Calculation of Total Inductance of a Straight Conductor of Finite Length
|
|
|
- Rolf Lawrence
- 7 years ago
- Views:
Transcription
1 Cacuation of Tota Inuctance of a Staigt Conucto of Finite Lengt PRIYANKA PATEL C.U. Sa Science Coege, Asam Roa, Ameaba 384 E-mai: jgos4@yaoo.com ASTRACT Tis atice pesents cacuation of tota inuctance of a staigt conucto. Supisingy, it is not easy to fin an expession fo te inuctance of a staigt piece of conucto. In tis atice, te tota inuctance of a staigt conucto is cacuate using te iot-savat aw. Te esut is vey usefu as a buiing bock fo moe compex stuctues, an aso because te inuctance of a conucto is impotant in ig fequency o ig spee eectica cicuits. Intouction Te pionee expeiments of Faaay on te inuction of a cuent in a conucto wen te magnetic fux inke wit te conucto is cange e to two vey impotant aws in pysics. Fist is te Faaay s Law an te secon is te Lenz s Law. Faaay s aw states tat te inuce eecto motive foce (e.m.f.) in a cicuit, wen te magnetic fie aoun it is cange, is equa to te ate of vaiation of te numbe of ines of magnetic inuction inke wit te cicuit. Lenz s aw states tat te iection of te inuce cuent ue to te inuce eecto motive foce is suc as to ty to stop te action taking pace, i.e. to oppose te vaiation of te magnetic fux inke wit te cicuit. Te magnetic fux is mae to incease positivey, so te e.m.f. opposes tis cange. Tis penomenon is cae te eectomagnetic inuction. Consequences of tis penomenon of eectomagnetic inuction ae te effects of sef-inuction an mutua inuction. Te coefficient of sef-inuctance, o te sef-inuctance L, is efine as te fux inke wit te cicuit wen unit cuent fows in it. Pysics Eucation Juy Septembe 9 93
2 Eaboating fute, wen an eectic cuent I fowing oun a cicuit it pouces a magnetic fie an ence a magnetic fux Φ toug te cicuit. Te atio of te magnetic fux to te cuent is cae te inuctance, o moe accuatey sef-inuctance of te cicuit. Te tem was coine by Oive Heavisie in Febuay 886. It is customay to use te symbo L fo inuctance, possiby in onou of te pysicist Heinic Lenz. Te quantitative efinition of te inuctance is teefoe L=ΦI, wee I is te cuent in te cucuit. It foows tat te SI units fo inuctance ae webes pe ampee. In onou of Josep Heny, te unit of inuctance as been given te name eny (H): H = Wb/A. Hence wen I = Ampee, L=Φ. Cacuation of Inuctance of a Staigt Conucto Atoug te inuctances of cicuit eements not associate wit magnetic mateias ae inepenent of te vaue of te cuent an epenent ony on te geomety of te system, it is ony in te simpest cases tat tese constants can be cacuate exacty. Supisingy, it is not easy to fin an expession fo te inuctance of a staigt piece of conucto of a finite engt. An yet tis esut is vey usefu as a buiing bock fo moe compex stuctues, an aso because te inuctance of a conucto is impotant in ig fequency o ig spee eectica cicuits. If we consie te conucto in isoation we ignoe te question of ow te cuent gets to te conucto. ut tat cuent, oweve it is eivee, wi affect te fux, wic is eveope in te vicinity (outsie) of te conucto an aso insie te conucto. In tis epot we cacuate te fux eveope pe unit cuent outsie an insie te conucto sepaatey an efine it as extena an intena inuctance espectivey. Te tota sefinuctance o te inuctance of te staigt conucto is ten given by aing te extena an intena inuctances. Cacuation of Extena Inuct- (a) ance We efine te extena inuctance of te staigt conucto as te fux eveope outsie te conucto ue to unit cuent passing toug te conucto in te egion boune by ines pepenicua to te beginning an en of te conucto. We eive te fomua in te simpest possibe manne, using te aw of iot an Savat in te iffeentia fom as it gives a bette pysica view of te vaious pobems consiee. Let A in Figue is a staigt conucto of engt. Let I cuent pass toug te conucto. Fist we use te iot-savat s aw to etemine te magnetic fie at a given point P outsie te conucto ue to constant cuent I. Let be a sma engt eement of te conucto. Te magnetic fie, at point P ue to cuent I in a sma engt eement of te conucto, accoing to bio-savat s aw is given by (Figue) μ I = () 3 wee, = engt of sma eement, = istance fom point P to sma eement, μ =pemeabiity constant = Tm/A. Let us assume tat te conucto is pace aong X-axis an P is any point on Y-axis ten te iection of wi be aong Z-axis. If we epesent te iection of X, Y an Z axis by î, ĵ an ˆk espectivey. Tus te magnitue of te magnetic fie at point P is μ = [sinθ + sin θ] () 94 Pysics Eucation Juy Septembe 9
3 θ 3 P θ θ θ A I I O x Q Figue : Magnetic fie cacuation at point P outsie te conucto ue to cuent I passing toug te conucto A of engt. Equation () gives te magnetic fie at a paticua point P ue to te cuent I passing toug a conucto of engt. Now, te magnetic fux Φ in a iffeentia aea at a fixe istance fom te conucto, i.e. Φ = S =. is given by μ Φ= = [sinθ + sin θ ] S To obtain te tota fux ove a of te aea we integate te above equation ove te engt of te conucto an ten ove te istance fom te conucto to infinity. Integating ove te engt of te conucto gives μ I (sin sin ) (3) = θ + θ μ I + π = Now, we integate te above equation ove te istance fom te ege of te conucto to infinity. Let te iamete of te conucto is ten we integate te above equation fom / to to obtain te tota magnetic fux outsie te conucto. Hence te tota fux is given by: Φ = = / μ + / π / / Pysics Eucation Juy Septembe 9 95
4 Φ= = Hence, / + / (4) / / Φ= = = / μ I 4 n + + π n Fom te efinition of inuctance, we obtain te extena inuctance by putting unit cuent, i.e. I = in te above equation. Teefoe te extena inuctance of a staigt conucto of finite engt is given by Lext = n ( + x) x+ Lext = n ( + x) x+ n wee x = + ( ) (b) Cacuation of Intena Inuctance H H I P I A Figue : Magnetic fie cacuation at point P insie te conucto ue to cuent I passing toug te conucto A of engt. We know tat wen a cuent, I, passes toug a conucto, te intena enegy stoe in te conucto is equa to LI. Wee, L m m is te intena inuctance of te conucto. Tis enegy is stoe in fom of magnetic enegy, wic is given by /μ pe unit voume. Te tota enegy stoe can be obtaine by integating ove tota voume of te conucto. Equating tis enegy to ½ L m I, we can cacuate te intena inuctance of te conucto. We know tat to a goo appoximation te tota magnetic fie ue to a cuent I, at any 96 Pysics Eucation Juy Septembe 9
5 point cose to te suface of te conucto wit its engt, >>> tan its aius,, is given by, I = μ (5) π wee, μ = pemeabiity an = aius. Te magnetic fie,, at any given point P insie te cyinica conucto, at a istance fom te axis of te conucto is given by μ I π = (6) wee, te cuent I is passing toug te conucto of aius. If te tota cuent, I, passes toug te conucto, ten te cuent I can be given in tems of I as, I = I ecause I=Jπ an I =Jπ Hence Substituting Eq. (7) in Eq. (6), we ave = μ I π (7) μi = (8) 4 μ Te voume eement of te conucto of aius is given by π. Te enegy in tis voume is ( π ) μ Integating tis equation wit espect to fom zeo an (= /, Figue ), te tota enegy insie te conucto can be obtaine μi V = (9) μ 6π We know tis enegy is equa to Hence, (c) L in Lin μi LI m = V= μ 6π m = 7 μi = = = = H Tota Inuctance LI, ence Tota inuctance of te staigt conucto is te sum of intena & extena inuctance an is given by: L Tota = H n ( + x) x+ + wee = engt of te conucto, = iamete of te conucto an x ( ) Concusion = +. μ I = 4 π Pysics Eucation Juy Septembe 9 97
6 We geneay associate inuctance wit a oop o coi of conucto. Howeve, even a staigt piece of conucto, as some sef-inuctance o inuctance. Te inuctance of a staigt conucto of finite engt is cacuate stating fom te fist pincipe. It is not easy to fin an expession fo te inuctance of a staigt piece of conucto of a finite engt. Te esuts ae vey usefu an can be use as a buiing bock fo moe compex stuctues. Fute, because te inuctance of a conucto is impotant in ig fequency o ig spee eectica cicuits, te fomua eive wi be vey usefu in api cacuation of te same. Acknowegements Fist, I wou ike to tank Vikam A. Saabai Community Science Cente, Ameaba fo giving me tis oppotunity to wok at Institute fo Pasma Reseac as a pat of A..Sc. (Pysics) Pogam. I am vey muc tankfu to D. Joyeep Gos an M. oosan Paaka fo poviing pope guiance uing te couse of tis wok an aso fo eping me in many ways. I am vey muc tankfu to te Diecto, I.P.R. fo aowing me to use te institute s faciities. I am vey tankfu to D. Ragvan Rangajan (Pysica Reseac Laboatoy, Ameaba), fo giving me suc a geat oppotunity. Refeence D. J. Giffit, Intouction to Eectoynamics (3 e.), (Engewoos Ciff: Pentice Ha) 998 SUSCRIPTION RENEWAL KINDLY RENEW YOUR SUSCRIPTION SOON FOR PHYSICS EDUCATION Vo 6 (Januay Decembe 9) Use te oe fom pinte at te en of tis issue an mai it, uy compete, wit emittance to Copies of No, ae sti avaiabe, sen you oe soon. SOUTH ASIAN PULISHERS PVT LTD. 5 Siat Encave, PO Jangpua, New Dei 4-6 Pones: , , e.mai: sapub@nb.vsn.net.in; soutasian@bo.net.in 98 Pysics Eucation Juy Septembe 9
7 Pysics Eucation Juy Septembe 9 99
Chapter 19: Electric Charges, Forces, and Fields ( ) ( 6 )( 6
Chapte 9 lectic Chages, Foces, an Fiels 6 9. One in a million (0 ) ogen molecules in a containe has lost an electon. We assume that the lost electons have been emove fom the gas altogethe. Fin the numbe
Analytical Proof of Newton's Force Laws
Analytical Poof of Newton s Foce Laws Page 1 1 Intouction Analytical Poof of Newton's Foce Laws Many stuents intuitively assume that Newton's inetial an gavitational foce laws, F = ma an Mm F = G, ae tue
CLOSE RANGE PHOTOGRAMMETRY WITH CCD CAMERAS AND MATCHING METHODS - APPLIED TO THE FRACTURE SURFACE OF AN IRON BOLT
CLOSE RANGE PHOTOGRAMMETR WITH CCD CAMERAS AND MATCHING METHODS - APPLIED TO THE FRACTURE SURFACE OF AN IRON BOLT Tim Suthau, John Moé, Albet Wieemann an Jens Fanzen Technical Univesit of Belin, Depatment
!( r) =!( r)e i(m" + kz)!!!!. (30.1)
3 EXAMPLES OF THE APPLICATION OF THE ENERGY PRINCIPLE TO CYLINDRICAL EQUILIBRIA We now use the Enegy Pinciple to analyze the stability popeties of the cylinical! -pinch, the Z-pinch, an the Geneal Scew
Determination of Dielectric Constant and Dissipation Factor of a Printed Circuit Board Material Using a Microstrip Ring Resonator Structure
Detemination of Dielectic Constant and Dissipation Facto of a Pinted Cicuit Boad Mateial Using a Micostip Ring Resonato Stuctue J-M. Heinola, K-P. Lätti, J-P. Stöm, M. Kettunen and P. Silventoinen Lappeenanta
9.3 Surface Area of Pyramids
Page 1 of 9 9.3 Suface Aea of Pyamids and Cones Goa Find the suface aeas of pyamids and cones. Key Wods pyamid height of a pyamid sant height of a pyamid cone height of a cone sant height of a cone The
Chapter 30: Magnetic Fields Due to Currents
d Chapte 3: Magnetic Field Due to Cuent A moving electic chage ceate a magnetic field. One of the moe pactical way of geneating a lage magnetic field (.1-1 T) i to ue a lage cuent flowing though a wie.
2 r2 θ = r2 t. (3.59) The equal area law is the statement that the term in parentheses,
3.4. KEPLER S LAWS 145 3.4 Keple s laws You ae familia with the idea that one can solve some mechanics poblems using only consevation of enegy and (linea) momentum. Thus, some of what we see as objects
SELF-INDUCTANCE AND INDUCTORS
MISN-0-144 SELF-INDUCTANCE AND INDUCTORS SELF-INDUCTANCE AND INDUCTORS by Pete Signell Michigan State Univesity 1. Intoduction.............................................. 1 A 2. Self-Inductance L.........................................
SAT Math Must-Know Facts & Formulas
SAT Mat Must-Know Facts & Formuas Numbers, Sequences, Factors Integers:..., -3, -2, -1, 0, 1, 2, 3,... Rationas: fractions, tat is, anyting expressabe as a ratio of integers Reas: integers pus rationas
Deflection of Electrons by Electric and Magnetic Fields
Physics 233 Expeiment 42 Deflection of Electons by Electic and Magnetic Fields Refeences Loain, P. and D.R. Coson, Electomagnetism, Pinciples and Applications, 2nd ed., W.H. Feeman, 199. Intoduction An
N V V L. R a L I. Transformer Equation Notes
Tnsfome Eqution otes This file conts moe etile eivtion of the tnsfome equtions thn the notes o the expeiment 3 wite-up. t will help you to unestn wht ssumptions wee neee while eivg the iel tnsfome equtions
SAT Math Facts & Formulas
Numbers, Sequences, Factors SAT Mat Facts & Formuas Integers:..., -3, -2, -1, 0, 1, 2, 3,... Reas: integers pus fractions, decimas, and irrationas ( 2, 3, π, etc.) Order Of Operations: Aritmetic Sequences:
Chapter 22. Outside a uniformly charged sphere, the field looks like that of a point charge at the center of the sphere.
Chapte.3 What is the magnitude of a point chage whose electic field 5 cm away has the magnitude of.n/c. E E 5.56 1 11 C.5 An atom of plutonium-39 has a nuclea adius of 6.64 fm and atomic numbe Z94. Assuming
Physics 235 Chapter 5. Chapter 5 Gravitation
Chapte 5 Gavitation In this Chapte we will eview the popeties of the gavitational foce. The gavitational foce has been discussed in geat detail in you intoductoy physics couses, and we will pimaily focus
Sections 3.1/3.2: Introducing the Derivative/Rules of Differentiation
Sections 3.1/3.2: Introucing te Derivative/Rules of Differentiation 1 Tangent Line Before looking at te erivative, refer back to Section 2.1, looking at average velocity an instantaneous velocity. Here
Financing Terms in the EOQ Model
Financing Tems in the EOQ Model Habone W. Stuat, J. Columbia Business School New Yok, NY 1007 hws7@columbia.edu August 6, 004 1 Intoduction This note discusses two tems that ae often omitted fom the standad
Episode 401: Newton s law of universal gravitation
Episode 401: Newton s law of univesal gavitation This episode intoduces Newton s law of univesal gavitation fo point masses, and fo spheical masses, and gets students pactising calculations of the foce
4.4 VOLUME AND SURFACE AREA
160 CHAPTER 4 Geomety 4.4 VOLUME AND SURFACE AREA Textbook Refeence Section 8.4 CLAST OBJECTIVES Calculate volume and uface aea Infe fomula fo meauing geometic figue Select applicable fomula fo computing
www.sakshieducation.com
Viscosity. The popety of viscosity in gas is due to ) Cohesive foces between the moecues ) Coisions between the moecues ) Not having a definite voume ) Not having a definite size. When tempeatue is inceased
Chapter 3 Savings, Present Value and Ricardian Equivalence
Chapte 3 Savings, Pesent Value and Ricadian Equivalence Chapte Oveview In the pevious chapte we studied the decision of households to supply hous to the labo maket. This decision was a static decision,
CRRC-1 Method #1: Standard Practice for Measuring Solar Reflectance of a Flat, Opaque, and Heterogeneous Surface Using a Portable Solar Reflectometer
CRRC- Method #: Standad Pactice fo Measuing Sola Reflectance of a Flat, Opaque, and Heteogeneous Suface Using a Potable Sola Reflectomete Scope This standad pactice coves a technique fo estimating the
1D STEADY STATE HEAT
D SEADY SAE HEA CONDUCION () Pabal alukda Aociate Pofeo Depatment of Mecanical Engineeing II Deli E-mail: pabal@mec.iitd.ac.in Palukda/Mec-IID emal Contact eitance empeatue ditibution and eat flow line
Lecture 10: What is a Function, definition, piecewise defined functions, difference quotient, domain of a function
Lecture 10: Wat is a Function, definition, piecewise defined functions, difference quotient, domain of a function A function arises wen one quantity depends on anoter. Many everyday relationsips between
Valuation of Floating Rate Bonds 1
Valuation of Floating Rate onds 1 Joge uz Lopez us 316: Deivative Secuities his note explains how to value plain vanilla floating ate bonds. he pupose of this note is to link the concepts that you leaned
PRICING MODEL FOR COMPETING ONLINE AND RETAIL CHANNEL WITH ONLINE BUYING RISK
PRICING MODEL FOR COMPETING ONLINE AND RETAIL CHANNEL WITH ONLINE BUYING RISK Vaanya Vaanyuwatana Chutikan Anunyavanit Manoat Pinthong Puthapon Jaupash Aussaavut Dumongsii Siinhon Intenational Institute
Experiment MF Magnetic Force
Expeiment MF Magnetic Foce Intoduction The magnetic foce on a cuent-caying conducto is basic to evey electic moto -- tuning the hands of electic watches and clocks, tanspoting tape in Walkmans, stating
Forces & Magnetic Dipoles. r r τ = μ B r
Foces & Magnetic Dipoles x θ F θ F. = AI τ = U = Fist electic moto invented by Faaday, 1821 Wie with cuent flow (in cup of Hg) otates aound a a magnet Faaday s moto Wie with cuent otates aound a Pemanent
Solution Derivations for Capa #8
Solution Deivations fo Capa #8 1) A ass spectoete applies a voltage of 2.00 kv to acceleate a singly chaged ion (+e). A 0.400 T field then bends the ion into a cicula path of adius 0.305. What is the ass
How Much Should a Firm Borrow. Effect of tax shields. Capital Structure Theory. Capital Structure & Corporate Taxes
How Much Should a Fim Boow Chapte 19 Capital Stuctue & Copoate Taxes Financial Risk - Risk to shaeholdes esulting fom the use of debt. Financial Leveage - Incease in the vaiability of shaeholde etuns that
Gauss Law. Physics 231 Lecture 2-1
Gauss Law Physics 31 Lectue -1 lectic Field Lines The numbe of field lines, also known as lines of foce, ae elated to stength of the electic field Moe appopiately it is the numbe of field lines cossing
Optical Fibers: History, Structure and the Weakly Guided Solution. May 30, 2008 Physics 464 Dr. La Rosa Portland State University.
Optica Fibes: Histoy, Stuctue and the Weaky Guided Soution May 30, 008 Physics 464 D. La Rosa Potand State Univesity by Tayo Biyeu Abstact In this pape, I wi tak about the histoy and deveopment of fibe
Gravitation. AP Physics C
Gavitation AP Physics C Newton s Law of Gavitation What causes YOU to be pulled down? THE EARTH.o moe specifically the EARTH S MASS. Anything that has MASS has a gavitational pull towads it. F α Mm g What
Excitation energies for molecules by Time-Dependent. based on Effective Exact Exchange Kohn-Sham potential
Excitation enegies fo molecules by Time-Dependent Density-Functional Theoy based on Effective Exact Exchange Kohn-Sham potential Fabio Della Sala National Nanotechnology Laboatoies Lecce Italy A. Göling
Figure 2. So it is very likely that the Babylonians attributed 60 units to each side of the hexagon. Its resulting perimeter would then be 360!
1. What ae angles? Last time, we looked at how the Geeks intepeted measument of lengths. Howeve, as fascinated as they wee with geomety, thee was a shape that was much moe enticing than any othe : the
Exam 3: Equation Summary
MASSACHUSETTS INSTITUTE OF TECHNOLOGY Depatment of Physics Physics 8.1 TEAL Fall Tem 4 Momentum: p = mv, F t = p, Fext ave t= t f t= Exam 3: Equation Summay total = Impulse: I F( t ) = p Toque: τ = S S,P
The LCOE is defined as the energy price ($ per unit of energy output) for which the Net Present Value of the investment is zero.
Poject Decision Metics: Levelized Cost of Enegy (LCOE) Let s etun to ou wind powe and natual gas powe plant example fom ealie in this lesson. Suppose that both powe plants wee selling electicity into the
Math 229 Lecture Notes: Product and Quotient Rules Professor Richard Blecksmith richard@math.niu.edu
Mat 229 Lecture Notes: Prouct an Quotient Rules Professor Ricar Blecksmit ricar@mat.niu.eu 1. Time Out for Notation Upate It is awkwar to say te erivative of x n is nx n 1 Using te prime notation for erivatives,
Vector Calculus: Are you ready? Vectors in 2D and 3D Space: Review
Vecto Calculus: Ae you eady? Vectos in D and 3D Space: Review Pupose: Make cetain that you can define, and use in context, vecto tems, concepts and fomulas listed below: Section 7.-7. find the vecto defined
CLASS XI CHAPTER 3. Theorem 1 (sine formula) In any triangle, sides are proportional to the sines of the opposite angles. That is, in a triangle ABC
CLASS XI Anneue I CHAPTER.6. Poofs and Simple Applications of sine and cosine fomulae Let ABC be a tiangle. By angle A we mean te angle between te sides AB and AC wic lies between 0 and 80. Te angles B
Magnetic Field and Magnetic Forces. Young and Freedman Chapter 27
Magnetic Field and Magnetic Foces Young and Feedman Chapte 27 Intoduction Reiew - electic fields 1) A chage (o collection of chages) poduces an electic field in the space aound it. 2) The electic field
AN IMPLEMENTATION OF BINARY AND FLOATING POINT CHROMOSOME REPRESENTATION IN GENETIC ALGORITHM
AN IMPLEMENTATION OF BINARY AND FLOATING POINT CHROMOSOME REPRESENTATION IN GENETIC ALGORITHM Main Golub Faculty of Electical Engineeing and Computing, Univesity of Zageb Depatment of Electonics, Micoelectonics,
Determining solar characteristics using planetary data
Detemining sola chaacteistics using planetay data Intoduction The Sun is a G type main sequence sta at the cente of the Sola System aound which the planets, including ou Eath, obit. In this inestigation
Solutions to Problems: Chapter 7
Solution to Poblem: Chapte 7 P7-1. P7-2. P7-3. P7-4. Authoized and available hae LG 2; Baic a. Maximum hae available fo ale Authoized hae 2,000,000 Le: Shae outtanding 1,400,000 Available hae 600,000 b.
The Electric Potential, Electric Potential Energy and Energy Conservation. V = U/q 0. V = U/q 0 = -W/q 0 1V [Volt] =1 Nm/C
![The Electric Potential, Electric Potential Energy and Energy Conservation. V = U/q 0. V = U/q 0 = -W/q 0 1V [Volt] =1 Nm/C](/thumbs/40/21051327.jpg "The Electric Potential, Electric Potential Energy and Energy Conservation. V = U/q 0. V = U/q 0 = -W/q 0 1V [Volt] =1 Nm/C")
Geneal Physics - PH Winte 6 Bjoen Seipel The Electic Potential, Electic Potential Enegy and Enegy Consevation Electic Potential Enegy U is the enegy of a chaged object in an extenal electic field (Unit
(a) The centripetal acceleration of a point on the equator of the Earth is given by v2. The velocity of the earth can be found by taking the ratio of
Homewok VI Ch. 7 - Poblems 15, 19, 22, 25, 35, 43, 51. Poblem 15 (a) The centipetal acceleation of a point on the equato of the Eath is given by v2. The velocity of the eath can be found by taking the
VISCOSITY OF BIO-DIESEL FUELS
VISCOSITY OF BIO-DIESEL FUELS One of the key assumptions fo ideal gases is that the motion of a given paticle is independent of any othe paticles in the system. With this assumption in place, one can use
Section 3.3. Differentiation of Polynomials and Rational Functions. Difference Equations to Differential Equations
Difference Equations to Differential Equations Section 3.3 Differentiation of Polynomials an Rational Functions In tis section we begin te task of iscovering rules for ifferentiating various classes of
Instantaneous Rate of Change:
Instantaneous Rate of Cange: Last section we discovered tat te average rate of cange in F(x) can also be interpreted as te slope of a scant line. Te average rate of cange involves te cange in F(x) over
AP Physics Electromagnetic Wrap Up
AP Physics Electomagnetic Wap Up Hee ae the gloious equations fo this wondeful section. F qsin This is the equation fo the magnetic foce acting on a moing chaged paticle in a magnetic field. The angle
Semipartial (Part) and Partial Correlation
Semipatial (Pat) and Patial Coelation his discussion boows heavily fom Applied Multiple egession/coelation Analysis fo the Behavioal Sciences, by Jacob and Paticia Cohen (975 edition; thee is also an updated
How many times have you seen something like this?
VOL. 77, NO. 4, OTOR 2004 251 Whee the amea Was KTHRN McL. YRS JMS M. HNL Smith ollege Nothampton, M 01063 jhenle@math.smith.eu How many times have you seen something like this? Then Now Souces: outesy
4a 4ab b 4 2 4 2 5 5 16 40 25. 5.6 10 6 (count number of places from first non-zero digit to
. Simplify: 0 4 ( 8) 0 64 ( 8) 0 ( 8) = (Ode of opeations fom left to ight: Paenthesis, Exponents, Multiplication, Division, Addition Subtaction). Simplify: (a 4) + (a ) (a+) = a 4 + a 0 a = a 7. Evaluate
Voltage ( = Electric Potential )
V-1 of 9 Voltage ( = lectic Potential ) An electic chage altes the space aound it. Thoughout the space aound evey chage is a vecto thing called the electic field. Also filling the space aound evey chage
The Binomial Distribution
The Binomial Distibution A. It would be vey tedious if, evey time we had a slightly diffeent poblem, we had to detemine the pobability distibutions fom scatch. Luckily, thee ae enough similaities between
883 Brochure A5 GENE ss vernis.indd 1-2
ess x a eu / u e a. p o.eu c e / :/ http EURAXESS Reseaches in Motion is the gateway to attactive eseach caees in Euope and to a pool of wold-class eseach talent. By suppoting the mobility of eseaches,
Lab #7: Energy Conservation
Lab #7: Enegy Consevation Photo by Kallin http://www.bungeezone.com/pics/kallin.shtml Reading Assignment: Chapte 7 Sections 1,, 3, 5, 6 Chapte 8 Sections 1-4 Intoduction: Pehaps one of the most unusual
FXA 2008. Candidates should be able to : Describe how a mass creates a gravitational field in the space around it.
Candidates should be able to : Descibe how a mass ceates a gavitational field in the space aound it. Define gavitational field stength as foce pe unit mass. Define and use the peiod of an object descibing
Continuous Compounding and Annualization
Continuous Compounding and Annualization Philip A. Viton Januay 11, 2006 Contents 1 Intoduction 1 2 Continuous Compounding 2 3 Pesent Value with Continuous Compounding 4 4 Annualization 5 5 A Special Poblem
est using the formula I = Prt, where I is the interest earned, P is the principal, r is the interest rate, and t is the time in years.
9.2 Inteest Objectives 1. Undestand the simple inteest fomula. 2. Use the compound inteest fomula to find futue value. 3. Solve the compound inteest fomula fo diffeent unknowns, such as the pesent value,
Carter-Penrose diagrams and black holes
Cate-Penose diagams and black holes Ewa Felinska The basic intoduction to the method of building Penose diagams has been pesented, stating with obtaining a Penose diagam fom Minkowski space. An example
Magnetic Bearing with Radial Magnetized Permanent Magnets
Wold Applied Sciences Jounal 23 (4): 495-499, 2013 ISSN 1818-4952 IDOSI Publications, 2013 DOI: 10.5829/idosi.wasj.2013.23.04.23080 Magnetic eaing with Radial Magnetized Pemanent Magnets Vyacheslav Evgenevich
Voltage ( = Electric Potential )
V-1 Voltage ( = Electic Potential ) An electic chage altes the space aound it. Thoughout the space aound evey chage is a vecto thing called the electic field. Also filling the space aound evey chage is
Verifying Numerical Convergence Rates
1 Order of accuracy Verifying Numerical Convergence Rates We consider a numerical approximation of an exact value u. Te approximation depends on a small parameter, suc as te grid size or time step, and
Energy Density / Energy Flux / Total Energy in 3D
Lecture 5 Phys 75 Energy Density / Energy Fux / Tota Energy in D Overview and Motivation: In this ecture we extend the discussion of the energy associated with wave otion to waves described by the D wave
INVERSE BORN SERIES FOR SCALAR WAVES * 1. Introduction
Jouna of Computationa Mathematics Vo.3, No.6, 22, 6 64. http://www.goba-sci.og/jcm doi:.428/jcm.25-m3935 INVERSE BORN SERIES FOR SCALAR WAVES * Kimbey Kigoe Shai Moskow Depatment of Mathematics, Dexe Univesity,
Structure and evolution of circumstellar disks during the early phase of accretion from a parent cloud
Cente fo Tubulence Reseach Annual Reseach Biefs 2001 209 Stuctue and evolution of cicumstella disks duing the ealy phase of accetion fom a paent cloud By Olusola C. Idowu 1. Motivation and Backgound The
Physics HSC Course Stage 6. Space. Part 1: Earth s gravitational field
Physics HSC Couse Stage 6 Space Pat 1: Eath s gavitational field Contents Intoduction... Weight... 4 The value of g... 7 Measuing g...8 Vaiations in g...11 Calculating g and W...13 You weight on othe
Finite-Length Analysis of Low-Density Parity-Check Codes on the Binary Erasure Channel
1570 IEEE TRANSACTIONS ON INFORMATION THEORY, VOL. 48, NO. 6, JUNE 2002 Finite-Length Anaysis of Low-Density Paity-Check Codes on the Binay Easue Channe Changyan Di, Student Membe, IEEE, David Poietti,
Bending Stresses for Simple Shapes
-6 Bendng Stesses fo Smple Sapes In bendng, te maxmum stess and amount of deflecton can be calculated n eac of te followng stuatons. Addtonal examples ae avalable n an engneeng andbook. Secton Modulus
The force between electric charges. Comparing gravity and the interaction between charges. Coulomb s Law. Forces between two charges
The foce between electic chages Coulomb s Law Two chaged objects, of chage q and Q, sepaated by a distance, exet a foce on one anothe. The magnitude of this foce is given by: kqq Coulomb s Law: F whee
AP Physics C: Mechanics 2005 Free-Response Questions
AP Phyic C: Mechanic 00 ee-repone Quetion he College Boa: Connecting Stuent to College Succe he College Boa i a not-fo-pofit membehip aociation whoe miion i to connect tuent to college ucce an oppotunity.
M(0) = 1 M(1) = 2 M(h) = M(h 1) + M(h 2) + 1 (h > 1)
Insertion and Deletion in VL Trees Submitted in Partial Fulfillment of te Requirements for Dr. Eric Kaltofen s 66621: nalysis of lgoritms by Robert McCloskey December 14, 1984 1 ackground ccording to Knut
Design of Wind Energy System on the Building Tower Applications
ISSN(Online): 39-8753 ISSN (Pint) :347-67 (An ISO 397: 7 Cetified Oganization) Vol. 4, Issue, Febuay 5 Design of Wind Enegy System on the Building owe Applications D.Anusha, L V Suesh Kuma, G.V. Nagesh
ON THE (Q, R) POLICY IN PRODUCTION-INVENTORY SYSTEMS
ON THE R POLICY IN PRODUCTION-INVENTORY SYSTEMS Saifallah Benjaafa and Joon-Seok Kim Depatment of Mechanical Engineeing Univesity of Minnesota Minneapolis MN 55455 Abstact We conside a poduction-inventoy
Math 113 HW #5 Solutions
Mat 3 HW #5 Solutions. Exercise.5.6. Suppose f is continuous on [, 5] and te only solutions of te equation f(x) = 6 are x = and x =. If f() = 8, explain wy f(3) > 6. Answer: Suppose we ad tat f(3) 6. Ten
YARN PROPERTIES MEASUREMENT: AN OPTICAL APPROACH
nd INTERNATIONAL TEXTILE, CLOTHING & ESIGN CONFERENCE Magic Wold of Textiles Octobe 03 d to 06 th 004, UBROVNIK, CROATIA YARN PROPERTIES MEASUREMENT: AN OPTICAL APPROACH Jana VOBOROVA; Ashish GARG; Bohuslav
Derivatives Math 120 Calculus I D Joyce, Fall 2013
Derivatives Mat 20 Calculus I D Joyce, Fall 203 Since we ave a good understanding of its, we can develop derivatives very quickly. Recall tat we defined te derivative f x of a function f at x to be te
The Role of Gravity in Orbital Motion
! The Role of Gavity in Obital Motion Pat of: Inquiy Science with Datmouth Developed by: Chistophe Caoll, Depatment of Physics & Astonomy, Datmouth College Adapted fom: How Gavity Affects Obits (Ohio State
SPATIAL EQUALISATION OF SOUND SYSTEMS IN CARS BY DIGITAL INVERSE FILTERING
SPATIAL EQUALISATION OF SOUND SYSTEMS IN CARS BY DIGITAL INVERSE FILTERING Angeo Faina (1), Emanuee Ugootti (2) (1) Dipatimento di Ingegneia Industiae, Univesità di Pama, Via dee Scienze - 43100 PARMA
Symmetric polynomials and partitions Eugene Mukhin
Symmetic polynomials and patitions Eugene Mukhin. Symmetic polynomials.. Definition. We will conside polynomials in n vaiables x,..., x n and use the shotcut p(x) instead of p(x,..., x n ). A pemutation
Geometric Stratification of Accounting Data
Stratification of Accounting Data Patricia Gunning * Jane Mary Horgan ** William Yancey *** Abstract: We suggest a new procedure for defining te boundaries of te strata in igly skewed populations, usual
Shaping the future of diabetes care
Shaping the futue of diabetes cae 1 Heino von Pondzynski Head of Roche Diagnostics 2 The idea Roche Diagnostics, the woldwide leade in Diabetes monitoing, and Disetonics, the woldwide numbe 2-playe in
PHYSICS 111 HOMEWORK SOLUTION #13. May 1, 2013
PHYSICS 111 HOMEWORK SOLUTION #13 May 1, 2013 0.1 In intoductoy physics laboatoies, a typical Cavendish balance fo measuing the gavitational constant G uses lead sphees with masses of 2.10 kg and 21.0
1 Basic concepts in geometry
1 asic concepts in geometry 1.1 Introduction We start geometry with the simpest idea a point. It is shown using a dot, which is abeed with a capita etter. The exampe above is the point. straight ine is
International Journal of Pure and Applied Sciences and Technology
Int. J. Pue App. Sci. Techno., 4(1) (211), pp. 41-48 Intenationa Jouna of Pue and Appied Science and Technoogy ISSN 2229-617 Avaiabe onine at www.ijopaaat.in Reeach Pape Effect of Roto Reitance Vaue of
MAGNT Research Report (ISSN. 1444-8939) Vol.3 (2). PP: 267-278
Analysis of Relationship between Knowlege Management an Paticipatoy Management base on the Moeating Role of Oganizational Cultue in Bank Melli of Razavi Khoasan Povince Ggolafshani 1. S. M. Ghayou 2 1,2
UNIT CIRCLE TRIGONOMETRY
UNIT CIRCLE TRIGONOMETRY The Unit Cicle is the cicle centeed at the oigin with adius unit (hence, the unit cicle. The equation of this cicle is + =. A diagam of the unit cicle is shown below: + = - - -
External Flow Correlations (Average, Isothermal Surface)
Externa Fow orreation (Average, Ioterma urface Fat Pate orreation Fow ondition aminar urbuent were Average et mber 1/ 0.66 Re 0. 6 /5 0.07 Re A 1/ 0.6 60 A /5 1/ 0.07 Rex, c 0.66Rex, c Re x, c Re 10 8
Lecture L25-3D Rigid Body Kinematics
J. Peraire, S. Winall 16.07 Dynamics Fall 2008 Version 2.0 Lecture L25-3D Rigi Boy Kinematics In this lecture, we consier the motion of a 3D rigi boy. We shall see that in the general three-imensional
7 Circular Motion. 7-1 Centripetal Acceleration and Force. Period, Frequency, and Speed. Vocabulary
7 Cicula Motion 7-1 Centipetal Acceleation and Foce Peiod, Fequency, and Speed Vocabulay Vocabulay Peiod: he time it takes fo one full otation o evolution of an object. Fequency: he numbe of otations o
1.6. Analyse Optimum Volume and Surface Area. Maximum Volume for a Given Surface Area. Example 1. Solution
1.6 Analyse Optimum Volume and Surface Area Estimation and oter informal metods of optimizing measures suc as surface area and volume often lead to reasonable solutions suc as te design of te tent in tis
Chapter 7 Numerical Differentiation and Integration
45 We ave a abit in writing articles publised in scientiþc journals to make te work as Þnised as possible, to cover up all te tracks, to not worry about te blind alleys or describe ow you ad te wrong idea
4.4 The Derivative. 51. Disprove the claim: If lim f (x) = L, then either lim f (x) = L or. 52. If lim x a. f (x) = and lim x a. g(x) =, then lim x a
Capter 4 Real Analysis 281 51. Disprove te claim: If lim f () = L, ten eiter lim f () = L or a a lim f () = L. a 52. If lim a f () = an lim a g() =, ten lim a f + g =. 53. If lim f () = an lim g() = L
An Introduction to Omega
An Intoduction to Omega Con Keating and William F. Shadwick These distibutions have the same mean and vaiance. Ae you indiffeent to thei isk-ewad chaacteistics? The Finance Development Cente 2002 1 Fom
Epdf Sulf petroleum, Eflecti and Eeflecti
ANALYSIS OF GLOBAL WARMING MITIGATION BY WHITE REFLECTING SURFACES Fedeico Rossi, Andea Nicolini Univesity of Peugia, CIRIAF Via G.Duanti 67 0615 Peugia, Italy T: +9-075-585846; F: +9-075-5848470; E: fossi@unipg.it
Hip Hop solutions of the 2N Body problem
Hip Hop solutions of the N Boy poblem Esthe Baabés baabes@ima.ug.es Depatament Infomàtica i Matemàtica Aplicaa, Univesitat e Giona. Josep Maia Cos cos@eupm.upc.es Depatament e Matemàtica Aplicaa III, Univesitat
10. Collisions. Before During After
10. Collisions Use conseation of momentum and enegy and the cente of mass to undestand collisions between two objects. Duing a collision, two o moe objects exet a foce on one anothe fo a shot time: -F(t)
PY1052 Problem Set 8 Autumn 2004 Solutions
PY052 Poblem Set 8 Autumn 2004 Solutions H h () A solid ball stats fom est at the uppe end of the tack shown and olls without slipping until it olls off the ight-hand end. If H 6.0 m and h 2.0 m, what
F G r. Don't confuse G with g: "Big G" and "little g" are totally different things.
G-1 Gavity Newton's Univesal Law of Gavitation (fist stated by Newton): any two masses m 1 and m exet an attactive gavitational foce on each othe accoding to m m G 1 This applies to all masses, not just