DOCSLIB.ORG

UNIT-1 Electrostatics

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
UNIT-1 Electrostatics UNIT-1 Electrostatics Structure of the Unit 1.0 Objectives 1.1 Introduction 1.2 Electric Field 1.3 Gauss’s Law 1.4 Illustrative Examples 1.5 Self Learning Exercise-I 1.6 Scalar Potential 1.7 Electrostatic Boundary Conditions 1.8 Discontinuity in Potential due to Dipole Layer 1.9 Illustrative Examples 1.10 Self Learning Exercise-II 1.11 Summary 1.12 Glossary 1.13 Answers to Self Learning Exercises 1.14 Exercise 1.15 Answers to Exercise References and Suggested Readings 1.0Objectives1.0 Objectives This unit constitutes the basic concepts of static (time invariant )electric field and potential. One can learn the Gauss’s law and its applications. We learn the usefulness of spherical and cylindrical coordinates for solving the certain kinds of problems in electrostatics. The better physical insight of behaviour of electric field and potential across the interface can be got by studying the boundary conditions at the interface. 1 1.1Introduction1.1 Introduction This unit introduces Coulomb’s law ,Gauss’s Law and boundary conditions on electric fields and potentials. Gauss’s law is developed and shown in both integral and differential form. The concept of circulation of the electric field is related to its conservative nature is discussed. The concept of boundary conditions for electric field and potential is introduced in this unit. 1.21.2 Electric Electric Field Field According to Coulomb’s law , electrostatic force F between two point charges q and Q which are placed in free space at a distance r is expressed mathematically as Qq F k r 2 This force acts along the line joining the charges. 1 N m2 k 9 109 4 C 2 0 C 2 8.854 1012 0 N m2 The constant 0 is called permittivity of free space. Force on q2 due to q1 can be written in vector form as 1q q 1 q q F 1 2rˆ 1 2 r (1) 42 4 3 0r 0 r q .2 r 1 2 r 2 .q 1 r 1 O rig in Figure1.1 2 1q q 1 q q 1 2ˆ 1 2 F1 2 2r 1 2 3 r 1 2 40r 1 2 4 0 r 1 2 1 q1 q 2 F1 2 3 r 2 r 1 4 r r 0 2 1 where r1 2 r 2 r 1 =Position vector of q2 −Position vector of q1 r1 2 r 2 r 1 From eq.(1) taking q1 Q(Source charge) and q2 q (test charge),we have 1 qQ F rˆ 4 2 0 r 1 Q ˆ F q 2 r 4 0 r F qE (Force on the test charge q) 1 Q E rˆ (2) 4 2 0 r F and E q E is called electric field (or electric field intensity) due to point charge Q. N SI unit of E is . C Thus “Electric field E at a point is the force experienced per unit charge at rest state at that point of space.” E E() r has a value at each point in the space, so it is called vector point field. For definition of electric field , we can write F E lim q0 q The test charge q should be infinitesimally small because large value of the test charge will disturb the original charge distribution of primary charges that produces E . 3 If there are more than two charges, then we use principle of superposition for determination of the force on a particular charge. If there are N point charges QQQQ1, 2 , 3 ,... N (source charges) placed respectively at distances r1, r 2 , r 3 ,... rN from charge q then by principle of superposition total force on the charge q(test charge)is given by FFFFF ... 1 2 3 N qQ qQ qQ 1ˆ 2 ˆN ˆ F k2r1 k 2 r 2 .... k 2 r N r1 r 2 r N Here position vectors of QQQQ, , ,... are r, r , r ,... r respectively and test 1 2 3 N 1 2 3 N charge q is located at position r , then r r, r r ,.... r1 1 r 2 2 QQ Q F q k1ˆ k 2 ˆ .... k N ˆ 2r1 2 r 2 2 r N r1 r 2 r N F qE QQ Q 1ˆ 2 ˆN ˆ where E k2r1 k 2 r 2 .... k 2 r N r1 r 2 r N Q E k i ˆ 2 r i r i or EEEEE1 2 3 ... N Above expression represents the principle of superposition for electric field. For continuous charge distribution 1 dq E rˆ 4 2 0 r Now we consider the Coulomb’s law for the general case of volume charge. dq Volume charge density is (in C/m3) ,where differential charge dq is d present in a differential volume d The electric field at a point r x,, y z in terms of integral over the volume charge distribution x,, y z is written as 4 1 r ˆ E() r r d 2 (3) 4 0 r For given charge distribution, E() r is a function of unprimed coordinates x,, y z r is a function of primed coordinates x,, y z ˆ ˆ ˆ r rr xxi yyj zzk ’ Volume elementd dx dy dz For line charge distribution 1 r ˆ E() r r dl 2 4 0 L r dq Line charge density is (in C/m),where differential charge dq is present on dl a differential length dl . For surface charge distribution 1 r ˆ E() r r dS 2 4 0 S r dq Surface charge density is (in C/m2),where differential charge dq is present dS on a differential area dS . 1.31.3 Gauss’s Gauss’s Law Law The theorem is stated mathematically as follows – q E. d S enclosed (4) 0 where qenclosed = q inside = algebraic sum of charges inside the enclosed volume. “That net outward electric flux through a closed surface is equal to the sum of the charges inside the enclosed volume divided by the permittivity of free space”. Here such a hypothetical closed surface is known as Gaussian Surface. Gauss’s law is the easiest way of calculating electric field in situations in which charge distribution has symmetry such as spherical distribution of charge, an infinite line charge etc. Gauss’s law is also true in non symmetrical situations, but 5 in that case it will not be so useful for the evaluation of electric fields. Important Points: 1. Electric flux E. d S is independent of the size and shape of the Gaussian surface as long as q enclosed is same. 2. Electric flux does not depend on the location of charge inside the closed surface S, whereas electric field at each point on surface S, is dependent on location of charge. 3. Electric flux is unaltered by the charge outside the closed surface S, but outside charge contributes in electric field at each point on the surface S. The Concept of Solid Angle: Solid angle is analogous in three dimensional of the ordinary two dimensional angle. Now we consider an infinitesimal small area dS which subtends an infinitesimal small solid angle d at a point O (see Fig. 1.2). Figure1.2 Here r is the distance from the vertex O to the surface element dS. Solid angle d is related to opening of cone around its vertex. Mathematically, we have dS d r 2 Unit of solid angle is “Steradian” . From the definition of solid angle, it is obvious that the solid angle is dimensionless quantity. (i) Suppose an elemental area vector vector d S makes an angle with radial vector r (see figure 1.3) 6 Figure1.3 Projection area perpendicular to r is dS cos . Now solid angle d is the ratio of this projected area to r 2 dScos d S . r i.e. d (5) r2 r 2 (ii) In figure 1.4, area elements dS1, dS2 and dS3 subtend same solid angle at the point O, because for them, opening of cone around its vertex O is same. Figure1.4 (iii)Solid angle subtended by sphere at the centre is4 dS d 2 r 1 dS r = constant 2 r 1 (4r 2 ) 4 r 2 7 4 = complete (full) solid angle Whatever may be shape or size of a closed surface, above result holds at any internal point surrounded by the closed surface. Therefore we have general result: Entire closed surface subtends solid angle 4 at an internal point (6) 0 at an external point Proof of Gauss’s Theorem:- We consider a point charge q surrounded by a hypothetical closed surface S of an arbitrary shape as shown in Figure1.5 Figure1.5 Electric flux through an infinitesimal area element dS is d , then d E.d S EdS cos where is the angle between electric field E and area vector d S 1 q Due to the point charge q, electric field at a distance r is given by E 2 r 4 0 r 1 q d EdS cos dS cos (7) 4 r 2 0 8 Since electric field is directed along r , therefore is the also angle between rˆ and d S .Here area element d S subtends an infinitesimal solid angle d at the point charge q . d S .rˆ From eq.(5) ,we have d r 2 dS cos d (8) r 2 From eq.(7) & (8) 1 d qd (9) 4 0 Total flux through the closed surface S is 1 d qd S S 4 0 q d 4 0 q (10) 4 0 Here the hypothetical closed surface S subtends the total solid angle at the point of location of the charge q.
Load more

Recommended publications
  • Electrostatics Vs Magnetostatics Electrostatics Magnetostatics
    Electrostatics vs Magnetostatics Electrostatics Magnetostatics Stationary charges ⇒ Constant Electric Field Steady currents ⇒ Constant Magnetic Field Coulomb’s Law Biot-Savart’s Law 1 ̂ ̂ 4 4 (Inverse Square Law) (Inverse Square Law) Electric field is the negative gradient of the Magnetic field is the curl of magnetic vector electric scalar potential. potential. 1 ′ ′ ′ ′ 4 |′| 4 |′| Electric Scalar Potential Magnetic Vector Potential Three Poisson’s equations for solving Poisson’s equation for solving electric scalar magnetic vector potential potential. Discrete 2 Physical Dipole ′′′ Continuous Magnetic Dipole Moment Electric Dipole Moment 1 1 1 3 ∙̂̂ 3 ∙̂̂ 4 4 Electric field cause by an electric dipole Magnetic field cause by a magnetic dipole Torque on an electric dipole Torque on a magnetic dipole ∙ ∙ Electric force on an electric dipole Magnetic force on a magnetic dipole ∙ ∙ Electric Potential Energy Magnetic Potential Energy of an electric dipole of a magnetic dipole Electric Dipole Moment per unit volume Magnetic Dipole Moment per unit volume (Polarisation) (Magnetisation) ∙ Volume Bound Charge Density Volume Bound Current Density ∙ Surface Bound Charge Density Surface Bound Current Density Volume Charge Density Volume Current Density Net , Free , Bound Net , Free , Bound Volume Charge Volume Current Net , Free , Bound Net ,Free , Bound 1 = Electric field = Magnetic field = Electric Displacement = Auxiliary
    [Show full text]
  • DI 101F.EN Real and Complex Analysis 7
    DI 101F.EN Real and Complex Analysis 1. Study program 1.1. University University of Bucharest 1.2. Faculty Faculty of Physics 1.3. Department Department of Theoretical physics, Mathematics, Optics, Plasma, and Lasers 1.4. Field of study Physics 1.5. Course of study Undergraduate/Bachelor of Science 1.6. Study program Physics (in English) 1.7. Study mode Full-time study 2. Course unit 2.1. Course unit title Real and Complex Analysis 2.2. Teacher Prof. dr. Claudia Timofte 2.3. Tutorials/Practicals instructor(s) Prof. dr. Claudia Timofte 2.4. Year of 2.5. 2.6. Type of 2.7. Type Content1) DC study 1 Semester I evaluation E of course unit Type2) DI 1) fundamental (DF), speciality (DS), complementary (DC); 2) compulsory (DI), elective (DO), optional (DFac) 3. Total estimated time (hours/semester) distribution: 3.1. Hours per week in curriculum 6 3 Practicals/Tutorials 3 Lecture 3.2. Total hours per semester distribution: 84 42 Practicals/Tutorials 42 Lecture Distribution of estimated time for study hours 3.2.1. Learning by using one’s own course notes, manuals, lecture notes, bibliography 30 3.2.2. Research in library, study of electronic resources, field research 27 3.2.3. Preparation for practicals/tutorials/projects/reports/homeworks 30 3.2.4. Examination 4 3.2.5. Other activities 0 3.3. Total hours of individual study 87 3.4. Total hours per semester 175 3.5. ECTS 7 4. Prerequisites (if necessary) 4.1. curriculum High school mathematics courses 4.2. competences Not applicable 5. Conditions/Infrastructure (if necessary) 5.1.
    [Show full text]
  • Review of Electrostatics and Magenetostatics
    Review of electrostatics and magenetostatics January 12, 2016 1 Electrostatics 1.1 Coulomb’s law and the electric field Starting from Coulomb’s law for the force produced by a charge Q at the origin on a charge q at x, qQ F (x) = 2 x^ 4π0 jxj where x^ is a unit vector pointing from Q toward q. We may generalize this to let the source charge Q be at an arbitrary postion x0 by writing the distance between the charges as jx − x0j and the unit vector from Qto q as x − x0 jx − x0j Then Coulomb’s law becomes qQ x − x0 x − x0 F (x) = 2 0 4π0 jx − xij jx − x j Define the electric field as the force per unit charge at any given position, F (x) E (x) ≡ q Q x − x0 = 3 4π0 jx − x0j We think of the electric field as existing at each point in space, so that any charge q placed at x experiences a force qE (x). Since Coulomb’s law is linear in the charges, the electric field for multiple charges is just the sum of the fields from each, n X qi x − xi E (x) = 4π 3 i=1 0 jx − xij Knowing the electric field is equivalent to knowing Coulomb’s law. To formulate the equivalent of Coulomb’s law for a continuous distribution of charge, we introduce the charge density, ρ (x). We can define this as the total charge per unit volume for a volume centered at the position x, in the limit as the volume becomes “small”.
    [Show full text]
  • We Continue to Compare the Electrostatic and Magnetostatic Fields. the Electrostatic Field Is Conservative
    We continue to compare the electrostatic and magnetostatic fields. The electrostatic field is conservative: This allows us to define the potential V: dl because a b is independent of the path. If a vector field has no curl (i.e., is conservative), it must be something's gradient. Gravity is conservative. Therefore you do see water flowing in such a loop without a pump in the physical world. For the magnetic field, If a vector field has no divergence (i.e., is solenoidal), it must be something's curl. In other words, the curl of a vector field has zero divergence. Let’s use another physical context to help you understand this math: Ampère’s law J ds 0 Kirchhoff's current law (KCL) S Since , we can define a vector field A such that Notice that for a given B, A is not unique. For example, if then , because Similarly, for the electrostatic field, the scalar potential V is not unique: If then You have the freedom to choose the reference (Ampère’s law) Going through the math, you will get Here is what means: Just notation. Notice that is a vector. Still remember what means for a scalar field? From a previous lecture: Recall that the choice for A is not unique. It turns out that we can always choose A such that (Ampère’s law) The choice for A is not unique. We choose A such that Here is what means: Notice that is a vector. Thus this is actually three equations: Recall the definition of for a scalar field from a previous lecture: Poisson’s equation for the magnetic field is actually three equations: Compare Poisson’s equation for the magnetic field with that for the electrostatic field: Given J, you can solve A, from which you get B by Given , you can solve V, from which you get E by Exams (Test 2 & Final) problems will not involve the vector potential.
    [Show full text]
  • Density Models for Streamer Discharges: Beyond Cylindrical Symmetry and Homogeneous Media
    Density models for streamer discharges: beyond cylindrical symmetry and homogeneous media A Luque IAA-CSIC, P.O. Box 3004, 18080 Granada, Spain U Ebert Centrum Wiskunde & Informatica (CWI), Amsterdam, The Netherlands, and Department of Applied Physics, Technische Universiteit Eindhoven, The Netherlands Abstract Streamer electrical discharges are often investigated with computer simulations of density models (also called drift-diffusion-reaction models). We review these models, detailing their physical foundations, their range of validity and the most relevant numerical algorithms employed in solving them. We focus particularly on schemes of adaptative refinement, used to resolve the multiple length scales in a streamer discharge without a high computational cost. We then report recent re- sults from these models, emphasizing developments that go beyond cylindrically symmetrical streamers propagating in homogeneous media. 1. Introduction Streamers [1–4] are transient electrical discharges that appear when a non- conducting medium is suddenly exposed to a high electric potential. While the average background field might be too low for plasma generation by electron im- pact on neutral molecules, the streamer discharge channel can enhance the electric field at its growing tip so strongly that it can create additional plasma and prop- arXiv:1011.2871v1 [physics.plasm-ph] 12 Nov 2010 agate nevertheless. The streamer achieves this through a very nonlinear dynam- ics with an intricate inner structure and locally very steep density gradients. This structure generates the local field enhancement and maintains propagation. There- fore, the accurate simulation of single, cylindrically symmetric streamer channels Email address: [email protected] (A Luque) PreprintsubmittedtoJournalofComputationalPhysics October 29, 2018 is far from trivial, even if the electrons are approximated by their densities as is conventionally done.
    [Show full text]
  • First-Year Electromagnetism Prof Laura Herz Www-Herz.Physics.Ox.Ac.Uk/Teaching.Html Electromagnetism in Everyday Life
    First-Year Electromagnetism Prof Laura Herz www-herz.physics.ox.ac.uk/teaching.html Electromagnetism in everyday life Electrostatics Magnetostatics Induction Electromagnetic waves Electromagnetism in ancient history Electrostatics Ancient Greece: rubbing amber against fur allows it to attract other light substances such as dust or papyrus Greek word for “amber”: + - ἤλεκτρον (elektron) - - - - + + Magnetostatics Magnesia (ancient Greek city in Ionia, today in Turkey): Naturally occurring minerals were found to attract metal objects (first references ~600BC). Crystals are referred to as: Iron ore, Lodestone, Magnetite, Fe3O4 Use of Lodestone compass for navigation in medieval China Electromagnetism in modern history 17th century AD to mid 18th century: Dominated by “frictional electrostatics” – arising from “triboelectric effect”: • When two different materials are brought into contact, - - - - charge flows to equalize their electro-chemical + + + - - + - + + potentials, bonds form across surface • Separating them may lead to charge remaining unequally distributed when bonds are broken • Rubbing enhances effect through repeat contact Focus on “electrostatic generators” – today’s van de Graaff Generators: Machines involved frictional passage of “positive” materials such as hair, silk, fur, leather against “negative” materials such as amber, sulfur 1660 Otto von Guericke, 1750ies, Hauksbee, Bose, Litzendorf, Wilson, Canton et al. But: not creating high electric energy density Electromagnetism in modern history From late 18th century: Rapid
    [Show full text]
  • Roadmap on Transformation Optics 5 Martin Mccall 1,*, John B Pendry 1, Vincenzo Galdi 2, Yun Lai 3, S
    Page 1 of 59 AUTHOR SUBMITTED MANUSCRIPT - draft 1 2 3 4 Roadmap on Transformation Optics 5 Martin McCall 1,*, John B Pendry 1, Vincenzo Galdi 2, Yun Lai 3, S. A. R. Horsley 4, Jensen Li 5, Jian 6 Zhu 5, Rhiannon C Mitchell-Thomas 4, Oscar Quevedo-Teruel 6, Philippe Tassin 7, Vincent Ginis 8, 7 9 9 9 6 10 8 Enrica Martini , Gabriele Minatti , Stefano Maci , Mahsa Ebrahimpouri , Yang Hao , Paul Kinsler 11 11,12 13 14 15 9 , Jonathan Gratus , Joseph M Lukens , Andrew M Weiner , Ulf Leonhardt , Igor I. 10 Smolyaninov 16, Vera N. Smolyaninova 17, Robert T. Thompson 18, Martin Wegener 18, Muamer Kadic 11 18 and Steven A. Cummer 19 12 13 14 Affiliations 15 1 16 Imperial College London, Blackett Laboratory, Department of Physics, Prince Consort Road, 17 London SW7 2AZ, United Kingdom 18 19 2 Field & Waves Lab, Department of Engineering, University of Sannio, I-82100 Benevento, Italy 20 21 3 College of Physics, Optoelectronics and Energy & Collaborative Innovation Center of Suzhou Nano 22 Science and Technology, Soochow University, Suzhou 215006, China 23 24 4 University of Exeter, Department of Physics and Astronomy, Stocker Road, Exeter, EX4 4QL United 25 26 Kingdom 27 5 28 School of Physics and Astronomy, University of Birmingham, Edgbaston, Birmingham, B15 2TT, 29 United Kingdom 30 31 6 KTH Royal Institute of Technology, SE-10044, Stockholm, Sweden 32 33 7 Department of Physics, Chalmers University , SE-412 96 Göteborg, Sweden 34 35 8 Vrije Universiteit Brussel Pleinlaan 2, 1050 Brussel, Belgium 36 37 9 Dipartimento di Ingegneria dell'Informazione e Scienze Matematiche, University of Siena, Via Roma, 38 39 56 53100 Siena, Italy 40 10 41 School of Electronic Engineering and Computer Science, Queen Mary University of London, 42 London E1 4FZ, United Kingdom 43 44 11 Physics Department, Lancaster University, Lancaster LA1 4 YB, United Kingdom 45 46 12 Cockcroft Institute, Sci-Tech Daresbury, Daresbury WA4 4AD, United Kingdom.
    [Show full text]
  • Electrostatics
    Ben Franklin, 1750 “Kite Experiment” – link between lightening and sparks Electrostatics “electrical” fire from the clouds Greeks noticed when they rubbed things against amber an invisible force of attraction occurred. Greek word for amber is elektron, which today represents the word “electrical” Electrostatics Study of electrical charges that can be collected and held in one place Energy at rest- nonmoving electric charge Involves: 1) electric charges, 2) forces between, & 3) their behavior in material An object that exhibits electrical interaction after rubbing is said to be charged Static electricity- electricity caused by friction Charged objects will eventually return to their neutral state Electric Charge “Charge” is a property of subatomic particles. Facts about charge: There are 2 types: positive (protons) and negative (electrons) Matter contains both types of charge ( + & -) occur in pairs, friction separates the two LIKE charges REPEL and OPPOSITE charges ATTRACT Charges are symbolic of fluids in that they can be in 2 states: STATIC or DYNAMIC. Microscopic View of Charge Electrical charges exist w/in atoms 1890, J.J. Thomson discovered the light, negatively charged particles of matter- Electrons 1909-1911 Ernest Rutherford, discovered atoms have a massive, positively charged center- Nucleus Positive nucleus balances out the negative electrons to make atom neutral Can remove electrons w/addition of energy, make atom positively charged or add to make them negatively charged ( called Ions) (+ cations) (- anions) Triboelectric Series Ranks materials according to their tendency to give up their electrons Material exchange electrons by the process of rubbing two objects Electric Charge – The specifics •The symbol for CHARGE is “q” •The SI unit is the COULOMB(C), named after Charles Coulomb •If we are talking about a SINGLE charged particle such as 1 electron or 1 proton we are referring to an ELEMENTARY charge and often use, Some important constants: e , to symbolize this.
    [Show full text]
  • Lecture 6 Basics of Magnetostatics
    Lecture 6 Basics of Magnetostatics Today’s topics 1. New topic – magnetostatics 2. Present a parallel development as we did for electrostatics 3. Derive basic relations from a fundamental force law 4. Derive the analogs of E and G 5. Derive the analog of Gauss’ theorem 6. Derive the integral formulation of magnetostatics 7. Derive the differential form of magnetostatics 8. A few simple problems General comments 1. What is magnetostatics? The study of DC magnetic fields that arise from the motion of charged particles. 2. Since charged particles are present, does this mean we also must have an electric field? No!! Electrons can flow through ions in such a way that current flows but there is still no net charge, and hence no electric field. This is the situation in magnetostatics 3. Magnetostatics is more complicated than electrostatics. 4. Single magnetic charges do not exist in nature. The simplest basic element in magnetostatics is the magnetic dipole, which is equivalent to two, closely paired equal and opposite charges in electrostatics. In magnetostatics the dipole forms from a small circular loop of current. 5. Magnetic geometries are also more complicated than in electrostatics. The vector nature of the magnetic field is less intuitive. 1 The basic force of magnetostatics 1. Recall electrostatics. qq rr = 12 1 2 F12 3 4QF0 rr12 2. In magnetostatics there is an equivalent empirical law which we take as a postulate qq vv×× ¯( rr ) = 12N 0 1212¢± F12 3 4Q rr12 3. The force is proportional to 1/r 2 . = 4. The force is perpendicular to v1 : Fv12¸ 1 0 .
    [Show full text]
  • Electricity and Magnetism
    Electricity and Magnetism Definition The Physical phenomena involving electric charges, their motions, and their effects. The motion of a charge is affected by its interaction with the electric field and, for a moving charge, the magnetic field. The electric field acting on a charge arises from the presence of other charges and from a time-varying magnetic field. The magnetic field acting on a moving charge arises from the motion of other charges and from a time-varying electric field. Thus electricity and magnetism are ultimately inextricably linked. In many cases, however, one aspect may dominate, and the separation is meaningful. See also Electric charge; Electric field; Magnetism. History of Electricity From the writings of Thales of Miletus it appears that Westerners knew as long ago as 600 B.C. that amber becomes charged by rubbing. There was little real progress until the English scientist William Gilbert in 1600 described the electrification of many substances and coined the term electricity from the Greek word for amber. As a result, Gilbert is called the father of modern electricity. In 1660 Otto von Guericke invented a crude machine for producing static electricity. It was a ball of sulfur, rotated by a crank with one hand and rubbed with the other. Successors, such as Francis Hauksbee, made improvements that provided experimenters with a ready source of static electricity. Today's highly developed descendant of these early machines is the Van de Graaf generator, which is sometimes used as a particle accelerator. Robert Boyle realized that attraction and repulsion were mutual and that electric force was transmitted through a vacuum (c.1675).
    [Show full text]
  • Chapter 2. Electrostatics
    Chapter 2. Electrostatics 2.1. The Electrostatic Field To calculate the force exerted by some electric charges, q1, q2, q3, ... (the source charges) on another charge Q (the test charge) we can use the principle of superposition. This principle states that the interaction between any two charges is completely unaffected by the presence of other charges. The force exerted on Q by q1, q2, and q3 (see Figure 2.1) is therefore equal to the vector sum of the force F1 exerted by q1 on Q, the force F2 exerted by q2 on Q, and the force F3 exerted by q3 on Q. Ftot F1 q3 F3 Q F2 q2 q1 Figure 2.1. Superposition of forces. The force exerted by a charged particle on another charged particle depends on their separation distance, on their velocities and on their accelerations. In this Chapter we will consider the special case in which the source charges are stationary. The electric field produced by stationary source charges is called and electrostatic field. The electric field at a particular point is a vector whose magnitude is proportional to the total force acting on a test charge located at that point, and whose direction is equal to the direction of - 1 - the force acting on a positive test charge. The electric field E , generated by a collection of source charges, is defined as F E = Q where F is the total electric force exerted by the source charges on the test charge Q. It is assumed that the test charge Q is small and therefore does not change the distribution of the source charges.
    [Show full text]
  • Electrostatics and Its Hazards
    A Study on Electrostatics and Its Hazards by NIRMALYA BASU (Master of Engineering in Electronics and Telecommunication Engineering) Date of Birth: May 3, 1984 Email: [email protected] Mobile: +919007757186 Address: 162/B/185 Lake Gardens, Kolkata, West Bengal, India, PIN: 700045. Contents Page 1. Introduction 1 2. Electrostatics in Liquids and Its Hazardous Implications 2 2.1. The Phenomenon of Flow Electrification 2 2.2. Hazards in the Industry 5 2.2.1. Metallic Fuel-handling Systems 6 2.2.2. Non-metallic Fuel-handling Systems 6 2.3. Liquid Charging Due to fragmentation and Hazards Arising Thereof 8 2.3.1. The Charging Phenomenon 8 2.3.2. Industrial Hazards 8 2.3.3. Remedial Measures 11 2.4. Standards on Recommended Practices 11 3. Electrostatics in Solids and Its Hazardous Implications 12 3.1. Phenomenon of Contact Charging or Tribocharging of Solids 12 3.1.1. Phenomenon of Charging of Two Metal Objects Brought in Contact with Each Other 12 3.1.2. Phenomenon of Contact Charging of Solids when Insulators are Involved 14 3.1.3. Charging of Two Identical Materials Brought in Contact with Each Other 18 3.1.4. Contact Charging of Granules 21 3.2. Hazards Caused in the Industry Due to Charging of Solids 21 3.2.1. Electrostatic Hazards in Particulate Processes 22 3.2.2. Electrostatic Hazards in the Semiconductor Industry 25 4. Principles of Fire 27 4.1. Combustion 27 4.2. Ignition: Piloted Ignition and Autoignition 27 4.3. Limits of Flammability 28 4.4. Fire Point 29 4.5.
    [Show full text]