Module M2-1 Electrical Engineering

Transcription

1 Module M2- Electrical Engineering LECTURE 2 COULOMB S LAW AND ELECTRIC FIELD INTENSITY AUGUST 8, 26 Topics 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 2 After this lecture, you will be able to 3 Electrostatics is the study of stationary or slow-moving electric charges 4 understand the phenomena and engineering applications related to electrostatics (ไฟฟ าสถ ต) compute the electrostatics force (Coulomb s law) and the electric field intensity describe the streamlines for the electric field intensity caused by or 2 charges Charges of opposite polarities attract Charges of the same polarity repel Electrostatic phenomena arise from the forces that electric charges exert on each other

2 Charge electron - e proton +e neutron Charges are part of atoms elementary charge e =.6 x -9 coulomb (C) All charges available must be integral multiples of e 5 To visualize, think of coulomb in terms of electrons or protons... C equals A charge C has protons more than electrons - C equals C protons e =.6 9 = protons e =.6 9 = electrons A charge - C has electrons more than protons C electrons Natural phenomena of electrostatics Ancient people observed that, after rubbing, some materials attract lightweight objects 8 7 CHARGE TRANSFER POLARIZATION ELECTROSTATIC DISCHARGE Example: rub amber (ยางสน) and fur together amber will attract fur The word electricity is derived from the Greek word for amber ήλεκτρον (elektron)

3 Scientists were so interested in this phenomenon that they made a table of what attracts what Example: At the beginning, silk and glass rod are charge-neutral glass silk wool 9 The further away the materials, the more attraction When rubbed, electrons move from top material to bottom top becomes + bottom becomes - SILK Glass Rod amber This table, known as the triboelectric series, first appeared in 757 (around the end of Ayutthaya period) because for each matter, the number of electrons and protons are equal As the glass rod is rubbed against silk, electrons are pulled off the glass onto the silk The silk has an excess of electrons and the rod has a deficit SILK SILK Glass Rod 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

4 Glass and silk are dielectric (ฉนวนไฟฟ า), so charges on them do not move Electrons move easily in a conductor and rarely move in a dielectric 3 In Lecture 4, we will cover dielectric and conductor (ต วนำไฟฟ า) in detail Conductor (ต วนำไฟฟ า) 4 Dielectric (ฉนวนไฟฟ า) SILK Electrons can easily move from atom to atom Electrons are bound in orbit to the nucleus in each atom Glass Rod When a charge is placed on a conductor, it redistributes to the outer surface. When charge is placed on a dielectric, it stays undistributed in one region Examples: metals (copper, gold, and aluminum) Examples: wood, plastic, glass, air, cloth Polarization is the separation of charges 5 conductor (metal can) (continued) Polarization 6 atom of a dielectric In a conductor, free electrons can move around the surface of the material leaving one side positive and the other side negative 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

5 [VDO 8] polarization of water Van de Graaff generator is an apparatus that generate and accumulate large amount of charges Duration: 2:9 min [VDO 84] Duration: :32 min (trimmed :-:32) Operation of the Van de Graaff generator Van de Graaff generator What do you think happen to this girl s hair? Electrostatic discharge is a sudden flow of charges between two objects 9 2 Electrostatic charge may cause by a contact [VDO 3] Van de Graaff generator, like charges repel Duration: :28 min [VDO 84] Explanation of what happens Duration: :32 min (trimmed :-:32) or by other means such as a dielectric breakdown

6 Grounding is a practice of connecting an object to a large body, like Earth 2 Applications of electrostatics 22 to remove any electric charge on the object Electrostatic spray painting 23 Electrostatic duster 24 [VDO 3] Electrostatic spraying Duration: :7 min; The object and paint particle have opposite charges Paint particles are attracted to the object, and few spray paint is lost Rubbing the duster across a surface causes the duster to become charged by friction Neutral dust particles stick to charged duster

7 Electrostatic precipitator Photocopying [VDO 94] Electrostatic precipitator, do-it-yourself Duration: :7 min; Selenium is an insulator but becomes a conductor is a device that removes dust particles from the exhaust gas (to clean up pollution, for example) when exposed to light [VDO 33] Photocopier; Duration: :42 min Capacitors A downside, electrostatics discharge can damage circuits and sensitive electrical components A normal circuit A damaged circuit due to static charges VIDEO 34: Charging capacitor; Duration: 7:6 min 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 Another example of a damaged circuit aaq.auburn.edu/node/276

8 (continued) electrostatics discharge can ignite flame or panic an air traveller 29 The experimental law of Couloumb 3 [VDO 59] electrostatic discharge at gas station Duration: :47 min (trimmed :42-:24) [VDO 6] Lightning strike Duration: :2 min (trimmed :2-:32) Coulomb is a French physicist Charles-Augustin de Coulomb born 736 deceased 86 His life overlaps with the reign of King Rama King Rama 4 He is best known for developing Coulomb's law The SI unit of electric charge, the coulomb, was named after him. 3 Recall Newton s law of gravitation 32 gravitational force ~F mass m mass m 2 distance R Newton The magnitude of the gravitational force is a constant product of the masses ~ F = G m m 2 R 2 distance square

9 Coulomb s law resembles Newton s law, but Coulomb s is for charges 33 In this class, we use the SI units 34 + electrostatic force ~F charge Q charge Q 2 distance R The magnitude of electrostatic force is a constant F ~ = Q Q 2 4 R 2 Direction of force is shown here for Q > and Q 2 < product of the charges (absolute value makes the magnitude ) distance square Symbol Name Unit Abbreviation F force newton N Q,Q 2 R This constant equals = F/m positive or negative quantities of charge coulomb distance meter m permittivity of free space farad per meter F/m farad is the same as C C 2 N m Coulomb s law implies that The force between two charges gets stronger as the charges move closer together ( R # =) F ~ " ) The force also gets stronger if the amount of charge becomes larger ( Q Q 2 " =) F ~ " ) 35 The direction of the electrostatic force. ~F (a vector) depends on the signs of charges Charges of opposite polarities attract Charges of the same polarity repel 36

10 [VDO 94] magnitude and direction of Coulomb's force 37 Review: which one is the vector that starts from point (, ) and ends at point (-2, )? 38 y (-2, ) (a) (b) (, ) x Duration: :22 min Review: which vector is the unit vector in the direction of point (2, 3) to point (-, )? (-, ) (a) (c) y ~R 3 p b 2 i + p b j 3 3 ba (2, 3) 39 R ba = ~ R ~ 3 b i +2 b j (b) 3 b i 2 b j (d) ~R =( 2) b i +( 3) b i x 3 p b 2 i p b j 3 3 There is a way to capture in a single equation both the magnitude and the direction of the force charge Q (can be + or ) This is called the vector form of Coulomb s law force on Q 2 4 The vector pointing from the position of Q to the position of Q 2 ~R 2 ~F 2 = Q Q 2 4 R 2 ba 2 charge Q 2 (can be + or ) product of charges (each charge can be + or ) a unit vector in the direction ~R 2 from Q to Q 2

11 Electric field intensity is the force per unit charge Electric field intensity 4 charge Q (can be + or ) 42 distance R t position P a test charge Q t (can be + or ) a t Put a test charge Q t at position P The force on Q t is given by Coulomb s law: Ft ~ = 4 Rt 2 Electric field intensity ~E is defined to be the force per unit charge, arising from Q t : F ~E = ~ t = Q Q t 4 Rt 2 ba t Q Q t ba t A formula for the electric field intensity. 43 ~E In this class, we will use the SI units 44 position P single point charge Q (can be + or ) ba R Symbol Name Unit Abbreviation E electric field intensity volt/meter V/m distance R At position P in the space, the electric field intensity of a single charge Q is can be + or volt is the same as joule per coulomb ( J/C ) or newton-meter per coulomb ( ) N m/c ~E = Q 4 R 2 ba R a unit vector pointing from the position of Q to the position P R = distance between Q and P

12 Electric field intensity ~E is an example of a vector field y (, ) charge Q 45 R =m Example: A charge Q =.5 C locates at the origin. The electric field intensity at position (, ) m is permittivity of free space = F/m ~E bar = b j Q ~E = 4 R ba 2 R =.45 b j V/m b j R= m x Concept question Vector field ค ออะไร ก. เวกเตอร ท ม ขนาด หน วย ข. ฟ งช นท ให ปร มาณเวกเตอร ณ ตำแหน งต างๆ ค. ปร มาณสเกลาร ท คำนวณจากส ตร q A 2 x + A 2 y + A 2 z 46 เราเร ยนเร อง Vector field ใน Tutorial Electric field intensity ~E is an example of a vector field 47 y (m) Charge Q =.5 C E(,.5) at the origin ~E(, ) Concept question ร ปใดแสดงเวกเตอร ~E(x, y) ท เก ดจากประจ บวก ณ origin y y 48 ~E(, ) ~E(, ) ~E(, ) E(.5, ) x (m) + x + x Here, we sketch some of vectors ~E(x, y) ก. เหม อนก บกรณ ประจ ลบ ข. เปล ยนท ศ 8

13 Superimposition of electric field intensities 49 ~E 2 ~E = E ~ + E ~ 2 Below are some vectors of. ~E(x, y) caused by two charges y (m) 4 5 ~E 2 charge Q (can be + or ) charge Q 2 (can be + or ) The Coulomb forces can be added So the electric field intensity ~E arising from two point charges Q and Q 2 is the sum of the electric field intensity ~E caused by Q and a positive charge.8 C located at (-2,) a negative charge.8 C located at (2,) the electric field intensity ~E 2 caused by Q 2 x (m) Streamlines and sketches of fields A plot of vectors can be difficult to see 52 5 แปลตามต ว: streamline = เส นทางท น ำหร อของเหลวไหล y (m) a proton at the origin: Q =.6 9 C Difficult to see the vector because the magnitude of ~E is small, about V/m here x (m)

14 (cont ) A plot of vectors can be difficult to see 53 Streamlines provide an easy way to visualize a vector field 54 y (m) a negative charge of C at the origin x (m) Difficult to see because the magnitudes of ~E are large, and the vectors are overlapped some vectors of streamlines of ~E ~ E (cont ) Streamlines provide an easy visualization 55 vectors streamlines some vectors of streamlines of ~E ~ E Definition: The streamlines of a vector field are the paths followed by a particle whose velocity field is the given vector field 56

15 A method to draw streamlines of a vector field Method : 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) Example: Streamlines of ~E for positive and negative charges of equal magnitude We will not ask you to draw the streamlines But you should be able to identify the streamlines for some basic cases some vectors of ~ E a positive charge.8 C a negative charge.8 C streamlines of ~ E Examples of the streamlines of the electric field intensity 59 the streamlines point outward from a + charge point inward to a charge q q 2 Concept Question 6 จากร ป streamlines ของ ~E ข อใดค อเคร องหมาย (polarity) ของประจ q และ q 2 ก. q เป น +, q 2 เป น + ข. q เป น +, q 2 เป น ค. q เป น, q 2 เป น + ง. q เป น, q 2 เป น (ด ดแปลงมาจากข อสอบ ป การศ กษา /2556)

16 [VDO 35] streamlines of two charges (3D), electric field of a dipole VDOs: Visualizing the presence of electric field, the streamlines of electric field 6 62 [VDO 63] Duration: :3 min (trimmed 4:57-6:) [VDO 64] Duration: :54 min (trimmed 3:5-4:9) [VDO 65] Duration: :46 min (trimmed :35-:2); The rod is positively charged Duration: :3 min Try these links outside the classroom 63 VIDEO 36: streamlines of electric field intensity (castor oil, semolina seeds) A webpage displaying the Coulomb forces (2 charges) 64 bu_semester2/c_magnitude.html

17 A webpage displaying the Coulomb forces (3 charges) Explore/InteractionEC/index.htm 65 A webpage displaying some vectors and the streamlines of ~E. electrostatic/applet/main.html 66 some vectors of streamlines of ~E ~ E A webpage displaying streamlines of the electric field intensity 67 Summary 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 ( ~F ) Analogy to Newton s law of universal gravity Formula in the vector form 68

18 Summary Electric field intensity ( ~E ) 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 69