topics module m2-1 2 electrical...
TRANSCRIPT
L E C T U R E 2 C O U L O M B ’ S L A W A N D E L E C T R I C F I E L D I N T E N S I T Y A U G U S T 1 8 , 2 0 1 6
Module M2-1 Electrical Engineering
Topics 2
� Phenomena related to electrostatics ¡ Transfer of charges ¡ Insulators and conductors ¡ Polarization
� Applications ¡ Electrostatic generator ¡ Electrostatic discharges ¡ Risks and applications of static electricity
� Coulomb’s law � Electric field intensity � Streamlines and sketches of fields
After this lecture, you will be able to 3
� understand the phenomena and engineering applications related to electrostatics (ไฟฟ้าสถิต)
� compute the electrostatics force (Coulomb’s law) and the electric field intensity
� describe the streamlines for the electric field intensity caused by 1 or 2 charges
Electrostatics is the study of stationary or slow-moving electric charges
4
� Electrostatic phenomena arise from the forces that electric charges exert on each other
Charges of the same polarity repel
Charges of opposite polarities attract
Charges are part of atoms 5
� All charges available must be integral multiples of “e”
Charge electron - e proton +e neutron 0
elementary charge e = 1.6 x 10-19 coulomb (C)
To visualize, think of coulomb in terms of electrons or protons
6
� 1 C equals � A charge 1 C has 6.25 × 1018 protons more than electrons
� -1 C equals � A charge -1 C has 6.25 × 1018 electrons more than protons
1
e=
1
1.6⇥ 10
�19= 6.25⇥ 10
18protons
1
e=
1
1.6⇥ 10
�19= 6.25⇥ 10
18electrons
����...
� ��
6.25 × 1018 protons
1 C
...
6.25 × 1018 electrons
-1 C
C H A R G E T R A N S F E R P O L A R I Z A T I O N
E L E C T R O S T A T I C D I S C H A R G E
7
Natural phenomena of electrostatics
Ancient people observed that, after rubbing, some materials attract lightweight objects
8
� Example: ¡ rub amber (ยางสน) and fur together ¡ amber will attract fur
� The word electricity is derived from the Greek word for amber ήλεκτρον (elektron)
Scientists were so interested in this phenomenon that they made a table of what attracts what
9
� This table, known as the triboelectric series, first appeared in 1757 (around the end of Ayutthaya period)
amber
glass
silk
wool
... ...
...
The further away the materials, the more attraction
When rubbed, electrons move from top material to bottom
top becomes + bottom becomes -
Example: At the beginning, silk and glass rod are charge-neutral
10
� because for each matter, the number of electrons and protons are equal
SILK
Glass Rod
As the glass rod is rubbed against silk, electrons are pulled off the glass onto the silk
11
SILK
Glass Rod
- +
� A chemical bond called adhesion is formed between some parts of the two surfaces
� Electrons move from one material to the other to equalize their electrochemical potential
The silk has an excess of electrons and the rod has a deficit
12
SILK
Glass Rod
- - +
+
Glass and silk are dielectric (ฉนวนไฟฟ้า), so charges on them do not move
13
SILK
Glass Rod
-
+ + + +
+
- - - -
In Lecture 4, we will cover dielectric and conductor (ตัวนำไฟฟ้า) in detail
Electrons move easily in a conductor and rarely move in a dielectric
14
Dielectric (ฉนวนไฟฟ้า) Conductor (ตัวนำไฟฟ้า)
Electrons are bound in orbit to the nucleus in each atom
Electrons can easily move from atom to atom
When charge is placed on a dielectric, it stays undistributed in one region
When a charge is placed on a conductor, it redistributes to the outer surface.
Examples: wood, plastic, glass, air, cloth
Examples: metals (copper, gold, and aluminum)
Polarization is the separation of charges 15
� In a conductor, “free” electrons can move around the surface of the material ¡ leaving one side positive and the other side negative
conductor (metal can)
(continued) Polarization 16
� In a dielectric, the electrons “realign” themselves within the atom (or molecule) ¡ leaving one side of the atom positive and the other side of the
atom negative
atom of a dielectric
[VDO 81] polarization of water 17
https://youtu.be/VhWQ-r1LYXY Duration: 2:09 min
Van de Graaff generator is an apparatus that generate and accumulate large amount of charges
18
Van de Graaff generator
[VDO 84] https://youtu.be/Z-77IzaXGcg Duration: 0:32 min (trimmed 0:00-0:32) Operation of the Van de Graaff generator
What do you think happen to this girl’s hair? 19
[VDO 30] Van de Graaff generator, like charges repel Duration: 0:28 min https://youtu.be/WS9ISUXBsa8
[VDO 84] Explanation of what happens Duration: 0:32 min (trimmed 0:00-0:32) https://youtu.be/Z-77IzaXGcg
Electrostatic discharge is a sudden flow of charges between two objects
20
Electrostatic charge may cause by a contact
or by other means such as a dielectric breakdown
Grounding is a practice of connecting an object to a large body, like Earth
21
� to remove any electric charge on the object
22
Applications of electrostatics
Electrostatic spray painting 23
� The object and paint particle have opposite charges � Paint particles are attracted to the object, and few
spray paint is lost
[VDO 31] Electrostatic spraying Duration: 1:07 min; http://youtu.be/LAEGkaqKZhQ
Electrostatic duster
24
� Rubbing the duster across a surface causes the duster to become charged by friction
� Neutral dust particles stick to charged duster
Electrostatic precipitator 25
� is a device that removes dust particles from the exhaust gas (to clean up pollution, for example)
[VDO 94] Electrostatic precipitator, do-it-yourself Duration: 1:07 min; https://youtu.be/x5YFK8mmeRQ
Photocopying 26
� Selenium is an insulator but becomes a conductor when exposed to light ¡ [VDO 33] Photocopier; Duration: 0:42 min
http://youtu.be/3wDaOAp31Bo
Capacitors 27
� A capacitor can be charged by connecting it to a battery or any other source of current
� A capacitor can be discharged by connecting it to any closed circuit that allows current to flow
VIDEO 34: Charging capacitor; Duration: 7:06 min https://youtu.be/enmQy_2qv4o
A downside, electrostatics discharge can damage circuits and sensitive electrical components
28
A damaged circuit due to static charges
www.technomicon.com
A normal circuit
aaq.auburn.edu/node/276
Another example of a damaged circuit
(continued) electrostatics discharge can ignite flame or panic an air traveller
29
[VDO 159] electrostatic discharge at gas station Duration: 0:47 min (trimmed 0:42-1:24) https://youtu.be/b89x8CAS6xU
[VDO 161] Lightning strike Duration: 0:12 min (trimmed 0:20-0:32) https://youtu.be/oqhUijxTjtI
30
The experimental law of Couloumb
Coulomb is a French physicist
� Charles-Augustin de Coulomb ¡ born 1736 – deceased 1806
¡ His life overlaps with the reign of King Rama 1 – King Rama 4
� He is best known for developing Coulomb's law � The SI unit of electric charge, the coulomb, was
named after him.
31
Recall Newton’s law of gravitation
� The magnitude of the gravitational force is
mass m1 mass m2
gravitational force
distance R Newton
distance square
product of the masses a constant
32
~F
|~F| = Gm1m2
R2
Coulomb’s law resembles Newton’s law, but Coulomb’s is for charges
33
� The magnitude of electrostatic force is
charge Q1 charge Q2
electrostatic force
distance R
Direction of force is shown here for Q1 > 0 and Q2 < 0
+ −
product of the charges (absolute value makes the magnitude ≥ 0)
distance square
a constant
~F
|~F| = 1
4⇡✏0
|Q1Q2|R2
In this class, we use the SI units 34
Symbol Name Unit Abbreviation force newton N positive or negative quantities of charge
coulomb C
distance meter m permittivity of free space farad per meter F/m ✏0
farad is the same as C2
N ·mThis constant equals
✏0 = 8.854⇥ 10�12 F/m
F
Q1, Q2
R
Coulomb’s law implies that
� The force between two charges gets stronger as the charges move closer together ( )
� The force also gets stronger if the amount of charge becomes larger ( )
35
R # =) |~F| "
|Q1Q2| " =) |~F| "
The direction of the electrostatic force . (a vector) depends on the signs of charges
36
Charges of the same polarity repel
Charges of opposite polarities attract
~F
[VDO 94] magnitude and direction of Coulomb's force
37
Duration: 0:22 min https://youtu.be/g_3vRfA1wSU
Review: which one is the vector that starts from point (0, 0) and ends at point (-2, 1)?
38
(-2, 1)
x
y
(0, 0)
(a) (b)
ba =~R
|~R|
Review: which vector is the unit vector in the direction of point (2, 3) to point (-1, 1)?
39
(2, 3)
(-1, 1)
x
y
~R
ba
(a)
� 3p13
bi� 2p13
bj3p13
bi+ 2p13
bj
3bi+ 2bj �3bi� 2bj(b)
(c) (d)
~R = (�1� 2)bi+ (1� 3)bi
0
There is a way to capture in a single equation both the magnitude and the direction of the force
40
� This is called the vector form of Coulomb’s law
charge Q1 (can be + or –)
charge Q2 (can be + or –)
product of charges (each charge can be + or –) force on Q2
a unit vector in the direction from Q1 to Q2
The vector pointing from the position of Q1 to the position of Q2
~R12
~F2 =Q1Q2
4⇡✏0R2ba12
~R12
41
Electric field intensity
Electric field intensity is the force per unit charge 42
� Put a test charge Qt at position P � The force on Qt is given by Coulomb’s law: � Electric field intensity is defined to be the force per
unit charge, arising from Qt:
charge Q1 (can be + or –)
position P
a test charge Qt (can be + or –)
distance R1t
a1t
~E1 =~Ft
Qt=
Q1
4⇡✏0R21t
ba1t
~E1
~Ft =Q1Qt
4⇡✏0R21t
ba1t
A formula for the electric field intensity .
43
� At position P in the space, the electric field intensity of a single charge Q is
single point charge Q (can be + or –)
distance R
position P
a unit vector pointing from the position of Q to the position P
R = distance between Q and P
~E =Q
4⇡✏0R2baR
baR
can be + or –
~E In this class, we will use the SI units 44
Symbol Name Unit Abbreviation electric field intensity volt/meter V/m E
volt is the same as joule per coulomb ( J/C ) or newton-meter per coulomb ( ) N · m/C
Electric field intensity is an example of a vector field
45
� Example: A charge Q = −0.5 × 10−10 C locates at the origin. The electric field intensity at position (0, 1) m is
x
y
0
charge Q R = 1 m
R= 1 m = 8.854⇥ 10�12 F/mpermittivity of free space
�
~E
~E =Q
4⇡✏0R2baR = �0.45bj V/m
~E baR = bj
bj
(0, 1)
Concept question 46
Vector field คืออะไร
ก. เวกเตอร์ที่มีขนาด 1 หน่วย
ข. ฟังชั่นที่ให้ปริมาณเวกเตอร์ ณ ตำแหน่งต่างๆ
ค. ปริมาณสเกลาร์ที่คำนวณจากสูตร
qA2
x
+A2y
+A2z
เราเรียนเรื่อง Vector field ใน Tutorial 1
Electric field intensity is an example of a vector field
47
x (m)
y (m)
0
Q = �0.5⇥ 10�10 CCharge
at the origin
E(1.5, 0)
E(0, 1.5)
� Here, we sketch some of vectors
� ~E(1, 0)
~E(0, 1)
~E(�1, 0)~E(0,�1)
~E
~E(x, y)
Concept question 48
รูปใดแสดงเวกเตอร์ ที่เกิดจากประจุบวก ณ origin y
x +
ก. เหมือนกับกรณีประจุลบ
y
x +
ข. เปลี่ยนทิศ 180°
~E(x, y)
Superimposition of electric field intensities 49
� The Coulomb forces can be added � So the electric field intensity arising from two
point charges Q1 and Q2 is the sum of ¡ the electric field intensity caused by Q1 and ¡ the electric field intensity caused by Q2
charge Q1 (can be + or –)
charge Q2 (can be + or –)
~E = ~E1 + ~E2
~E2
~E1
~E
~E2
~E1
Below are some vectors of . caused by two charges
50
−4 −2 0 2 4−4
−2
0
2
4y (m)
x (m)
a positive charge 0.8 × 10�10 C located at (-2,0)
a negative charge �0.8 × 10�10 C located at (2,0)
~E(x, y)
แปลตามตัว: streamline = “เส้นทางที่น้ำหรือของเหลวไหล”
51
Streamlines and sketches of fields
−1 0 1−1
0
1
A plot of vectors can be difficult to see 52
a proton at the origin: Q = 1.6 × 10�19 C
Difficult to see the vector because the magnitude of is small, about 3.6 × 10�8 V/m here
y (m)
x (m)
~E
(cont’) A plot of vectors can be difficult to see 53
−1 0 1−1
0
1
y (m)
x (m)
a negative charge of �10�10 C at the origin
Difficult to see because the magnitudes of are large, and the vectors are overlapped
~E
Streamlines provide an easy way to visualize a vector field
54
streamlines of
−1 0 1−1
0
1
some vectors of
−1 0 1−1
0
1
~E ~E
(cont’) Streamlines provide an easy visualization 55
−1 0 1−1
0
1
streamlines of some vectors of
−1 0 1−1
0
1
~E ~E
0 10
1
56
Definition: The streamlines of a vector field are the paths followed by a particle whose velocity field is the given vector field
0 10
1
vectors streamlines 0 10
1
A method to draw streamlines of a vector field 57
� Method 1: use function streamline or streamslice in Matlab
� Method 2: solve a differential equation (not covered in this course)
� Method 3: experimentation (see VDOs at the end of lecture)
� We will not ask you to draw the streamlines � But you should be able to identify the streamlines for
some basic cases
Example: Streamlines of for positive and negative charges of equal magnitude
58
−4 −2 0 2 4−4
−2
0
2
4
a positive charge 0.8 × 10�10 C
a negative charge �0.8 × 10�10 C
−4 −2 0 2 4−4
−2
0
2
4
streamlines of some vectors of ~E ~E
~E
Examples of the streamlines of the electric field intensity
59
the streamlines • point outward from a + charge • point inward to a � charge
Concept Question 60
ก. q1 เป็น +, q2 เป็น + ข. q1 เป็น +, q2 เป็น − ค. q1 เป็น −, q2 เป็น + ง. q1 เป็น −, q2 เป็น −
q1 q2 จากรูป streamlines ของ ข้อใดคือเครื่องหมาย (polarity) ของประจุ q1 และ q2
(ดัดแปลงมาจากข้อสอบ ปีการศึกษา 1/2556)
~E
[VDO 35] streamlines of two charges (3D), electric field of a dipole
61
Duration: 0:13 min http://www.youtube.com/watch?v=bG9XSY8i_q8
VDOs: Visualizing the presence of electric field, the streamlines of electric field
62
VIDEO 36: streamlines of electric field intensity (castor oil, semolina seeds) http://www.youtube.com/watch?v=7vnmL853784
[VDO 163] Duration: 1:03 min (trimmed 4:57-6:00) https://youtu.be/Y6YdC2UoDYY
[VDO 164] Duration: 0:54 min (trimmed 3:15-4:09) https://youtu.be/bOLd2KVK-Mo
[VDO 165] Duration: 0:46 min (trimmed 0:35-1:21); The rod is positively charged https://youtu.be/bOLd2KVK-Mo
63
Try these links outside the classroom
A webpage displaying the Coulomb forces (2 charges)
64
� http://webphysics.davidson.edu/physlet_resources/bu_semester2/c01_magnitude.html
A webpage displaying the Coulomb forces (3 charges)
65
� http://www.rmutphysics.com/charud/virtualexperiment/Explore/InteractionEC/index.htm
A webpage displaying some vectors and the streamlines of .
66
� http://www.dgp.toronto.edu/~mjmcguff/research/electrostatic/applet1/main.html
streamlines of some vectors of
~E
~E ~E
A webpage displaying streamlines of the electric field intensity
67
Summary 68
� Phenomena related to electrostatics ¡ Transfer of charges ¡ Insulators and conductors ¡ Polarization
� Applications ¡ Electrostatic generator ¡ Electrostatic discharges ¡ Risks and applications of static electricity
� Coulomb’s law for electrostatic force ( ) ¡ Analogy to Newton’s law of universal gravity ¡ Formula in the vector form
~F
Summary 69
� Electric field intensity ( ) ¡ Definition ¡ Formula in the vector form ¡ Electric field intensity caused by multiple charges
� Streamlines and sketches of fields ¡ Definition of streamlines ¡ Examples of streamlines for
~E
~E