SCS CS 139 39 Applied plied Ph Physics ysics II Dr. Prapun - - PowerPoint PPT Presentation

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SCS CS 139 39

Applied plied Ph Physics ysics II

• Dr. Prapun Suksompong

prapun@siit.tu.ac.th www.prapun.com

Office Hours: Library (Rangsit) Mon 16:20-16:50 BKD 3601-7 Wed 9:20-11:20

About Me

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 Ph.D. from Cornell University, USA  In Electrical and Computer Engineering  Minor: Mathematics (Probability Theory)  Ph.D. Research: Neuro-Information Theory

 Modeling and analyzing neurons in human brain

from communication engineering perspective.

 Current Research: Wireless Communication

 Mobile Communications, WiFi (802.11)

 2009 SIIT Best Teaching Award  2011 SIIT Research Award

prapun.com

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 Please check the course website

regularly.

 Announcements  References  Handouts (Posted before

corresponding lectures)

 Annotated Notes/Slides (Posted

after corresponding lectures)

 Assignments and Solutions

Course Web Site

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www2.siit.tu.ac.th/prapun/scs139/

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Course Website: Notes & Slides

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 Some PDF notes/slides will be posted before the corresponding

lectures.

 Hard copies can be purchased from the copy center.

 In lectures…

 PDF notes/slides will be highlighted and updated with examples /

comments.

 The annotated pdf files will be posted after the corresponding

lectures.

 Put all of your energy into understanding the material.

 Remind me the day after the lecture if the notes/slides from the

day before are still not posted on the web.

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SCS CS 139 39

II II.1 1 Ma Magnetic tic Force ces s an and Fields elds (I (I)

• Dr. Prapun Suksompong

prapun@siit.tu.ac.th

B

F qv B   F iL B  

Office Hours: Library (Rangsit) Mon 16:20-16:50 BKD 3601-7 Wed 9:20-11:20

Reference

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 Principles of Physics  Ninth Edition, International Student Version  David Halliday, Robert Resnick,

and Jearl Walker

 Chapter 28 Magnetic Fields

 28-1 What Is Physics?  28-2 What Produces a Magnetic Field?  28-3 The Definition of 𝐶  28-6 A Circulating Charged Particle  28-8 Magnetic Force on a Current-

Carrying Wire

 28-9 Torque on a Current Loop

Magnet

7

What Produces a Magnetic Field?

8

 Use moving electrically charged particles,

such as a current in a wire, to make an electromagnet.

 Magnetic field is a basic characteristic of elementary particles

(such as electrons) just as mass and electric charge (or lack of charge) are basic characteristics.

 These particles have an intrinsic magnetic field around them.  Permanent magnet: The magnetic fields of the electrons in

certain materials add together to give a net magnetic field around the material.

 In other materials, the magnetic fields of the electrons cancel

• ut, giving no net magnetic field surrounding the material.

Applications

9

 You are surrounded by magnets.  Old: Magnetic recording of music and images on audiotape and

videotape.

 Magnets control CD and DVD players and computer hard drives.  Magnets drive the speaker cones in headphones, TVs, computers,

and telephones.

 A modern car comes equipped with dozens of magnets because

they are required in the motors for engine ignition, automatic window control, sunroof control, and windshield wiper control.

 Most security alarm systems, doorbells, and automatic door

latches employ magnets.

Application: Neodymium magnet toys

10

 NeoCube, BuckyBalls, CyberCube, EuroCube, MagCube

Magnetic stripe (magstripe)

11

 Credit, debit, and ATM cards: All of these cards have a

magnetic strip on one side.

 The magstripe is made up of tiny iron-based magnetic

particles (about 20 millionths of an inch long) in a plastic-like film.

Hard disk drives

12

 Hard disk drives record data on a thin magnetic coating

Magnetic resonance imaging

13

Collect and transport scrap metal

14

 Using an electromagnet to collect and transport scrap metal

at a steel mill.

Magnetic Field Lines

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 the field around an ordinary bar magnet

Viewing the field

16

S N

Magnetic Field Viewers

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 Magnetic field viewing film

iPad 2 - Smart Cover + Magnets

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Turn off the iPad 2's screen. The rest are used to either clamp to the iPad on the right side (the far-right column of magnets), or to form the triangular shape used to create a stand for the iPad 2.

iPad 2 - Smart Cover + Magnets

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Ferrofluid

20

Magnetic Field Lines

21

 Run from the north pole to the south pole.

bar magnet horseshoe magnet C-shaped magnet

Magnetic Field (𝐶 ) and Field Lines

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 A vector quantity.  We can represent magnetic fields

with field lines.

 Rule 1: The direction of the tangent

to a magnetic field line at any point gives the direction of 𝐶 at that point

 Rule 2: The spacing of the lines

represents the magnitude of 𝐶

 The magnetic field is stronger where

the lines are closer together, and conversely.

Unit for B

23

 B = magnitude of 𝐶  SI Unit: tesla (T)

 Defined in 1960 in honour of Nikola Tesla

 Earlier non-SI unit: “gauss”  1 T (tesla) = 104 G (gauss)  Some approximate magnetic fields:

 Earth’s magnetic field near the planet’s surface:

1 G = 100 T

 In magnetically shielded room

(MSR): 10-14 T = 10 fT

2

N N s T Cm/s Cm N N C/sm A m Wb m     

Earth's Magnetic Field

24

 On Earth’s surface, we can detect magnetic field

with a compass, which is essentially a slender bar magnet.

 The earth’s geographical

north pole is actually its magnetic south pole.

 Magnetoception:

Migratory birds and sea turtles can sense the earth’s magnetic field, using it for navigation.

MEG

25

 Magnetoencephalography  A powerful and noninvasive

method for studying human brain activity.

 Work by detecting the tiny

(femtotesla) magnetic fluctuations at the surface of the head that arise from the brain’s electrical activity.

Uniform 𝐶

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 Array of dots (which represent the

tips of arrows) represents a field directed out of the plane.

 Array of Xs

represents a field directed into that plane.

Magnetic Forces and Fields

27

 Charged particle moving through a magnetic field

experience magnetic force.

 A magnetic field 𝐶

is defined in terms of the force 𝐺

𝐶

acting on a test particle with charge q moving through the field with velocity 𝑤 :

 The magnitude of 𝐺

𝐶:

B

F qv B   sin

B

F q vB  

Example

28

 A uniform magnetic field with magnitude 1.2 mT, is directed

vertically upward throughout the volume of a laboratory

• chamber. A proton enters the chamber, moving horizontally

from south to north with speed 3.2107 m/s.

 What magnetic deflecting force acts on the proton as it

enters the chamber? (Neglect Earth’s magnetic field.)

Direction of 𝐺

𝐶

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 Right-hand rule: The thumb of the right hand points in the

direction of 𝑤 × 𝐶 when the fingers sweep 𝑤 into 𝐶 .

 Perpendicular to the direction of 𝑤  Perpendicular to the direction of 𝐶

B

F qv B  

Exercise

30

A Charged Particle Circulating in 𝐶

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A charged particle with mass m and charge magnitude |𝑟| moving with velocity 𝑤 perpendicular to a uniform magnetic field 𝐶 will travel in a circle. The magnetic force plays the role of centripetal force.

Uniform 𝐶

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A Charged Particle Circulating in 𝐶

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 The radius r of the circle is  The period T is given by | | mv r q B  2 2 | | r m T v q B    

Example: Mass spectrometer

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 An ion of mass m (to be

measured) and charge q is produced in source S.

 The initially stationary ion is

accelerated by the electric field due to a potential difference V.

 The ion leaves S and enters a separator chamber in which a

uniform magnetic field is perpendicular to the path of the ion.

 A wide detector lines the bottom wall of the chamber, and

the 𝐶 causes the ion to move in a semicircle and thus strike the detector.

Example: Mass spectrometer

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 Suppose that B = 80.000 mT, V = 1000.0 V

, and ions of charge q = +1.6022×10-19C strike the detector at a point that lies at x = 1.6254 m.

 What is the mass m of the individual ions?

B

F

Magnetic Force on a Current-Carrying Wire

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A straight wire carrying a current i in a uniform magnetic field experiences a sideways force

F iL B   sin F iLB  

𝑀 is a length vector that has magnitude L and is directed along the wire segment in the direction of the (conventional) current.

Exercise

37

Example

38

Application: Loudspeaker

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 The permanent magnet creates a magnetic field that exerts forces

• n the current in the voice coil.

 For a current I in the direction shown, the force is to the right.  If the electric current in the voice coil oscillates, the speaker cone

attached to the voice coil oscillates at the same frequency.

Magnetic Force on a Current-Carrying Wire

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 Note that it does not matter whether we

consider negative charges drifting downward in the wire (the actual case) or positive charges drifting upward. The direction of the deflecting force on the wire is the same.

dF idL B    If the wire is not straight or the field is not uniform,

 we can imagine the wire broken up into small straight segments.

 In the differential limit, we can write

 The force on the wire as a whole is then the vector sum of all the

forces on the segments that make it up.

Torque on a Current Loop

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 Electric motor.  A rectangular loop of wire,

carrying a current and free to rotate about a fixed axis, is placed in a magnetic field.

 Magnetic forces on the wire

produce a torque that rotates the loop.

Side 2 Side 4

Normal vector

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 To define the orientation of the

loop in the magnetic field, we use a normal vector 𝒐 that is perpendicular to the plane of the loop.

 Useful Fact: The loop will rotate

so that 𝑜 has the same direction as 𝐶.

Right-hand rule: To find the direction

• f 𝑜, point or curl the fingers of your

right hand in the direction of the current at any point on the loop. Your extended thumb then points in the direction of the normal vector .

Forces

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𝐺 1 = 𝐺 3 = 𝑗𝑏𝐶

The normal vector 𝑜 is shown at an arbitrary angle  to the direction of 𝐶.

𝐺 2 = 𝐺

4 = 𝑗𝑐𝐶 sin 90 − 𝜄 = 𝑗𝑐𝐶 cos 𝜄

 𝐺

2 and 𝐺

4 have the same magnitude but opposite directions.

Thus, they cancel out exactly. Their net force is zero.

 𝐺

1 and 𝐺

3 have the same magnitude but opposite directions. Thus, they do not tend to move the loop up or down.

Torques

43

 𝐺

2 and 𝐺

4: Their common line

• f action is through the center
• f the loop. Therefore, their

net torque is also zero.

 𝐺

1 and 𝐺 3: Do not share the same line of action; so they produce a net torque.

r F   

2 sin sin sin 2 b iaB iabB iAB                   

Area enclosed by the coil

General formula

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 Use a coil of N loops or turns  Flat coil assumption: Assume that the turns are wound

tightly enough that they can be approximated as all having the same dimensions and lying in a plane.

 Total torque  The formula holds for all flat coils no matter what their

shape.

 For the circular coil, we have sin NiAB   

Area enclosed by the coil

2 sin

Ni r B    

Strong Magnets Can be Dangerous

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magnet Think of the pencil as your finger

Strong Magnets Can be Dangerous

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1

SCS CS 139 39

II.2 .2 Ma Magne netic tic For

• rce

ces s an and Fields elds (I (II)

• Dr. Prapun Suksompong

prapun@siit.tu.ac.th

Office Hours: Library (Rangsit) Mon 16:20-16:50 BKD 3601-7 Wed 9:20-11:20

2

ˆ 4

enc

i ds r dB r B ds i       



Magnetic Field Due to a Current in a Long Straight Wire

3

 Fact: When a current flows

through a wire, it can produce a magnetic field.

 For long (infinite) straight wire

carrying a current i,

i B R 

Perpendicular distance

Another Right-Hand Rule

4

Wrap your right hand around the wire with your thumb in the direction of the current. The fingers reveal the field vector’s direction, which is tangent to a circle.

Application: Magnetic field of two wires

2

 Computer cables, or cables for audio-video

equipment, create little or no magnetic field.

 This is because within each cable,

closely spaced wires carry current in both directions along the length of the cable. The magnetic fields from these opposing currents cancel each other.

Contribution of a small piece

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Biot-Savart Law: The contribution 𝑒 𝐶 to the magnetic field produced by a current-length element 𝑗 𝑒 𝑡 at a point P located a distance r from the current element can be found by:

permeability constant = 4×10-7 T∙m/A  1.26×10-6 T∙m/A

2 2

ˆ 4 sin 4 i ds r dB r ids dB r        

(experimentally deduced)

Recipe

6

To find the magnetic field produced at a point

 Step 1: Find the contribution from each (single) current-

length element

 Step 2: Integrate (superimposing/adding/summing the

contributions from all current-length elements) to find the net field produced by all the current-length elements.

2

ˆ 4 i ds r dB r     B dB  

Ex 1: Long (infinite) straight wire

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 

2 2 2 3 3 2 2 2 2

sin( ) 4 sin( ) 2 4 4 1 1 2 2 1 2 2 i ds dB r i i R r B ds ds r r iR iR ds ds r s R iR i R R                

    

       

   

• Difficult. Easier to derive via the Ampere’s law. (TBD)

Ex 2: Easy case

8

 Consider a wire consists of two straight sections (1 and 2)

and a circular arc (3), and carries current i.

 What magnetic field (magnitude and direction) does the

current produce at C?

 For now, focus on the two straight sections (1 and 2).

 Their extensions intersect the center C of the arc.

Conclusion: Current directly toward or away from C does not create any magnetic field there.

Ex 3: At center of a circular arc of wire

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 Consider only point P at the center of the arc (point C)

2 2 2

sin(90 ) 4 4 4 4 i ds i ds i R d dB r R R i B R              

Ex 2: (a revisit)

10

 Consider a wire consists of two straight sections (1 and 2)

and a circular arc (3), and carries current i.

 What magnetic field (magnitude and direction) does the

current produce at C?

1 2 4 8 i i B R R      

Ex 4: Magnetic Field of a Coil

11

Consider point P on the central perpendicular axis of the loop

 

2 3 2 2 2

2

• iR

B R z    A Current-Carrying Coil as a Magnetic Dipole: Observation: One side of the loop acts as a north pole and the other side as a south pole, as suggested by the lightly drawn magnet.

Ex 4: Derivation

12

From the symmetry, the vector sum of all the perpendicular components due to all the loop elements is zero.

 

2 2

sin 90 4 4 i ds i dB ds r r      

   

 

// 3 2 2 2 3 2

cos cos 4 4 4 i d dB iR iR ds ds r R z B ds r             

   

 

 

3 2 2 2 // 3 3 2 2 2 2 2 2 2

2 4 4 2 i iR R z R iR B dB ds R R z R z             

 

 

cos R r  

Force Between Two Parallel Currents

13

 Two long parallel wires carrying currents exert forces on

each other.

 

sin 90 2 2

a a b ba b a b

i Li i F i LB i L d d             

Force Between Two Parallel Currents

14

 Two long parallel wires carrying currents exert forces on

each other.

 Two wires with parallel

currents attract each other.

 Two wires with antiparallel

currents repel each other.

Applications

15

 Basis for the definition of ampere

 The ampere is that constant current which, if maintained in

two straight, parallel conductors of infinite length, of negligible circular cross section, and placed 1 m apart in vacuum, would produce on each of these conductors a force of magnitude 2×10-7 N/m of wire length.

 Rail gun

Exercise

16

 Three long straight parallel equally-spaced wires with

identical currents either into or out of the page.

 Rank the wires according to the magnitude of the force on

each due to the currents in the other two wires, greatest first.

Net 𝐶

17

 Net magnetic field

due to the three currents:

𝑪

i1 i2 i3

Ampere’s Law

18

0 enc

B ds i   



Net current encircled by (passing through) the loop cos d B s    The field component tangent to the loop

ienc

19

 Use the curled–straight right-hand

rule to determine the signs for currents

 May have to integrate the current

density.

 For conducting cylinder,

enc

i J dA  



1 2 enc

i i i  

  

2

enc

i J r r dr   

Remark: The integration is over the area encircled by the loop.

Exercise

20

Choosing the Amperian Loop

21

 Use one that create symmetry.  Draw the loop so that 𝐶cos𝜄 is constant.  In which case, cos B ds B ds   

 

In addition, if the magnetic field is always tangent to the loop

B ds B ds  

 

Example: Long Straight Wire with Current

22

 B outside:  B inside:

With uniformly distributed current,

 

2 2 B r B ds i i B r       



 

2 2 2

2 2 r B r B ds i R i r B R               



Application

23

 Magnetic fields are associated with a signal-carrying coaxial cable.  If the current is the same magnitude in each direction, the

magnetic field outside the coaxial cable is zero.

 The absence of

𝐶 fields around a coaxial cable results in no interference in nearby electrical equipment and wires

Ex: Magnetic Field of a Solenoid

24

A solenoid carrying current i. A vertical cross section through the central axis of a “stretched-out” solenoid.

 The field inside the coil is fairly

strong and uniform over the cross section of the coil.

 At points inside and reasonably far

from the wire, 𝐶 is approximately parallel to the (central) solenoid axis.

 The external field, however, is

relatively weak.

Ex: Long Ideal Solenoid

25

 Infinitely long  Consist of tightly packed (close-packed) turns of square wire  The magnetic field outside the solenoid is zero.  This is practically holds for real solenoid if

 its length is much greater than its diameter  we consider points that are well away from the solenoid ends

0 enc

B ds i   



 

i h Bh B n n i    

#turns per unit length

1

SCS CS 139 39

II.3 .3 Induction duction an and Inductance ductance

• Dr. Prapun Suksompong

prapun@siit.tu.ac.th

Office Hours: Library (Rangsit) Mon 16:20-16:50 BKD 3601-7 Wed 9:20-11:20

B L

d dt di L dt     

Reference

2

 Principles of Physics  Ninth Edition, International Student Version  David Halliday, Robert Resnick,

and Jearl Walker

 Chapter 30

 30-2 Two Experiments  30-3 Faraday’s Law of Induction  30-4 Lenz’s Law  30-7 Inductors and Inductance  30-8 Self-Induction  30-9 RL Circuits

Review + New Fact

3

 Review

 Force occurs when a charged particle moves through a magnetic

field.

 Force occurs when a current-carrying wire is placed in a

magnetic field.

 Magnetic field is found around a current-carrying wire.

 New Fact: Change in magnetic field can produce

(induce) a current in a loop of wire

Application: TMS

14

 TMS = Transcranial Magnetic Stimulation  A technique for studying (or stimulating or deactivating

(suppressing)) the function of various parts of the brain.

 A coil held to the subject’s head carries a varying electric

current, and so produces a varying magnetic field. This field causes an induced emf, and that triggers electric activity in the region of the brain underneath the coil.

Experiment 1

4

 Moving a magnet bar toward or away from a (conducting) loop

• f wire can produces (induces) a current in the loop.

 The current produced in the loop is called an induced current.  Observation:

 Current only occurs when there is a

relative motion between the loop and the magnet.

 Faster motion produces a greater

current

 Direction (CW or CCW) of the

(induced) current depends on the direction of motion and polarity of the magnet.

Experiment 2

5

 When the switch is suddenly closed (i.e. current flows

through the right-hand loop) the ammeter will show a brief current appearing in the left-hand loop.

 When the switch is suddenly

• pened (i.e. no current flows

through the right-hand loop) the ammeter will again show a brief current appearing in the left-hand loop, but in the

• pposite direction.

Induction

6

 The current produced in the loop is called an induced

current.

 The work done per unit charge to produce that current (to

move the conduction electrons that constitute the current) is called an induced emf.

 The process of producing the current and emf is called

induction.

 Faraday’s law of induction:

An emf is induced in a loop when the amount of magnetic field that passes through the loop is changing.

(number of magnetic field line)

Magnetic flux

7

 Need to quantify the amount of magnetic field that passes

through the loop

 Magnetic flux through a loop enclosing an area A  Unit: weber (Wb)

 1 weber = 1 Wb = 1 T·m2

B

d B A   



Vector of magnitude dA that is perpendicular to a differential area dA Dot product

Changing magnetic flux through a coil

8

Here are the general means by which we can change the magnetic flux through a coil:

 Change the magnitude B of the magnetic field within the

coil.

 Change either the total area of the coil or the portion of that

area that lies within the magnetic field (for example, by expanding the coil or sliding it into or out of the field).

 Change the angle between the direction of the magnetic field

𝐶 and the plane of the coil (for example, by rotating the coil so that field 𝐶 is first perpendicular to the plane of the coil and then is along that plane).

Faraday’s law of induction

9

 The magnitude of the emf induced in a conducting loop is equal to

the rate at which the magnetic flux 𝛸𝐶 through the loop changes with time.

 The negative sign is there because the induced emf tends to

• ppose the flux change. (TBD)

 If we change the magnetic flux through a coil of N turns, an

induced emf appears in every turn and the total emf induced in the coil is the sum of these individual induced emfs

B

d dt   

B

d N dt   

Assume that the coil is tightly wound (closely packed), so that the same magnetic flux passes through all the turns.

Exercise

10

 The graph gives the magnitude B(t) of a uniform magnetic

field that exists throughout a conducting loop,with the direction of the field perpendicular to the plane of the loop.

 Rank the five regions of the graph according to the

magnitude of the emf induced in the loop, greatest first.

Ex: Induced emf due to a solenoid

11

 A long solenoid has 220 turns/cm and carries a current i

=1.5 A; its diameter D is 3.2 cm.

 At the center we place a 130 turn closely packed coil C of

diameter d = 2.1 cm. The current in the long solenoid is reduced to zero at a constant rate in 25 ms.

 What is the magnitude of the induced emf in coil C?

Lenz’s law

12

 “An induced current has a direction

such that the magnetic field due to the current opposes the change in the magnetic flux that induces the current.”

Ex: Lenz’s law

13

Note carefully that the flux of 𝐶

𝑗𝑜𝑒 always opposes the change in the flux of 𝐶

. Does not mean that 𝐶

𝑗𝑜𝑒 always points opposite 𝐶

.

• Ex. Induction due to a changing B

14

 Consider a conducting loop consisting of a half-circle of radius r

= 0.20 m and three straight sections. The half-circle lies in a uniform magnetic field that is directed out of the page; the field magnitude is given by B = 4.0t2 +2.0t + 3.0, with B in teslas and t in seconds.

 An ideal battery with emf ℰ𝑐𝑏𝑢

= 2.0 V is connected to the loop.

 The resistance of the loop is 2.0

Ω

• Ex. Induction due to a changing B

15

 r = 0.20 m, B = 4.0t2 +2.0t + 3.0, ℰ𝑐𝑏𝑢 = 2.0 V

, R = 2.0 Ω

a)

What are the magnitude and direction of the emf ℰ𝑗𝑜𝑒 induced around the loop by field 𝐶 at t = 10 s?

b)

What is the current in the loop at t = 10 s?

Self-Induction

16

 An induced emf appears in any coil in which the current is

changing.

 This process is called self-induction.  The emf that appears is called a self-induced emf.  Still obeys Faraday’s law

and Lenz’s law.

Inductors and Inductance

17

 An inductor is an electrical component

typically made by coiling a conductor around a core.

 Solenoid is our basic type of inductor.

 The inductance of the inductor is  Unit: henry

 1 henry = 1 H = 1 T∙m2/A.

B

N L i  

the number of turns

  

solenoid 2 B N

n in A L i n A    

Inductor: self-induced emf

18

 Let’s combine self induction and inductance.  In any inductor (such as a solenoid) a self-induced emf

appears whenever the current changes with time.

 The direction can be obtained by Lenz’s law.  For an ideal inductor with negligible resistance, the

magnitude of the potential difference VL across the inductor is equal to the magnitude of the self-induced emf ℰ𝑀.

   

B B L

d d d di N L dt d N Li t dt dt          

Faraday’s law

Inductance

B

N L i  

RL Circuit

19

 Kirchhoff’s voltage law

• Example. RL

L ci circu cuit it

20

 Consider a circuit that contains three identical resistors with

resistance R = 9.0 , two identical inductors with inductance L = 2.0 mH, and an ideal battery with emf ℰ = 18 V .

 What is the current i through the battery just after the switch

is closed?

• Example. RL

L ci circu cuit it

21

 What is the current i through the battery long after the

switch has been closed?

1

SCS CS 139 39

II.4 .4 Alt lterna ernati ting ng Cur urrent rent

• Dr. Prapun Suksompong

prapun@siit.tu.ac.th

Office Hours: Library (Rangsit) Mon 16:20-16:50 BKD 3601-7 Wed 9:20-11:20

R R C C L L

v i R dv i C dt di v L dt   

Reference

2

 Principles of Physics  Ninth Edition, International Student Version  David Halliday, Robert Resnick,

and JearlWalker

 Chapter 31

 31-6 Alternating Current  31-7 Forced Oscillations  31-8 Three Simple Circuits

Alternating-Current Generator

3

 A conducting loop rotates (with constant angular speed ) in

an external (uniform and constant) magnetic field.

 Connections from each end of the loop to the external

circuit are made by means of that end’s slip ring.

Sinusoids

4

 A sinusoid (or sinusoidal signal) is a signal (e.g. voltage or

current) that has the form of the sine or cosine function.

 Turn out that you can express them all under the same notation

using only cosine (or only sine) function.

 We will use cosine.

 A sinusoidal current is referred to as alternating current

(ac).

 Circuits driven by sinusoidal (current or voltage) sources are

called ac circuits.

 We use the term ac source for any device that supplies a

sinusoidally varying voltage (potential difference) or current

 The usual circuit-diagram symbol for an ac source is

Sinusoids: Standard Form

5

 General sinusoidal signal (in cosine form)  Xm: amplitude of the sinusoid

 Nonnegative when expressed in standard form

 T: period (the time of one complete cycle)  f: frequency

 #cycles per second

• r hertz (Hz)

 ω: angular frequency in radians/s (or rad/s)  𝜚: phase

 Between −180◦and +180◦ in standard form

( ) cos( ) cos(2 ).

m m

x t X t X ft         1 2 f T    

Around the World: Voltages and Frequencies

6

Japan: 100 V; 50 Hz (East), 60 Hz (West) Thailand: 220 V; 50 Hz US: 120 V; 60 Hz

Conversions to standard form

7

 When the signal is given in the sine form, it can be converted

into its cosine form via the identity

In particular,

 We can avoid having Xm with negative sign by the following

conversion:

In particular,

 Note that usually you do not have the choice between +180◦or

−180◦. The one that you need to use is the one that makes 𝜚±180◦ falls somewhere between −180◦and +180◦.

sin( ) cos( 90 ). x x   sin( ) cos( 90 ).

m m

X t X t         cos( ) cos( 180 ). x x    cos( ) cos(2 180 ). A t A ft         

Exercise

8

Express the following sinusoids in their standard forms

       

5cos 2 45 5sin 2 45 5cos 2 45 5sin 2 45 t t t t      

Exercise

9

10  5  5 10 6  4  2  2 4 6 5 cos 2 t  ( )  t 10  5  5 10 6  4  2  2 4 6 5 cos 2 t  45 deg   ( )  t 10  5  5 10 6  4  2  2 4 6 5  cos 2 t  45 deg   ( )  5 cos 2 t  135 deg   ( )  t 10  5  5 10 6  4  2  2 4 6 5 sin 2 t  45 deg   ( )  5 cos 2 t  135 deg   ( )  t 10  5  5 10 6  4  2  2 4 6 5  sin 2 t  45 deg   ( )  5 cos 2 t  45 deg   ( )  t

Application: Measuring Body Fat by Bioelectric Impedance Analysis

10

 The electrodes attached to this

• verweight patient’s chest are

applying a small ac voltage of frequency 50 kHz.

 The attached instrumentation

measures the amplitude and phase angle of the resulting current through the patient’s body.

 These depend on the relative

amounts of water and fat along the path followed by the current, and so provide a sensitive measure of body composition.

1

SCS CS 139 39

II.5 .5 El Electr ectrom

• magnet

agnetic ic Waves es

• Dr. Prapun Suksompong

prapun@siit.tu.ac.th

Office Hours: Library (Rangsit) Mon 16:20-16:50 BKD 3601-7 Wed 9:20-11:20

Reference

2

 Principles of Physics  Ninth Edition, International Student Version  David Halliday, Robert Resnick,

and JearlWalker

 Chapter 32

 32-2 Gauss’ Law for Magnetic Fields  32-3 Induced Magnetic Fields  32-5 Maxwell’s Equations

 Chapter 33

 33-2 Maxwell’s Rainbow  33-3 The Traveling Electromagnetic

Wave, Qualitatively

Gauss’s Law

3

 GLE: Gauss’s Law for Electric Fields: The net electric

flux through a closed Gaussian surface is proportional to the net electric charge qenc enclosed by the surface.

 GLB: Gauss’s Law for Magnetic Fields:

Net magnetic flux through any closed Gaussian surface is zero.

B

B dA    



enc E

q E dA     



Integrals are taken over a closed Gaussian surface

Implication of GLB

4

 Magnetic monopoles (single magnetic poles) do

not exist (as far as we know).

 The simplest magnetic structure that can exist is a

magnetic dipole

 which consists of both a source and a sink for the field

lines.

 Thus, there must always be as much magnetic flux into

the surface as out of it, and the net magnetic flux must always be zero.

 If you break a magnet, each fragment becomes a

separate magnet, with its own north and south poles.

 Even if we break the magnet down to its individual

atoms and then to its electrons and nuclei. Each fragment still has a north pole and a south pole.

Laws of Induction

5

 Faraday’s law of induction: A changing magnetic flux

induces an electric field.

 Maxwell’s law of induction: A changing electric flux

induces a magnetic field.

B

d dt   

B

d E ds dt    



E

d B ds dt     



Electric field induced along a closed loop by the changing magnetic flux encircled by that loop. Magnetic field induced along a closed loop by the changing electric flux in the region encircled by that loop.

Ampere–Maxwell Law

6

Magnetic field is produced by a current and/or by a changing electric field:

0 enc

B ds i   



E

dt d d B s     



d,e nc enc en E c

i d d i s dt B i           



Displacement current (id)

Maxwell’s Law of Induction (Maxwell’s Extension of Ampere’s Law) Ampere’s Law

Maxwell’s Equations

7

Maxwell’s equations, displayed below summarize electromagnetism and form its foundation, including optics.

James Clerk Maxwell (1831–1879) was the first person to truly understand the fundamental nature of light. Einstein described Maxwell’s accomplishments as “the most profound and the most fruitful that physics has experienced since the time of Newton.”

7 Equations

8

that changed the world … and still rule everyday life

9

Traveling Electromagnetic Wave

10

 Do not require material medium. Can travel across empty space.  The magnetic field varies sinusoidally and induces (via Faraday’s

law of induction) a perpendicular electric field that also varies sinusoidally.

 Electric field is varying sinusoidally and induces (via Maxwell’s law

• f induction) a perpendicular magnetic field that also varies

sinusoidally.

 And so on.  The two fields continuously create each other via induction, and

the resulting sinusoidal variations in the fields travel as a electromagnetic wave.

Characteristics of EM Waves (1)

11

 Transverse wave:

𝐹and 𝐶 are always perpendicular to the direction in which the wave travels.



𝐹 is always perpendicular to 𝐶.

 The cross product,

𝐹  𝐶 gives the direction of propagation.

snapshot

Characteristics of EM Waves (2)

12

 The

𝐹and 𝐶 fields vary with the same frequency and in-phase with each other.

 For an EM wave that is assume that is traveling positive direction

• f an x axis, with

𝐹 oscillating parallel to the y axis, and 𝐶

• scillating parallel to the z axis,

cos( ) cos( )

m m

E E kx t B B kx t      

amplitudes of the fields angular frequency angular wave number Electric wave component Magnetic wave component

1

m m

E E c k B B       

Wave speed amplitude ratio magnitude ratio The meter has now been defined so that the speed of light (any EM wave) in vacuum has the exact value c = 299 792 458 m/s,

EM spectrum (Maxwell’s Rainbow)

13

 We now know a wide spectrum (or range) of electromagnetic

(EM) waves.

 Certain regions are identified by familiar labels. These labels

denote roughly defined wavelength ranges within which certain kinds of sources and detectors

• f EM waves are

in common use.

Ultraviolet Vision

14

 Many insects and birds can see ultraviolet wavelengths that

humans cannot.

[http://www.nature.com/scitable/blog/the-artful-brain/alternate_realities]

UV Vision (bright = UV). The center target is vastly larger than the version we see. Also observe a faint UV glow in the center Simulated (red- blind) bee vision (UV+G+B) Some species, such as birds, along with most reptiles, have four types

• f photoreceptors

(UV+R+G+B) [Dr.Klaus Schmitt] Human vision

Ultraviolet Vision

15

Gazania flower shot using white light Gazania flower shot using ultraviolet light to make

• therwise invisible patterns visible.

Ultraviolet Vision

16

 Many birds with ultraviolet vision have ultraviolet patterns on their bodies that

make them even more vivid to each other than they appear to us.

 Ultraviolet reflecting plumage in starlings had profound effects on observed

mating preferences, while plumage in the human visible spectrum did not predict choice. Their ultraviolet feathers are part of their mating call!

Electromagnetic Spectrum

17

[Gosling , 1999, Fig 1.1 and 1.2]

c f  

Wavelength Frequency

8

3 10 m/s 

Radio-frequency spectrum

18

 Commercially exploited bands

c f  

Wavelength Frequency

8

3 10 m/s 

[http://www.britannica.com/EBchecked/topic-art/585825/3697/Commercially-exploited-bands-of-the-radio-frequency-spectrum]

Note that the freq. bands are given in decades; the VHF band has 10 times as much frequency space as the HF band.

Spectrum Allocation

19

 Spectral resource is limited.  Most countries have government agencies responsible for

allocating and controlling the use of the radio spectrum.

 Commercial spectral allocation is governed

 globally by the International Telecommunications Union (ITU)

 ITU Radiocommunication Sector (ITU-R) is responsible for radio

communication.  in the U.S. by the Federal Communications Commission (FCC)  in Europe by the European Telecommunications Standards Institute

(ETSI)

 in Thailand by the National Broadcasting and Telecommunications

Commission (NBTC; คณะกรรมการกิจการกระจายเสียง กิจการโทรทัศน์และกิจการ โทรคมนาคมแห่งชาติ ; กสทช.)

 Blocks of spectrum are now commonly assigned through spectral

auctions to the highest bidder.

20

Thailand Freq. Allocations Chart

21

http://www.ntc.or.th/uploadfiles/freq_chart_thai.htm

News: Thailand 2.1GHz Auction

22

  4.5bn baht per license (freq chunk)

 1 license (chunk) = 5 MHz (UL) + 5 MHz (DL)   450 million baht per MHz   30 million baht per MHz per year

Application: GPS

23

 GPS = Global Positioning System  Original application in the (US) military  Created in the early 1990s.  Allow a person to determine the time and the person's

precise location (latitude, longitude, and altitude) anywhere

• n earth.

GPS Satellites

24

 A minimum of 24 GPS satellites are in orbit at 20,200

kilometers (12,600 miles) above the Earth.

 The satellites are spaced so that from any point on Earth, at

least four satellites will be above the horizon.

How GPS Works?

25

 A GPS receiver measuring its distance from a group of

satellites in space which are acting as precise reference points.

 All the satellites have atomic clocks of unbelievable precision on

board and are synchronized.

 The satellite are continuously transmitting the information about

their location and time.

 GPS receiver on the ground is in synchronism with the satellites.

 Off by an (unknown) amount .  For now, assume  = 0.

 By measuring the propagation time, the receiver can compute

distance d from that satellite.

GPS-Trilateration

26

 Intersection of three sphere narrows down the location to

just two points.

 In practice, there are four unknowns, the coordinates in the

three-dimensional space of the user along with  within the user’s receiver.

 Need a distance measurement from a fourth satellite.

[Lathi ,1998, Fig. 9.6 ]