x

zzzyzx

yzyyyx

xzxyxx

z

y

x

ARARARARARARARARAR

AAA

RRRRRRRRR

AAA


∑=

=′→⋅=′3

1jjiji ARAARA

rtr

Vector Transformation• The rotation matrix is an example of a unitary

transformation: one that does not change the magnitude of the object on which it operates:

Rt

• If is unitary, thenAAAAandARA =′→=′⋅=′

rrrtr

∑=

δ=3

1ijkikij RR

⎧ =if1 kj

Rt

Electromagnetism

where (Kronecker delta)


⎩⎨⎧ =

=δotherwise0if1 kj

jk

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Vector Transformation• A reflection or inversion is given by the transformation

matrix: which changes the right-handed coordinate system into a left-handed coordinate system.

ijijR δ−=

z axis

x axis

y axis

rrz’ axis

x’ axis

y’ axis

r ′r

Electromagnetism

• The vector transform into . Reversing the direction of the coordinate system and changing the sign of the components give .

• Vectors with this property are called polar vectors.


),,( zyxr =r

rr rr ′=

),,(),,( zyxzyxr −−−=′′′=′r

Vector Transformation• A fundamental difference is encountered when a vector is

defined as the cross-product of two polar vectors, , . and are polar vectors. When the coordinate axes are

BACrrr

×=Br

Ar

inverted, the cross-product vector does not behave like polar vectors under inversion, i.e

iikkjjkjijki CCBBAABAC ′+→′−→′−→ε= yields,with,

Cr

z’ axis

x’ axisCr

y axis

Ar

Br

A′r

Br′

Electromagnetism

• Vectors with this property are called axial or pseudo-vectors. Magnetic field is an example of a pseudo vector.


y’ axisz axis

x axis

B

Cr′

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Relative Position• Most of the time, we will consider sources at and we

wanted to know the electric field at an observation point .r ′r

rr

Pq1

q2 qi

irr

irr

ir ′r

Electromagnetism

• Define the relative position as


rrrrrr′−′−

=′−= rr

rrrrr rr ˆ

handout lecture01 introduction and vector analysis

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