COMPUTATIONS OF ELECTROMAGNETIC FIELDS RADIATED FROM COMPLEX LIGHTNING CHANNELS

Size: px
Start display at page:

Download "COMPUTATIONS OF ELECTROMAGNETIC FIELDS RADIATED FROM COMPLEX LIGHTNING CHANNELS"

Transcription

1 Pogess In Electomagnetics Reseach, PIER 73, , 2007 COMPUTATIONS OF ELECTROMAGNETIC FIELDS RADIATED FROM COMPLEX LIGHTNING CHANNELS T.-X. Song, Y.-H. Liu, and J.-M. Xiong School of Mechanical Engineeing Hubei Univesity of Technology Wuhan , China Abstact In this pape, thee methods fo calculating electomagnetic fields adiated fom complex lightning channels ae discussed, which includes channel obliqueness, banches and totuosity. By otating and moving the coodinate system of the vetical channel, diffeential expessions of electomagnetic fields fom the iegula channel can be deived fom the conclusions of the staight and vetical channel. Though analyzing calculation esults of two examples eveals that channel totuosity and banch is to intoduce the highe fequency content above 100 khz into lightning electomagnetic fields. 1. INTRODUCTION In most computations of lightning electomagnetic fields, the etunstoke channel is assumed to be staight and vetical 1, while it is known to be totuous on scales anging fom less than 1 m to ove 1 km 2. In the case of natual lightning, only subsequent stokes wee consideed. The effects of channel totuosity on etun-stoke adiation fields may be studied theoetically using a piecewise linea epesentation of the lightning channel. In geneal, the effect of totuosity is to intoduce fine stuctue into the time-domain adiation field wavefom and consequently to incease the highe fequency content above 100 khz. At each kink, that is, point at which the linea segments joint, thee is a change in the diection of the popagation of the cuent wave and such changes will intoduce apid vaiations in the adiation field. If consideation fo banches, adiation fields should be ovelaid with electomagnetic fields fom main channel and banches. In Refeence 3, we assume the lightning channel is a staight and vetical antenna, its electomagnetic fields ae calculated with dipole method. Based on Refeence 3, we pesent the methods to calculate

2 94 Song, Liu, and Xiong electic fields and magnetic fields adiated fom a totuous channel with banches in this pape. 2. OBLIQUE LIGHTNING CHANNEL In lightning engineeing model, we fist assume a lightning channel is oblique, and oblique angle is α see Fig. 1. Afte otating cylindical coodinate system see Fig. 2, channel s length is H and height of etun-stoke cuent is h, the infinitesimal cuent element dz can be looked as an electic dipole at a height z, which moves upwad along the channel at a speed v. The obsevation point P has a Cloud H* h* z '* dz' v iz'*,t R R 0 R H z* P,φ, z z α Gound * Figue 1. Model of oblique lightning channel. x* z H dz' z' Φ z* H* R P z' α E z * * Φ E * E y x * y* Figue 2. Rotating cylindical coodinate system.

3 Pogess In Electomagnetics Reseach, PIER 73, hoizontal distance fom the lightning channel and a height z, and R is the distance fom the electic dipole. The gound has a pefect conductivity and the ai has a pemittivity ε 0 and pemeability u 0. The cuent iz,t in channel is a function vaying with channel height and time 4. If we find out coesponding elations between two coodinate systems, and substitute them into the fomulations fo the vetical channel in Refeence 3, we will be able to obtain equations to calculate electomagnetic fields of oblique lightning channel. Accoding to geometic elations in Fig. 2, we can obtain = 2 + z 2 sinα tg 1 z 1 2 z = tgα tg 1 z = + z 2 sinα tg 1 z tgα tg 1 z 2 h = h sin α 3 H = H sin α 4 z = z sin α 5 whee z,, h, and z denote the coelative distance in oiginal coodinate system x, y, z espectively. So the distance fom Point P to the bottom of etun-stoke cuent is R 0 = 2 + z 2 6 The distance fom Point P to the top of etun-stoke cuent is R H = 2 +h z 2 { = 2 + z 2 sin 2 α tg 1 z + h 2 sin α + z 2 sin α tg 1 z 2 tg α tg 1 z The distance fom Point P to the dipole dz is R = z z { = 2 + z 2 sin 2 α tg 1 z z 2 sin α tg 1 z 2 tg α tg 1 z z sin α 1/2 1/2 7 8

4 96Song, Liu, and Xiong We still use dipole method to solve Maxwell s equations. Substituting, h into the fomulations fo the vetical channel in Refeence 3, analytical expessions of electic fields and magnetic fields at Point P, φ, 0 in otating coodinate system x,y,z can be deived as following H φ, 0,t= I 0 2π h /2 + E z, 0,t= I 0 th + 2h 2 v + 2 v 2πε 0 h /2 1 v h c v h h h /2 9 2 c 2 h /2 1 v + 10 h c h whee h denotes the height of lightning etun-stoken cuent in otating coodinate system, it can be calculated with Equation 3; denotes hoizontal distance between Point P and the point that lightning stik falls to the gound, it can be calculated with Equation 1. Consequently, in ode to evaluate electomagnetic fields of any point in lightning space, substituting z, z, R into the fomulations in Refeence 3, we can get diffeential expessions of electic fields and magnetic fields in the otating cylindical coodinate system as following de = dz 3 z z t 4πε 0 R 5 it R/cdt + 3 z z 0 cr 4 it R/c + z z it R/c c 2 R 3 11 de z = dz 2z z 2 2 t 4πε 0 R 5 it R/cdt 0 + 2z z 2 2 cr 4 it R/c 2 it R/c c 2 R 3 12 db φ = µ 0dz it R/c it R/c+ 4π R3 cr 2 13 whee R can be computed with Equation 8, z can be computed with Equation 2, z can be computed with Equation 5, can be computed with Equation 1.

5 Pogess In Electomagnetics Reseach, PIER 73, LIGHTNING CHANNEL BRANCHES 3.1. Calculation Method As we know, a lightning channel is iegula, so its geneal field intensity is the sum of electomagnetic fields fom main channel and banches 5. But the diection of eithe coodinate system is diffeent, thus electic fields and magnetic fields should be added in vecto. Assuming the main channel is staight and vetical, the banch is oblique see Fig. 3, electomagnetic fields fom the main channel can still be calculated with the fomulations in Refeence 3, while field intensity expessions of the banch is deived as following. z H P z R* L z'* α O' * z' O R z* z Figue 3. Cylindical coodinate system fo banches. In Fig. 3, Point O is oiginal point, its location is diffeent fom the oblique channel, we need to calculate the displacement at diection once again. The hoizontal distance between Point P and main channel is, the distance between Point P and Point O is +L cos α, theefoe = + L cos α 2 + z 2 sin α tg 1 z 14 + L cos α z = + L cos α 2 + z 2 cos α tg 1 z 15 + L cos α R = z z { = + L cos α 2 + z 2 sin 2 α tg 1 z + +L cos α 2 +z 2 cos + L cos α α tg 1 z 2 } 1/2 z 16 +L cos α sin α

6 98 Song, Liu, and Xiong Replacing, z and R in Equations 11, 12, 13 with above thee expessions, field intensity fom the banch at Point P can be witten as de = dz 3 z z t 4πε 0 R 5 it R /cdt + 3 z z 0 cr 4 it R /c + z z it R /c c 2 R 3 17 de z = dz 2z z 2 2 t 4πε 0 R 5 it R /cdt 0 + 2z z 2 2 cr 4 it R /c 2 it R /c c 2 18 R 3 db φ = µ 0dz 4π R 3 it R /c+ it R c cr 2 19 In above thee expessions, R can be calculated with Equation 16, z can be calculated with Equation 15, can be calculated with Equation 14. Assuming E z, E and B φ epesent electomagnetic fields of main channel, Ez, E and Bφ epesent electomagnetic fields of banches see Fig. 4. Fom this figue we may know that electonic fields of both channels have diffeent diections, while the diections of magnetic fields ae same. Theefoe, geneal field intensity at Point P can be evaluated as following. E z B Φ* B Φ E z * P α α E * E Figue 4. Ovelay of electomagnetic fields. Electonic field at z diection: Ez = E z + E z sin α E cos α 20

7 Pogess In Electomagnetics Reseach, PIER 73, magnetic field at diection: E = E + E z cos α E sin α 21 geneal electonic field: E = Ez 2 + E 2 22 geneal magnetic field: Bφ = B φ + B φ An Evaluation Example fo Banches We choose a vetical main channel with a banch as an example to evaluate field intensity and compae calculation esults with a vetical channel without banches see Fig. 5. The banch s oblique angle is 60 and its height is 100 m, whole main channel s height is 200 m. At fist we solve electomagnetic fields of both channels espectively, then add thei field intensity in vecto, thus we will be able to get geneal field intensity. The banch s electomagnetic fields can be evaluated accoding to above oblique channel s fomulations, while main channel s electomagnetic fields ae still calculated with the method fo vetical channel. The calculation esults ae shown in Fig. 6 and Fig. 7 fom which we can know that values of main channel with a banch is moe than those who have no banches, thee ae some high fequency contents at stating point of the wavefom, and moe ae banches, moe ae high fequency contents. Main channel H 2 =100m Banch L H 1 =100m 60 o Figue 5. A vetical channel with a banch.

8 100 Song, Liu, and Xiong Vetical Channel with Banches Vetical Channel Figue 6. Vetical electonic field fom banches = 10 km, z = 0. Vetical Channel with Banches Vetical Channel Figue 7. Azimuthal magnetic field fom banches = 10 km, z = LIGHTNING CHANNEL TORTUOSITY 4.1. Calculation Method Actually natue lightning is totuous and has many banches. In ode to calculate its electomagnetic fields we may divide a totuous channel into many linea segments which may be looked as oblique channels to poceed, so geneal field intensity can be obtained though adding electonic fields and magnetic fields of all linea segments. In Fig. 8, we assume that thee is a totuous lightning channel including two oblique linea segments which length ae L and L 1, oblique angle ae

9 Pogess In Electomagnetics Reseach, PIER 73, α and α 1 espectively in cylindical coodinate system. Thus Point P s electomagnetic fields fom OO 1 can be evaluated diectly with Equations 11, 12, 13, while field intensity fom O 1 O 2 can not be calculated diectly with these thee equations. Only afte the coodinate system is moved to Point O 1, these thee equations can be used. z z 1 O 2 E z B Φ L 1 R 1 P, z E R Lsinα L O 1 α O Lcosα α 1 1 Figue 8. Coodinate system fo totuous channel. In coodinate system z-o-, Point O 1 s coodinate is L cos α, L sin α, Point P s coodinate is, z. Afte this coodinate system is moved to Point O 1, Point O 1 s coodinate is 0, 0, Point P s coodinate is -L cos α, z-l sin α. Theefoe, eplacing in Equation 1 though 5 with -L cos α, eplacing z with z-l sin α, we can obtain the values of z, z, R 1, and h egading channel O 1 O 2 as following = L cos α 2 +z L sin α 2 1 z L sin α sin α 1 tg 24 L cos α L cos α 2 +z L sin α 2 sin z = tg α 1 tg 1 z L sin α L cos α z L sin α a 1 tg L cos α 25 z = z z L sin α 26 sin α 1 R 1 = 2 +z z 2 { = L cos α 2 +z L sin α 2 sin 2 1 z L sin α a 1 tg L sin α L cos α 2 +z L sin α 2 sin α 1 tg 1 z L sin α L cos α tg α 1 tg 1 z L sin α L cos α

10 102 Song, Liu, and Xiong z z L sin α 2 } 1/2 27 sin α 1 h = = h sin α 1 ξ 1 ξ 2 ct ξz L sin α sin α 1 ξct z L sin α 2 + L cos α 2 1 ξ 2 28 whee ξ = v/c, c is the tavel speed of electomagnetic wave which equals light speed m/s in ai medium. Substituting above expessions into Equations , Point P s field intensity fom channel O 1 O 2 can be witten as db φ = µ 0dz 4π R1 3 it R 1 /c+ it R 1 /c cr de = dz 3 z z t 4πε 0 R1 5 it R 1 /cdt z z cr1 4 it R 1 /c+ z z it R 1 /c c 2 R de z = dz 2z z 2 2 t it R 1 /cdt 4πε 0 0 R z z 2 2 cr1 4 it R 1 /c 2 c 2 R1 3 it R 1 /c 31 whee R 1 can be got fom Equation 27, z can be got fom Equation 25, z can be got fom Equation 26, can be got fom Equation 24. Consequently, Point P electonic fields and magnetic fields may be calculated espectively with diffeent equations. Equations should be used in the case of etun-stoke cuent going though L, o time t L/v v is the speed of etun-stoke cuent, Equations should be used in the case of etun-stoke cuent going though L 1, o time t > L/v An Evaluation Example fo Totuous Channel In Fig. 9 we assume that a totuous channel is composed of two linea oblique channels. Fom above discussion we know the fist linea

11 Pogess In Electomagnetics Reseach, PIER 73, segment may be calculated with the equations of oblique channel diectly, while the second segment can be calculated only afte the coodinate system is moved. Figue 9. A totuous channel. L 1 NO.2 H 2 =100m o 60 L NO.1 H 1 =100m 30 o In ode to compae evaluation esults with a vetical channel, we assume the oblique angle of NO. 1 segment α is 30, the angle of NO. 2 segment α 1 is 60, the height of each segment is 100 m and the height of the vetical channel is 200 m, thei lightning cuent paametes ae the same as Refeence 6, etun-stoke speed is m/s 7. Evaluation esults ae shown as Fig. 10 and Fig. 11, the eal line denotes electomagnetic fields fom the totuous channel, the dashed line denotes electomagnetic fields fom the vetical channel. Fom these two figues we can see that initial values of electonic fields and magnetic fields ae diffeent and the values at stating pat of wavefom of totuous channel ae much geate, which illuminate that thee ae Totuous Channel Vetical Channel Figue 10. Vetical electonic field fom totuous channel = 10 km, z = 0.

12 104 Song, Liu, and Xiong Totuous Channel Vetical Channel Figue 11. Azimuthal magnetic field fom totuous channel = 10 km, z = 0. high fequency contents above 100 khz emeged in electomagnetic fields. While initial values fom the vetical channel ae almost zeo, which illuminate that thee ae no high fequency contents coming fom a vetical channel. Othewise, the values of electomagnetic fields fom the vetical channel ae geate than totuous channel on the same conditions. Theefoe channel totuosity will intoduce highe fequency contents into electomagnetic fields, and moe ae totuosity, moe ae high fequency contents 8, CONCLUSION In this pape, thee methods fo calculating electomagnetic fields adiated fom complex lightning channels have been discussed, which includes channel obliqueness, banches and totuosity. By otating and moving the coodinate system of the vetical channel, diffeential expessions of electomagnetic fields fom the oblique channel can be deived fom the conclusions of the vetical channel. Electomagnetic fields fom the channel banch may be evaluated though ovelaying electonic fields and magnetic fields fom a vetical main channel and oblique channels. The totuous channel can be divided into many linea oblique segments fom which field intensity can be added to obtain geneal electomagnetic fields fom whole totuous channel. Though analyzing calculation esults of two examples eveals that channel totuosity and banches ae to intoduce the highe

13 Pogess In Electomagnetics Reseach, PIER 73, fequency contents above 100 khz into electomagnetic fields, and moe ae totuosity and banches, moe ae highe fequency contents. Meanwhile, field intensity fom a channel with banches is geate than single vetical channel. REFERENCES 1. Rubinstein, M. and M. A. Uman, Methods fo calculating the electomagnetic fields fom a known souce distibution: application to lightning, IEEE Tansactions on Electomagnetic Compatibility, Vol. 31, No. 2, , Uman, M. A., Natual lightning, IEEE Tansactions on Industy Applications, Vol. 30, No. 3, , Song, T.-X. and C. Wang, Two numeical methods fo calculating electomagnetic fields adiated fom natue lightning, Jounal of Electomagnetic Waves and Applications, Vol. 19, No. 4, , Nucci, C. A., et al., Lightning etun stoke cuent models with specified channel-base cuent: a eview and compaison, J. Geophys. Res., Vol. 95, , Rakov, V. A. and M. A. Uman, Review and evaluation of lightning etun stoke models including some aspects of thei application, IEEE Tansactions on Electomagnetic Compatibility, Vol. 40, No. 4, , Zhao, X. and K. Huang, Calculation of pobability distibution of Maximal eceived powe of electonic eceive in lightning electomagnetic envionment, Jounal of Electomagnetic Waves and Applications, Vol. 19, No. 2, , Mu, M. K., J. T. Huangfu, L. X. Ran, and K. Zang, Design of lightning potecto compatible fo both 2G and 3G cellula systems, Jounal of Electomagnetic Waves and Applications, Vol. 20, No. 15, , Li, J. Y. and Y.-B. Gan, Multi-band chaacteistic of open sleeve antenna, Pogess In Electomagnetics Reseach, PIER 58, , Sijhe, T. S. and A. A. Kishk, Antenna modeling by infinitesimal dipoles using genetic algoithms, Pogess In Electomagnetics Reseach, PIER 52, , 2005.

Mathematical Model of Magnetometric Resistivity. Sounding for a Conductive Host. with a Bulge Overburden

Mathematical Model of Magnetometric Resistivity. Sounding for a Conductive Host. with a Bulge Overburden Applied Mathematical Sciences, Vol. 7, 13, no. 7, 335-348 Mathematical Model of Magnetometic Resistivity Sounding fo a Conductive Host with a Bulge Ovebuden Teeasak Chaladgan Depatment of Mathematics Faculty

More information

Antennas & Propagation

Antennas & Propagation Antennas & Popagation 1 Oveview of Lectue II -Wave Equation -Example -Antenna Radiation -Retaded potential THE KEY TO ANY OPERATING ANTENNA ot H = J +... Suppose: 1. Thee does exist an electic medium,

More information

8. СОВЕТУВАЊЕ. Охрид, септември ANALYSIS OF LIGHTNING PROBABILITY STROKE TO THREE DIMENSIONAL STRUCTURES

8. СОВЕТУВАЊЕ. Охрид, септември ANALYSIS OF LIGHTNING PROBABILITY STROKE TO THREE DIMENSIONAL STRUCTURES 8. СОВЕТУВАЊЕ Охрид, 4 септември Yuval Beck Holon Institute of Technology Aie Baunstein Tel-Aviv Univesity ANALYSIS OF LIGHTNING PROBABILITY STROKE TO THREE DIMENSIONAL STRUCTURES ABSTRACT This pape pesents

More information

Modeling and Calculation of Optical Amplification in One Dimensional Case of Laser Medium Using Finite Difference Time Domain Method

Modeling and Calculation of Optical Amplification in One Dimensional Case of Laser Medium Using Finite Difference Time Domain Method Jounal of Physics: Confeence Seies PAPER OPEN ACCESS Modeling and Calculation of Optical Amplification in One Dimensional Case of Lase Medium Using Finite Diffeence Time Domain Method To cite this aticle:

More information

Electromagnetic scattering. Graduate Course Electrical Engineering (Communications) 1 st Semester, Sharif University of Technology

Electromagnetic scattering. Graduate Course Electrical Engineering (Communications) 1 st Semester, Sharif University of Technology Electomagnetic scatteing Gaduate Couse Electical Engineeing (Communications) 1 st Semeste, 1390-1391 Shaif Univesity of Technology Geneal infomation Infomation about the instucto: Instucto: Behzad Rejaei

More information

MAGNETIC FIELD AROUND TWO SEPARATED MAGNETIZING COILS

MAGNETIC FIELD AROUND TWO SEPARATED MAGNETIZING COILS The 8 th Intenational Confeence of the Slovenian Society fo Non-Destuctive Testing»pplication of Contempoay Non-Destuctive Testing in Engineeing«Septembe 1-3, 5, Potoož, Slovenia, pp. 17-1 MGNETIC FIELD

More information

Gaussian beam propagation through a metamaterial lens

Gaussian beam propagation through a metamaterial lens Calhoun: The NPS Institutional Achive Faculty and Reseache Publications Faculty and Reseache Publications 4 Gaussian beam popagation though a metamateial lens Zhou, Hong Gaussian beam popagation though

More information

3. Electromagnetic Waves II

3. Electromagnetic Waves II Lectue 3 - Electomagnetic Waves II 9 3. Electomagnetic Waves II Last time, we discussed the following. 1. The popagation of an EM wave though a macoscopic media: We discussed how the wave inteacts with

More information

Appendix B The Relativistic Transformation of Forces

Appendix B The Relativistic Transformation of Forces Appendix B The Relativistic Tansfomation of oces B. The ou-foce We intoduced the idea of foces in Chapte 3 whee we saw that the change in the fou-momentum pe unit time is given by the expession d d w x

More information

PHYS 110B - HW #7 Spring 2004, Solutions by David Pace Any referenced equations are from Griffiths Problem statements are paraphrased

PHYS 110B - HW #7 Spring 2004, Solutions by David Pace Any referenced equations are from Griffiths Problem statements are paraphrased PHYS 0B - HW #7 Sping 2004, Solutions by David Pace Any efeenced euations ae fom Giffiths Poblem statements ae paaphased. Poblem 0.3 fom Giffiths A point chage,, moves in a loop of adius a. At time t 0

More information

DonnishJournals

DonnishJournals DonnishJounals 041-1189 Donnish Jounal of Educational Reseach and Reviews. Vol 1(1) pp. 01-017 Novembe, 014. http:///dje Copyight 014 Donnish Jounals Oiginal Reseach Pape Vecto Analysis Using MAXIMA Savaş

More information

11) A thin, uniform rod of mass M is supported by two vertical strings, as shown below.

11) A thin, uniform rod of mass M is supported by two vertical strings, as shown below. Fall 2007 Qualifie Pat II 12 minute questions 11) A thin, unifom od of mass M is suppoted by two vetical stings, as shown below. Find the tension in the emaining sting immediately afte one of the stings

More information

A NEW VARIABLE STIFFNESS SPRING USING A PRESTRESSED MECHANISM

A NEW VARIABLE STIFFNESS SPRING USING A PRESTRESSED MECHANISM Poceedings of the ASME 2010 Intenational Design Engineeing Technical Confeences & Computes and Infomation in Engineeing Confeence IDETC/CIE 2010 August 15-18, 2010, Monteal, Quebec, Canada DETC2010-28496

More information

Duality between Statical and Kinematical Engineering Systems

Duality between Statical and Kinematical Engineering Systems Pape 00, Civil-Comp Ltd., Stiling, Scotland Poceedings of the Sixth Intenational Confeence on Computational Stuctues Technology, B.H.V. Topping and Z. Bittna (Editos), Civil-Comp Pess, Stiling, Scotland.

More information

EFFECTS OF FRINGING FIELDS ON SINGLE PARTICLE DYNAMICS. M. Bassetti and C. Biscari INFN-LNF, CP 13, Frascati (RM), Italy

EFFECTS OF FRINGING FIELDS ON SINGLE PARTICLE DYNAMICS. M. Bassetti and C. Biscari INFN-LNF, CP 13, Frascati (RM), Italy Fascati Physics Seies Vol. X (998), pp. 47-54 4 th Advanced ICFA Beam Dynamics Wokshop, Fascati, Oct. -5, 997 EFFECTS OF FRININ FIELDS ON SINLE PARTICLE DYNAMICS M. Bassetti and C. Biscai INFN-LNF, CP

More information

School of Electrical and Computer Engineering, Cornell University. ECE 303: Electromagnetic Fields and Waves. Fall 2007

School of Electrical and Computer Engineering, Cornell University. ECE 303: Electromagnetic Fields and Waves. Fall 2007 School of Electical and Compute Engineeing, Conell Univesity ECE 303: Electomagnetic Fields and Waves Fall 007 Homewok 8 Due on Oct. 19, 007 by 5:00 PM Reading Assignments: i) Review the lectue notes.

More information

General Solution of EM Wave Propagation in Anisotropic Media

General Solution of EM Wave Propagation in Anisotropic Media Jounal of the Koean Physical Society, Vol. 57, No. 1, July 2010, pp. 55 60 Geneal Solution of EM Wave Popagation in Anisotopic Media Jinyoung Lee Electical and Electonic Engineeing Depatment, Koea Advanced

More information

7.2. Coulomb s Law. The Electric Force

7.2. Coulomb s Law. The Electric Force Coulomb s aw Recall that chaged objects attact some objects and epel othes at a distance, without making any contact with those objects Electic foce,, o the foce acting between two chaged objects, is somewhat

More information

Conservative Averaging Method and its Application for One Heat Conduction Problem

Conservative Averaging Method and its Application for One Heat Conduction Problem Poceedings of the 4th WSEAS Int. Conf. on HEAT TRANSFER THERMAL ENGINEERING and ENVIRONMENT Elounda Geece August - 6 (pp6-) Consevative Aveaging Method and its Application fo One Heat Conduction Poblem

More information

J. Electrical Systems 1-3 (2005): Regular paper

J. Electrical Systems 1-3 (2005): Regular paper K. Saii D. Rahem S. Saii A Miaoui Regula pape Coupled Analytical-Finite Element Methods fo Linea Electomagnetic Actuato Analysis JES Jounal of Electical Systems In this pape, a linea electomagnetic actuato

More information

On the integration of the equations of hydrodynamics

On the integration of the equations of hydrodynamics Uebe die Integation de hydodynamischen Gleichungen J f eine u angew Math 56 (859) -0 On the integation of the equations of hydodynamics (By A Clebsch at Calsuhe) Tanslated by D H Delphenich In a pevious

More information

ANTENNAS. Vector and Scalar Potentials. Maxwell's Equations. D = εe. For a linear, homogeneous, isotropic medium µ and ε are contant.

ANTENNAS. Vector and Scalar Potentials. Maxwell's Equations. D = εe. For a linear, homogeneous, isotropic medium µ and ε are contant. ANTNNAS Vecto and Scala Potentials Maxwell's quations jωb J + jωd D ρ B (M) (M) (M3) (M4) D ε B Fo a linea, homogeneous, isotopic medium and ε ae contant. Since B, thee exists a vecto A such that B A and

More information

Qualifying Examination Electricity and Magnetism Solutions January 12, 2006

Qualifying Examination Electricity and Magnetism Solutions January 12, 2006 1 Qualifying Examination Electicity and Magnetism Solutions Januay 12, 2006 PROBLEM EA. a. Fist, we conside a unit length of cylinde to find the elationship between the total chage pe unit length λ and

More information

Review: Electrostatics and Magnetostatics

Review: Electrostatics and Magnetostatics Review: Electostatics and Magnetostatics In the static egime, electomagnetic quantities do not vay as a function of time. We have two main cases: ELECTROSTATICS The electic chages do not change postion

More information

Chapter 3 Optical Systems with Annular Pupils

Chapter 3 Optical Systems with Annular Pupils Chapte 3 Optical Systems with Annula Pupils 3 INTRODUCTION In this chapte, we discuss the imaging popeties of a system with an annula pupil in a manne simila to those fo a system with a cicula pupil The

More information

Coupled Electromagnetic and Heat Transfer Simulations for RF Applicator Design for Efficient Heating of Materials

Coupled Electromagnetic and Heat Transfer Simulations for RF Applicator Design for Efficient Heating of Materials Coupled Electomagnetic and Heat Tansfe Simulations fo RF Applicato Design fo Efficient Heating of Mateials Jeni Anto 1 and Raj C Thiagaajan 2 * 1 Reseache, Anna Univesity, Chennai, 2 ATOA Scientific Technologies

More information

Liquid gas interface under hydrostatic pressure

Liquid gas interface under hydrostatic pressure Advances in Fluid Mechanics IX 5 Liquid gas inteface unde hydostatic pessue A. Gajewski Bialystok Univesity of Technology, Faculty of Civil Engineeing and Envionmental Engineeing, Depatment of Heat Engineeing,

More information

12th WSEAS Int. Conf. on APPLIED MATHEMATICS, Cairo, Egypt, December 29-31,

12th WSEAS Int. Conf. on APPLIED MATHEMATICS, Cairo, Egypt, December 29-31, th WSEAS Int. Conf. on APPLIED MATHEMATICS, Caio, Egypt, Decembe 9-3, 7 5 Magnetostatic Field calculations associated with thick Solenoids in the Pesence of Ion using a Powe Seies expansion and the Complete

More information

Finite Element Computational Model for Defect Simulation and Detection by Eddy Currents Non Destructive Testing

Finite Element Computational Model for Defect Simulation and Detection by Eddy Currents Non Destructive Testing Finite Element Computational Model fo Defect Simulation and Detection by Eddy Cuents Non Destuctive Testing M. RACHEK, M. ZAOUA, H. DENOUN, C. BROUCHE Faculté de Génie Electique et de l nfomatique. Dépatement

More information

Designing a Sine-Coil for Measurement of Plasma Displacements in IR-T1 Tokamak

Designing a Sine-Coil for Measurement of Plasma Displacements in IR-T1 Tokamak Designing a Sine-Coil fo Measuement of Plasma Displacements in IR-T Tokamak Pejman Khoshid, M. Razavi, M. Ghoanneviss, M. Molaii, A. TalebiTahe, R. Avin, S. Mohammadi and A. NikMohammadi Dept. of Physics,

More information

THE INFLUENCE OF THE MAGNETIC NON-LINEARITY ON THE MAGNETOSTATIC SHIELDS DESIGN

THE INFLUENCE OF THE MAGNETIC NON-LINEARITY ON THE MAGNETOSTATIC SHIELDS DESIGN THE INFLUENCE OF THE MAGNETIC NON-LINEARITY ON THE MAGNETOSTATIC SHIELDS DESIGN LIVIU NEAMŢ 1, ALINA NEAMŢ, MIRCEA HORGOŞ 1 Key wods: Magnetostatic shields, Magnetic non-lineaity, Finite element method.

More information

Module 9: Electromagnetic Waves-I Lecture 9: Electromagnetic Waves-I

Module 9: Electromagnetic Waves-I Lecture 9: Electromagnetic Waves-I Module 9: Electomagnetic Waves-I Lectue 9: Electomagnetic Waves-I What is light, paticle o wave? Much of ou daily expeience with light, paticulaly the fact that light ays move in staight lines tells us

More information

Gravitational Radiation from Oscillating Gravitational Dipole

Gravitational Radiation from Oscillating Gravitational Dipole Gavitational Radiation fom Oscillating Gavitational Dipole Fan De Aquino Maanhao State Univesity, Physics Depatment, S.Luis/MA, Bazil. deaquino@uema.b Abstact. The concept of Gavitational Dipole is intoduced

More information

Chem 453/544 Fall /08/03. Exam #1 Solutions

Chem 453/544 Fall /08/03. Exam #1 Solutions Chem 453/544 Fall 3 /8/3 Exam # Solutions. ( points) Use the genealized compessibility diagam povided on the last page to estimate ove what ange of pessues A at oom tempeatue confoms to the ideal gas law

More information

Graphs of Sine and Cosine Functions

Graphs of Sine and Cosine Functions Gaphs of Sine and Cosine Functions In pevious sections, we defined the tigonometic o cicula functions in tems of the movement of a point aound the cicumfeence of a unit cicle, o the angle fomed by the

More information

ELASTIC ANALYSIS OF CIRCULAR SANDWICH PLATES WITH FGM FACE-SHEETS

ELASTIC ANALYSIS OF CIRCULAR SANDWICH PLATES WITH FGM FACE-SHEETS THE 9 TH INTERNATIONAL CONFERENCE ON COMPOSITE MATERIALS ELASTIC ANALYSIS OF CIRCULAR SANDWICH PLATES WITH FGM FACE-SHEETS R. Sbulati *, S. R. Atashipou Depatment of Civil, Chemical and Envionmental Engineeing,

More information

Review Notes on Maxwell's Equations

Review Notes on Maxwell's Equations ELEC344 Micowave Engineeing, Sping 2002 Handout #1 Kevin Chen Review Notes on Maxwell's Equations Review of Vecto Poducts and the Opeato The del, gad o nabla opeato is a vecto, and can be pat of a scala

More information

ME 210 Applied Mathematics for Mechanical Engineers

ME 210 Applied Mathematics for Mechanical Engineers Tangent and Ac Length of a Cuve The tangent to a cuve C at a point A on it is defined as the limiting position of the staight line L though A and B, as B appoaches A along the cuve as illustated in the

More information

B. Spherical Wave Propagation

B. Spherical Wave Propagation 11/8/007 Spheical Wave Popagation notes 1/1 B. Spheical Wave Popagation Evey antenna launches a spheical wave, thus its powe density educes as a function of 1, whee is the distance fom the antenna. We

More information

Sensor and Simulation Notes. Note 525. Oct Lens Design for a Prolate-Spheroidal Impulse radiating Antenna (IRA)

Sensor and Simulation Notes. Note 525. Oct Lens Design for a Prolate-Spheroidal Impulse radiating Antenna (IRA) Senso and Simulation Notes Note 55 Oct 7 Lens Design fo a Polate-Spheoidal Impulse adiating Antenna (IRA) Sehat Altunc, Cal E. Baum, Chistos G. Chistodoulou and Edl Schamiloglu Univesity of New Mexico

More information

A new approach in classical electrodynamics to protect principle of causality

A new approach in classical electrodynamics to protect principle of causality A new appoach in classical electodynamics to potect pinciple of causality Biswaanjan Dikshit * Lase and Plasma Technology Division Bhabha Atomic Reseach Cente, Mumbai-400085 INDIA * Coesponding autho E-mail:

More information

Physics 2A Chapter 10 - Moment of Inertia Fall 2018

Physics 2A Chapter 10 - Moment of Inertia Fall 2018 Physics Chapte 0 - oment of netia Fall 08 The moment of inetia of a otating object is a measue of its otational inetia in the same way that the mass of an object is a measue of its inetia fo linea motion.

More information

On the Sun s Electric-Field

On the Sun s Electric-Field On the Sun s Electic-Field D. E. Scott, Ph.D. (EE) Intoduction Most investigatos who ae sympathetic to the Electic Sun Model have come to agee that the Sun is a body that acts much like a esisto with a

More information

Magnetic Dipoles Challenge Problem Solutions

Magnetic Dipoles Challenge Problem Solutions Magnetic Dipoles Challenge Poblem Solutions Poblem 1: Cicle the coect answe. Conside a tiangula loop of wie with sides a and b. The loop caies a cuent I in the diection shown, and is placed in a unifom

More information

On Physical Behavior of Elementary Particles in Force Fields

On Physical Behavior of Elementary Particles in Force Fields On Physical Behavio of Elementay Paticles in Foce Fields Daniele Sasso * Abstact The physical behavio of elementay paticles, massive and enegetic, in foce fields is studied in this pape. In paticula let

More information

( ) [ ] [ ] [ ] δf φ = F φ+δφ F. xdx.

( ) [ ] [ ] [ ] δf φ = F φ+δφ F. xdx. 9. LAGRANGIAN OF THE ELECTROMAGNETIC FIELD In the pevious section the Lagangian and Hamiltonian of an ensemble of point paticles was developed. This appoach is based on a qt. This discete fomulation can

More information

Force between two parallel current wires and Newton s. third law

Force between two parallel current wires and Newton s. third law Foce between two paallel cuent wies and Newton s thid law Yannan Yang (Shanghai Jinjuan Infomation Science and Technology Co., Ltd.) Abstact: In this pape, the essence of the inteaction between two paallel

More information

4. Electrodynamic fields

4. Electrodynamic fields 4. Electodynamic fields D. Rakhesh Singh Kshetimayum 1 4.1 Intoduction Electodynamics Faaday s law Maxwell s equations Wave equations Lenz s law Integal fom Diffeential fom Phaso fom Bounday conditions

More information

School of Electrical and Computer Engineering, Cornell University. ECE 303: Electromagnetic Fields and Waves. Fall 2007

School of Electrical and Computer Engineering, Cornell University. ECE 303: Electromagnetic Fields and Waves. Fall 2007 School of Electical and Compute Engineeing, Conell Univesity ECE 33: Electomagnetic Fields and Waves Fall 7 Homewok 6 Due on Oct. 5, 7 by 5: PM Reading Assignments: i) Review the lectue notes. ii) Review

More information

APPLICATION OF MAC IN THE FREQUENCY DOMAIN

APPLICATION OF MAC IN THE FREQUENCY DOMAIN PPLICION OF MC IN HE FREQUENCY DOMIN D. Fotsch and D. J. Ewins Dynamics Section, Mechanical Engineeing Depatment Impeial College of Science, echnology and Medicine London SW7 2B, United Kingdom BSRC he

More information

RADIATION OF ANTENNA ARRAYS WITH GENERALLY ORIENTED DIPOLES

RADIATION OF ANTENNA ARRAYS WITH GENERALLY ORIENTED DIPOLES Jounal of ELECTRICAL ENGINEERING, VOL. 53, NO. 7-8, 22, 22 27 RADIATION OF ANTENNA ARRAYS WITH GENERALLY ORIENTED DIOLES Štefan Beník ete Hajach The aim of this aticle is to show the possibilities of shaping

More information

The Laws of Motion ( ) N SOLUTIONS TO PROBLEMS ! F = ( 6.00) 2 + ( 15.0) 2 N = 16.2 N. Section 4.4. Newton s Second Law The Particle Under a Net Force

The Laws of Motion ( ) N SOLUTIONS TO PROBLEMS ! F = ( 6.00) 2 + ( 15.0) 2 N = 16.2 N. Section 4.4. Newton s Second Law The Particle Under a Net Force SOLUTIONS TO PROBLEMS The Laws of Motion Section 4.3 Mass P4. Since the ca is moving with constant speed and in a staight line, the esultant foce on it must be zeo egadless of whethe it is moving (a) towad

More information

Swissmetro: design methods for ironless linear transformer

Swissmetro: design methods for ironless linear transformer Swissmeto: design methods fo ionless linea tansfome Nicolas Macabey GESTE Engineeing SA Scientific Pak PSE-C, CH-05 Lausanne, Switzeland Tel (+4) 2 693 83 60, Fax. (+4) 2 693 83 6, nicolas.macabey@geste.ch

More information

Kunming, , R.P. China. Kunming, , R.P. China. *Corresponding author: Jianing He

Kunming, , R.P. China. Kunming, , R.P. China. *Corresponding author: Jianing He Applied Mechanics and Mateials Online: 2014-04-28 ISSN: 1662-7482, Vol. 540, pp 92-95 doi:10.4028/www.scientific.net/amm.540.92 2014 Tans Tech Publications, Switzeland Reseach on Involute Gea Undecutting

More information

COLLISIONLESS PLASMA PHYSICS TAKE-HOME EXAM

COLLISIONLESS PLASMA PHYSICS TAKE-HOME EXAM Honou School of Mathematical and Theoetical Physics Pat C Maste of Science in Mathematical and Theoetical Physics COLLISIONLESS PLASMA PHYSICS TAKE-HOME EXAM HILARY TERM 18 TUESDAY, 13TH MARCH 18, 1noon

More information

2. Electrostatics. Dr. Rakhesh Singh Kshetrimayum 8/11/ Electromagnetic Field Theory by R. S. Kshetrimayum

2. Electrostatics. Dr. Rakhesh Singh Kshetrimayum 8/11/ Electromagnetic Field Theory by R. S. Kshetrimayum 2. Electostatics D. Rakhesh Singh Kshetimayum 1 2.1 Intoduction In this chapte, we will study how to find the electostatic fields fo vaious cases? fo symmetic known chage distibution fo un-symmetic known

More information

Multipole Radiation. February 29, The electromagnetic field of an isolated, oscillating source

Multipole Radiation. February 29, The electromagnetic field of an isolated, oscillating source Multipole Radiation Febuay 29, 26 The electomagnetic field of an isolated, oscillating souce Conside a localized, oscillating souce, located in othewise empty space. We know that the solution fo the vecto

More information

Power efficiency and optimum load formulas on RF rectifiers featuring flow-angle equations

Power efficiency and optimum load formulas on RF rectifiers featuring flow-angle equations LETTE IEICE Electonics Expess, Vol.10, No.11, 1 9 Powe efficiency and optimum load fomulas on F ectifies featuing flow-angle equations Takashi Ohia a) Toyohashi Univesity of Technology, 1 1 Hibaigaoka,

More information

Electrodynamic Forces in Steel Strip during Induction Heating

Electrodynamic Forces in Steel Strip during Induction Heating Intenational Scientific Colloquium Modelling fo Electomagnetic Pocessing Hannove, Mach 4-6, 3 Electodynamic Foces in Steel Stip duing Induction Heating H. Kasjanow, H. Schülbe,. Nikanoov bstact Tangential

More information

Fresnel Diffraction. monchromatic light source

Fresnel Diffraction. monchromatic light source Fesnel Diffaction Equipment Helium-Neon lase (632.8 nm) on 2 axis tanslation stage, Concave lens (focal length 3.80 cm) mounted on slide holde, iis mounted on slide holde, m optical bench, micoscope slide

More information

Spherical Solutions due to the Exterior Geometry of a Charged Weyl Black Hole

Spherical Solutions due to the Exterior Geometry of a Charged Weyl Black Hole Spheical Solutions due to the Exteio Geomety of a Chaged Weyl Black Hole Fain Payandeh 1, Mohsen Fathi Novembe 7, 018 axiv:10.415v [g-qc] 10 Oct 01 1 Depatment of Physics, Payame Noo Univesity, PO BOX

More information

Field emission of Electrons from Negatively Charged Cylindrical Particles with Nonlinear Screening in a Dusty Plasma

Field emission of Electrons from Negatively Charged Cylindrical Particles with Nonlinear Screening in a Dusty Plasma Reseach & Reviews: Jounal of Pue and Applied Physics Field emission of Electons fom Negatively Chaged Cylindical Paticles with Nonlinea Sceening in a Dusty Plasma Gyan Pakash* Amity School of Engineeing

More information

Reconstruction of 3D Anisotropic Objects by VIE and Model-Based Inversion Methods

Reconstruction of 3D Anisotropic Objects by VIE and Model-Based Inversion Methods Pogess In Electomagnetics Reseach C, Vol. 8, 97, 08 Reconstuction of D Anisotopic Objects by VIE and Model-Based Invesion Methods Lin E. Sun, * and Mei Song Tong Abstact A model-based invesion algoithm

More information

Phys 201A. Homework 5 Solutions

Phys 201A. Homework 5 Solutions Phys 201A Homewok 5 Solutions 3. In each of the thee cases, you can find the changes in the velocity vectos by adding the second vecto to the additive invese of the fist and dawing the esultant, and by

More information

Superluminal Group Velocity of Electromagnetic Near-fields *

Superluminal Group Velocity of Electromagnetic Near-fields * Supeluminal Goup Velocity of Electomagnetic Nea-fields * WANG Zhi-Yong( 王智勇 )**, XIONG Cai-Dong( 熊彩东 ) School of Physical Electonics, Univesity of Electonic Science and Technology of China, Chengdu 60054

More information

Levitation force analysis of ring and disk shaped permanent magnet-high temperature superconductor

Levitation force analysis of ring and disk shaped permanent magnet-high temperature superconductor Inn Jounal of Pue & Applied Physics Vol. 55, Apil 017, pp. 61-68 Levitation foce analysis of ing and disk shaped pemanent magnet-high tempeatue supeconducto Sinan Basaan & Selim Sivioglu* Depatment of

More information

2 Governing Equations

2 Governing Equations 2 Govening Equations This chapte develops the govening equations of motion fo a homogeneous isotopic elastic solid, using the linea thee-dimensional theoy of elasticity in cylindical coodinates. At fist,

More information

STUDY ON 2-D SHOCK WAVE PRESSURE MODEL IN MICRO SCALE LASER SHOCK PEENING

STUDY ON 2-D SHOCK WAVE PRESSURE MODEL IN MICRO SCALE LASER SHOCK PEENING Study Rev. Adv. on -D Mate. shock Sci. wave 33 (13) pessue 111-118 model in mico scale lase shock peening 111 STUDY ON -D SHOCK WAVE PRESSURE MODEL IN MICRO SCALE LASER SHOCK PEENING Y.J. Fan 1, J.Z. Zhou,

More information

DOING PHYSICS WITH MATLAB COMPUTATIONAL OPTICS

DOING PHYSICS WITH MATLAB COMPUTATIONAL OPTICS DOING PHYIC WITH MTLB COMPUTTIONL OPTIC FOUNDTION OF CLR DIFFRCTION THEORY Ian Coope chool of Physics, Univesity of ydney ian.coope@sydney.edu.au DOWNLOD DIRECTORY FOR MTLB CRIPT View document: Numeical

More information

Pearson s Chi-Square Test Modifications for Comparison of Unweighted and Weighted Histograms and Two Weighted Histograms

Pearson s Chi-Square Test Modifications for Comparison of Unweighted and Weighted Histograms and Two Weighted Histograms Peason s Chi-Squae Test Modifications fo Compaison of Unweighted and Weighted Histogams and Two Weighted Histogams Univesity of Akueyi, Bogi, v/noduslód, IS-6 Akueyi, Iceland E-mail: nikolai@unak.is Two

More information

COUPLED MODELS OF ROLLING, SLIDING AND WHIRLING FRICTION

COUPLED MODELS OF ROLLING, SLIDING AND WHIRLING FRICTION ENOC 008 Saint Petesbug Russia June 30-July 4 008 COUPLED MODELS OF ROLLING SLIDING AND WHIRLING FRICTION Alexey Kieenkov Ins ti tu te fo P ob le ms in Me ch an ic s Ru ss ia n Ac ad em y of Sc ie nc es

More information

Hydroelastic Analysis of a 1900 TEU Container Ship Using Finite Element and Boundary Element Methods

Hydroelastic Analysis of a 1900 TEU Container Ship Using Finite Element and Boundary Element Methods TEAM 2007, Sept. 10-13, 2007,Yokohama, Japan Hydoelastic Analysis of a 1900 TEU Containe Ship Using Finite Element and Bounday Element Methods Ahmet Egin 1)*, Levent Kaydıhan 2) and Bahadı Uğulu 3) 1)

More information

High precision computer simulation of cyclotrons KARAMYSHEVA T., AMIRKHANOV I. MALININ V., POPOV D.

High precision computer simulation of cyclotrons KARAMYSHEVA T., AMIRKHANOV I. MALININ V., POPOV D. High pecision compute simulation of cyclotons KARAMYSHEVA T., AMIRKHANOV I. MALININ V., POPOV D. Abstact Effective and accuate compute simulations ae highly impotant in acceleatos design and poduction.

More information

Solving Problems of Advance of Mercury s Perihelion and Deflection of. Photon Around the Sun with New Newton s Formula of Gravity

Solving Problems of Advance of Mercury s Perihelion and Deflection of. Photon Around the Sun with New Newton s Formula of Gravity Solving Poblems of Advance of Mecuy s Peihelion and Deflection of Photon Aound the Sun with New Newton s Fomula of Gavity Fu Yuhua (CNOOC Reseach Institute, E-mail:fuyh945@sina.com) Abstact: Accoding to

More information

Application of homotopy perturbation method to the Navier-Stokes equations in cylindrical coordinates

Application of homotopy perturbation method to the Navier-Stokes equations in cylindrical coordinates Computational Ecology and Softwae 5 5(): 9-5 Aticle Application of homotopy petubation method to the Navie-Stokes equations in cylindical coodinates H. A. Wahab Anwa Jamal Saia Bhatti Muhammad Naeem Muhammad

More information

Analysis of high speed machining center spindle dynamic unit structure performance Yuan guowei

Analysis of high speed machining center spindle dynamic unit structure performance Yuan guowei Intenational Confeence on Intelligent Systems Reseach and Mechatonics Engineeing (ISRME 0) Analysis of high speed machining cente spindle dynamic unit stuctue pefomance Yuan guowei Liaoning jidian polytechnic,dan

More information

FREE TRANSVERSE VIBRATIONS OF NON-UNIFORM BEAMS

FREE TRANSVERSE VIBRATIONS OF NON-UNIFORM BEAMS Please cite this aticle as: Izabela Zamosa Fee tansvese vibations of non-unifom beams Scientific Reseach of the Institute of Mathematics and Compute Science Volume 9 Issue pages 3-9. The website: http://www.amcm.pcz.pl/

More information

EELE 3331 Electromagnetic I Chapter 4. Electrostatic fields. Islamic University of Gaza Electrical Engineering Department Dr.

EELE 3331 Electromagnetic I Chapter 4. Electrostatic fields. Islamic University of Gaza Electrical Engineering Department Dr. EELE 3331 Electomagnetic I Chapte 4 Electostatic fields Islamic Univesity of Gaza Electical Engineeing Depatment D. Talal Skaik 212 1 Electic Potential The Gavitational Analogy Moving an object upwad against

More information

INTRODUCTION. 2. Vectors in Physics 1

INTRODUCTION. 2. Vectors in Physics 1 INTRODUCTION Vectos ae used in physics to extend the study of motion fom one dimension to two dimensions Vectos ae indispensable when a physical quantity has a diection associated with it As an example,

More information

Lecture 10. Vertical coordinates General vertical coordinate

Lecture 10. Vertical coordinates General vertical coordinate Lectue 10 Vetical coodinates We have exclusively used height as the vetical coodinate but thee ae altenative vetical coodinates in use in ocean models, most notably the teainfollowing coodinate models

More information

A Double Exponential Function Fitting Algorithm for Optimize Parameter of µh Curve

A Double Exponential Function Fitting Algorithm for Optimize Parameter of µh Curve Advanced Mateials Reseach Online: 214-6-18 ISSN: 1662-8985, Vols. 96-961, pp 1146-115 doi:1.428/www.scientific.net/amr.96-961.1146 214 Tans Tech Publications, Switzeland A Double Exponential Function Fitting

More information

A New Approach to General Relativity

A New Approach to General Relativity Apeion, Vol. 14, No. 3, July 7 7 A New Appoach to Geneal Relativity Ali Rıza Şahin Gaziosmanpaşa, Istanbul Tukey E-mail: aizasahin@gmail.com Hee we pesent a new point of view fo geneal elativity and/o

More information

Contribution to the cavity model for analysis of microstrip patch antennas

Contribution to the cavity model for analysis of microstrip patch antennas JOURNAL OF OPTOELECTRONICS AND ADVANCED MATERIALS Vol. 8, No. 1, Febauy 006, p. 339-344 Contibution to the cavity model fo analysis of micostip patch antennas D. D. SANDU *, O. G. AVADANEI, A. IOACHIM

More information

Easy. P4.2 Since the car is moving with constant speed and in a straight line, the. resultant force on it must be regardless of whether it is moving

Easy. P4.2 Since the car is moving with constant speed and in a straight line, the. resultant force on it must be regardless of whether it is moving Chapte 4 Homewok Solutions Easy P4. Since the ca is moving with constant speed and in a staight line, the zeo esultant foce on it must be egadless of whethe it is moving (a) towad the ight o the left.

More information

Lecture 2 Date:

Lecture 2 Date: Lectue 2 Date: 5.1.217 Definition of Some TL Paametes Examples of Tansmission Lines Tansmission Lines (contd.) Fo a lossless tansmission line the second ode diffeential equation fo phasos ae: LC 2 d I

More information

An Exact Solution of Navier Stokes Equation

An Exact Solution of Navier Stokes Equation An Exact Solution of Navie Stokes Equation A. Salih Depatment of Aeospace Engineeing Indian Institute of Space Science and Technology, Thiuvananthapuam, Keala, India. July 20 The pincipal difficulty in

More information

A dual-reciprocity boundary element method for axisymmetric thermoelastodynamic deformations in functionally graded solids

A dual-reciprocity boundary element method for axisymmetric thermoelastodynamic deformations in functionally graded solids APCOM & ISCM 11-14 th Decembe, 013, Singapoe A dual-ecipocity bounday element method fo axisymmetic themoelastodynamic defomations in functionally gaded solids *W. T. Ang and B. I. Yun Division of Engineeing

More information

3D Engineering Model of Downburst Evolution in Thunderstorm

3D Engineering Model of Downburst Evolution in Thunderstorm Available online at www.sciencediect.com Pocedia Engineeing 17 (11 141 15 The nd Intenational Symposium on Aicaft Aiwothiness (ISAA 11 3D Engineeing Model of Downbust Evolution in Thundestom TANG Chu a

More information

20th Century Atomic Theory - Hydrogen Atom

20th Century Atomic Theory - Hydrogen Atom 0th Centuy Atomic Theoy - Hydogen Atom Ruthefod s scatteing expeiments (Section.5, pp. 53-55) in 1910 led to a nuclea model of the atom whee all the positive chage and most of the mass wee concentated

More information

Chapter 12: Kinematics of a Particle 12.8 CURVILINEAR MOTION: CYLINDRICAL COMPONENTS. u of the polar coordinate system are also shown in

Chapter 12: Kinematics of a Particle 12.8 CURVILINEAR MOTION: CYLINDRICAL COMPONENTS. u of the polar coordinate system are also shown in ME 01 DYNAMICS Chapte 1: Kinematics of a Paticle Chapte 1 Kinematics of a Paticle A. Bazone 1.8 CURVILINEAR MOTION: CYLINDRICAL COMPONENTS Pola Coodinates Pola coodinates ae paticlaly sitable fo solving

More information

F Q E v B MAGNETOSTATICS. Creation of magnetic field B. Effect of B on a moving charge. On moving charges only. Stationary and moving charges

F Q E v B MAGNETOSTATICS. Creation of magnetic field B. Effect of B on a moving charge. On moving charges only. Stationary and moving charges MAGNETOSTATICS Ceation of magnetic field. Effect of on a moving chage. Take the second case: F Q v mag On moving chages only F QE v Stationay and moving chages dw F dl Analysis on F mag : mag mag Qv. vdt

More information

Multiple Criteria Secretary Problem: A New Approach

Multiple Criteria Secretary Problem: A New Approach J. Stat. Appl. Po. 3, o., 9-38 (04 9 Jounal of Statistics Applications & Pobability An Intenational Jounal http://dx.doi.og/0.785/jsap/0303 Multiple Citeia Secetay Poblem: A ew Appoach Alaka Padhye, and

More information

Hammerstein Model Identification Based On Instrumental Variable and Least Square Methods

Hammerstein Model Identification Based On Instrumental Variable and Least Square Methods Intenational Jounal of Emeging Tends & Technology in Compute Science (IJETTCS) Volume 2, Issue, Januay Febuay 23 ISSN 2278-6856 Hammestein Model Identification Based On Instumental Vaiable and Least Squae

More information

The physics of induction stoves

The physics of induction stoves The physics of uction stoves This is an aticle fom my home page: www.olewitthansen.dk Contents 1. What is an uction stove...1. Including self-uctance...4 3. The contibution fom the magnetic moments...6

More information

Multi-state Electric Field Analysis of 1-tower-double-circuit HVDC Transmission Lines Based On Charge Simulation Method

Multi-state Electric Field Analysis of 1-tower-double-circuit HVDC Transmission Lines Based On Charge Simulation Method Applied Mechanics and Mateials Online: 04-0-06 ISSN: 66-748, Vol. 5, pp 3-39 doi:0.408/www.scientific.net/amm.5.3 04 Tans Tech Publications, Switzeland Multi-state Electic Field Analysis of -towe-double-cicuit

More information

Physics 11 Chapter 3: Vectors and Motion in Two Dimensions. Problem Solving

Physics 11 Chapter 3: Vectors and Motion in Two Dimensions. Problem Solving Physics 11 Chapte 3: Vectos and Motion in Two Dimensions The only thing in life that is achieved without effot is failue. Souce unknown "We ae what we epeatedly do. Excellence, theefoe, is not an act,

More information

Energy Levels Of Hydrogen Atom Using Ladder Operators. Ava Khamseh Supervisor: Dr. Brian Pendleton The University of Edinburgh August 2011

Energy Levels Of Hydrogen Atom Using Ladder Operators. Ava Khamseh Supervisor: Dr. Brian Pendleton The University of Edinburgh August 2011 Enegy Levels Of Hydogen Atom Using Ladde Opeatos Ava Khamseh Supeviso: D. Bian Pendleton The Univesity of Edinbugh August 11 1 Abstact The aim of this pape is to fist use the Schödinge wavefunction methods

More information

INFLUENCE OF GROUND INHOMOGENEITY ON WIND INDUCED GROUND VIBRATIONS. Abstract

INFLUENCE OF GROUND INHOMOGENEITY ON WIND INDUCED GROUND VIBRATIONS. Abstract INFLUENCE OF GROUND INHOMOGENEITY ON WIND INDUCED GROUND VIBRATIONS Mohammad Mohammadi, National Cente fo Physical Acoustics, Univesity of Mississippi, MS Caig J. Hicey, National Cente fo Physical Acoustics,

More information

arxiv:gr-qc/ v2 8 Jun 2006

arxiv:gr-qc/ v2 8 Jun 2006 On Quantization of the Electical Chage Mass Dmitiy M Palatnik 1 6400 N Sheidan Rd 2605, Chicago, IL 60626 axiv:g-qc/060502v2 8 Jun 2006 Abstact Suggested a non-linea, non-gauge invaiant model of Maxwell

More information

ScienceDirect. The modelling of the electric field generated by the electrical transport lines

ScienceDirect. The modelling of the electric field generated by the electrical transport lines Available online at www.sciencediect.com ScienceDiect Enegy ocedia 85 (016) 170 177 Sustainable Solutions fo Enegy and Envionment, EENVIRO - YRC 015, 18-0 Novembe 015, Buchaest, Romania The modelling of

More information