H=,-J 17xE (2) where E and II are respectively the electric and the magnetic field vectors, k,

Size: px
Start display at page:

Download "H=,-J 17xE (2) where E and II are respectively the electric and the magnetic field vectors, k,"

Transcription

1 t THE CHARACTERISTICS OF THE TE, MODE WAVES IN A CIRCULAR WAVEGUIDE FILLED WITH RADIALLY NONUNIFORM PLASMA. (THE CASE WHERE THE PLASMA ELECTRON FREQUENCY ON THE AXIS EXCEEDS THE WAVE FREQUENCY) by Mitsugu KoNoMi and Yoshio KAGE SUMMARY One of the authors has dealt with the characteristics of the TE waves in a waveguide of circular cross section fi11ed with dissipationless Lorentz plasma whose radial distribution is parabolic. The author's view has hitherto been restricted to the case where the plasma electron frequency on the waveguide axis is always lower than the wave frequency. In present paper, however, we shall treat the waves which are not subjected to such restriction on frequency. The function that satisfies the field equation is determined by the aid of an electronic computer. Some results are shown in graphs. 1. FIELD EQUATIONS The equation that must be satisfied by both the electric and the magnetic field in a dissipationless medium are VXVX.E-ko2rceE=O (1) opt H=,-J 17xE (2) where E and II are respectively the electric and the magnetic field vectors, k, the wave number in the vacuum and w the radian frequency of the wave. rc, is the specific inductive capacity. pt is the magnetic permeability of the medium. Eq. (1) yields e and z components of the field vector for the cylindrical coordinates system (r, e, z) respectively -l- -Qa-bEi- -Qe2117-/ -t-a, {-IL- a(5ee))+ aa, (-l- {l3ee') -k,2rc,e,-o (3) il- (-8T, (r aaei) - 8, (r aal;2) -il- aa2e,,z+aae2gs)- k,2rc,e. =-o (4) Hereafter, we shall discuss only the transverse electric waves of axially symmetrical configuration, viz. TEo waves. We have now (1)

2 ;- -i;.t (" ddåë,)+ (ko2rce-b2-",)åë ==O (6) where Åë is the function to be determined which is defined by Ee=Åë(r)ei`BZ-tot' (7) B is the phase constant. As previously done{iår' (2)' (3), we put rce==1- So2(1-X2) (8) where S, is the plasma electron frequency on the waveguide axis normalized by the wave frequency, and x the radial coordinate normalized by the inner radius of the waveguide, say, R. Substituting Eq. (8) into Eq. (6), we have N" litdi(x-dd9-)+(-k2+h,2x2-f,)åë-o (g) k2 and ho2 are respectively and k2 =- {k,2(s,2-1)+b"}r2 (10) ho2= (ko So R)2 (11) As noted above, S,;}iil is the present case, so k2 in Eq. (10) has always a positive sign within the transmission band of the wave. One is reminded that the solution of Eq. (9) was discussed in the previous reports on the premise that the sign of k2 is always negative. 2. SOLUTION OF THE FIELD EQUATIONS By the transformation and k2 Eq. (9) can be converted to dipur,. + (a - {) va-o (14) where a-(tdeh)2 (ls) (2)

3 The sign of p in Eq. (14) is now positive, whereas it was not in the former reports. In order to determine the function ur (a, p), we expand it into an ascending series of p, viz., W(a, p) -= :i]b.pm"i (16) m=o Substituting Eq. (16) into Eq. (14), we have bo=1, bi=-1 (17) The coefficient of higher order can be obtained from the following recurrence relation m(m+1) b.-2b. -i+ab.-2 =-O (18) Fig. 1-a and Fig. 1-b show VV(a, p), and Fig. 2-a and Fig. 2-b the first derivatives of M7(a, p) with respect to p. These functions are determined by the aid of an ' electronic computer. The condition that must be satisfied by the electric field on the inner wall of the waveguide is ur(a, e')-o ag) For a given value of a the numerable roots of Eq. (14) can successively be found from the curves in Figs. 1-a and 1-b, say, ki2/8, k22/8 and so on. Combining these values with Eq. (15), we have eigenvalues ki, k2, etc. for a given value of ho Fig.3 shows the results for the TEoi and TEo2 modes. The phase constant of the wave along the waveguide axis is given by (BR) 2- (k,r) 2-r2 (20) where r2 === h,2- k2 (21) Fig. 4 shows r2 plotted against ho. Each component of the field can be written down as follows: Er=Ez=O NI E, --cw(a., P)i (22) H.--c.B pt M7(a., p) He=O.1 2 dor(a, p) Hz =" ==J- d CtuptR p (3) (23)

4 C is a constant. REIERENcaS (1) M. Konomi, Y. Tokumitsu, H. Nishino and Y. Mieno : Bulletin of the Kyushu Inst. of Tech. (Technology), No. 18, p 101, March (in Japanese) (2) M. Konomi, Y. Mieno, K. Miyamoto and S.Sato:ibid., No. 19, p123, March (in Japanese) (3) M. Konomi, Y. Sato and M. Matsumoto: ibid., No. 20, p 79, March ioo. 80 o.7" o,6 T e. o 20 %sll. B too O to t2 t4 16 f8 20 f- Fig. 1-a. (4)

5 t6 t :y.o B i2 --i6 P- Fig. 1-b. (5)

6 . L ' 40 so 1 io 20 g" *s AxTa ssa va.-. o!:; -to -20 gv O O 2 Zi- 6 8 to 12 t4 t6 t Fig. 2-a. S2 ops Å~-.- tro,27 tr } rs B KP fb P-- Fig. 2-b. (6)

7 t6 t4 12 i -slrl IO N ico} 8 6 to t2f4t6l N h.9- Fig oo 1 3oo KVe7 pt f" 200 'reei ioo o to t2 t4 16 f :: he - Fig. 4. (7)

P a g e 5 1 of R e p o r t P B 4 / 0 9

P a g e 5 1 of R e p o r t P B 4 / 0 9 P a g e 5 1 of R e p o r t P B 4 / 0 9 J A R T a l s o c o n c l u d e d t h a t a l t h o u g h t h e i n t e n t o f N e l s o n s r e h a b i l i t a t i o n p l a n i s t o e n h a n c e c o n n e

More information

Charge to Mass Ratio of the Electron

Charge to Mass Ratio of the Electron Charge to Mass Ratio of the Electron 1. Purpose: To determine the charge to mass ratio of the electron, e/m, by subjecting a beam of electrons to a magnetic field and examining their trajectories. It can

More information

ANALYTICAL SOLUTION TO EDDY CURRENT TESTING OF CYLINDRICAL PROBLEMS WITH VARYING PROPERTIES

ANALYTICAL SOLUTION TO EDDY CURRENT TESTING OF CYLINDRICAL PROBLEMS WITH VARYING PROPERTIES CANADIAN APPLIED MATHEMATICS QUARTERLY Volume 2, Number 3. Summer 1994 ANALYTICAL SOLUTION TO EDDY CURRENT TESTING OF CYLINDRICAL PROBLEMS WITH VARYING PROPERTIES A.A. KOLYSHKIN AND R$MI VAILLANCOURT ABSTRACT.

More information

Charged particle motion in external fields

Charged particle motion in external fields Chapter 2 Charged particle motion in external fields A (fully ionized) plasma contains a very large number of particles. In general, their motion can only be studied statistically, taking appropriate averages.

More information

T h e C S E T I P r o j e c t

T h e C S E T I P r o j e c t T h e P r o j e c t T H E P R O J E C T T A B L E O F C O N T E N T S A r t i c l e P a g e C o m p r e h e n s i v e A s s es s m e n t o f t h e U F O / E T I P h e n o m e n o n M a y 1 9 9 1 1 E T

More information

Lecture 3 Fiber Optical Communication Lecture 3, Slide 1

Lecture 3 Fiber Optical Communication Lecture 3, Slide 1 Lecture 3 Optical fibers as waveguides Maxwell s equations The wave equation Fiber modes Phase velocity, group velocity Dispersion Fiber Optical Communication Lecture 3, Slide 1 Maxwell s equations in

More information

Formula Sheet. ( γ. 0 : X(t) = (A 1 + A 2 t) e 2 )t. + X p (t) (3) 2 γ Γ +t Γ 0 : X(t) = A 1 e + A 2 e + X p (t) (4) 2

Formula Sheet. ( γ. 0 : X(t) = (A 1 + A 2 t) e 2 )t. + X p (t) (3) 2 γ Γ +t Γ 0 : X(t) = A 1 e + A 2 e + X p (t) (4) 2 Formula Sheet The differential equation Has the general solutions; with ẍ + γẋ + ω 0 x = f cos(ωt + φ) (1) γ ( γ )t < ω 0 : X(t) = A 1 e cos(ω 0 t + β) + X p (t) () γ = ω ( γ 0 : X(t) = (A 1 + A t) e )t

More information

176 5 t h Fl oo r. 337 P o ly me r Ma te ri al s

176 5 t h Fl oo r. 337 P o ly me r Ma te ri al s A g la di ou s F. L. 462 E l ec tr on ic D ev el op me nt A i ng er A.W.S. 371 C. A. M. A l ex an de r 236 A d mi ni st ra ti on R. H. (M rs ) A n dr ew s P. V. 326 O p ti ca l Tr an sm is si on A p ps

More information

Chapter 8. Chapter Spherical Pressure Vessels

Chapter 8. Chapter Spherical Pressure Vessels Chapter 8 Chapter 8-1-8-3 Spherical Pressure Vessels Here are examples of spherical pressure vessels. Let s determine how to analyze them. Consider Figures 8-2 and 8-3 below. 1 Figure 8-2 illustrates the

More information

Version: A. Earth s gravitational field g = 9.81 N/kg Mass of a Proton m p = kg

Version: A. Earth s gravitational field g = 9.81 N/kg Mass of a Proton m p = kg PHYS 2212 G & J Quiz and Exam Formulæ & Constants Fall 2017 Fundamental Charge e = 1.602 10 19 C Mass of an Electron m e = 9.109 10 31 kg Earth s gravitational field g = 9.81 N/kg Mass of a Proton m p

More information

A GENERAL APPROACH FOR CALCULATING COUPLING IMPEDANCES OF SMALL DISCONTINUITIES

A GENERAL APPROACH FOR CALCULATING COUPLING IMPEDANCES OF SMALL DISCONTINUITIES Presented at 16th IEEE Particle Accelerator Conference (PAC 95) and Int l Conference on on High Energy Accelerators, 5/1/1995-5/5/1995, Dallas, TX, USA SLAC-PUB-9963 acc-phys/9504001 A GENERAL APPROACH

More information

PSI AP Physics C Sources of Magnetic Field. Multiple Choice Questions

PSI AP Physics C Sources of Magnetic Field. Multiple Choice Questions PSI AP Physics C Sources of Magnetic Field Multiple Choice Questions 1. Two protons move parallel to x- axis in opposite directions at the same speed v. What is the direction of the magnetic force on the

More information

Title General Eigenvalue Solver for Large with Zero Filtering Author(s) Iwaashita, Yoshihisa Citation Bulletin of the Institute for Chemi University (1989), 67(1): 32-39 Issue Date 1989-03-31 URL http://hdl.handle.net/2433/77286

More information

A Proposed Experiment to Disprove Special Relativity

A Proposed Experiment to Disprove Special Relativity A Proposed Experiment to Disprove Special Relativity Musa D. Abdullahi 12 Bujumbura Street, Wuse 2, Abuja, Nigeria e-mail: musadab@outlook.com Abstract According to classical and relativistic electrodynamics,

More information

Exam 2 Solutions. Note that there are several variations of some problems, indicated by choices in parentheses.

Exam 2 Solutions. Note that there are several variations of some problems, indicated by choices in parentheses. Exam 2 Solutions Note that there are several variations of some problems, indicated by choices in parentheses. Problem 1 Part of a long, straight insulated wire carrying current i is bent into a circular

More information

Ranking accounting, banking and finance journals: A note

Ranking accounting, banking and finance journals: A note MPRA Munich Personal RePEc Archive Ranking accounting, banking and finance ournals: A note George Halkos and Nickolaos Tzeremes University of Thessaly, Department of Economics January 2012 Online at https://mpra.ub.uni-muenchen.de/36166/

More information

Department of Physics Preliminary Exam January 2 5, 2013

Department of Physics Preliminary Exam January 2 5, 2013 Department of Physics Preliminary Exam January 2 5, 2013 Day 2: Electricity, Magnetism and Optics Thursday, January 3, 2013 9:00 a.m. 12:00 p.m. Instructions: 1. Write the answer to each question on a

More information

Haus, Hermann A., and James R. Melcher. Electromagnetic Fields and Energy. Englewood Cliffs, NJ: Prentice-Hall, ISBN:

Haus, Hermann A., and James R. Melcher. Electromagnetic Fields and Energy. Englewood Cliffs, NJ: Prentice-Hall, ISBN: MIT OpenCourseWare http://ocw.mit.edu Haus, Hermann A., and James R. Melcher. Electromagnetic Fields and Energy. Englewood Cliffs, NJ: Prentice-Hall, 1989. ISBN: 9780132490207. Please use the following

More information

PHYS4210 Electromagnetic Theory Spring Final Exam Wednesday, 6 May 2009

PHYS4210 Electromagnetic Theory Spring Final Exam Wednesday, 6 May 2009 Name: PHYS4210 Electromagnetic Theory Spring 2009 Final Exam Wednesday, 6 May 2009 This exam has two parts. Part I has 20 multiple choice questions, worth two points each. Part II consists of six relatively

More information

Course theme. Three hours of lab Complete E1 (Parts 1, 2, 3, 4, and 5B) Prepare discussion presentation Prepare team report.

Course theme. Three hours of lab Complete E1 (Parts 1, 2, 3, 4, and 5B) Prepare discussion presentation Prepare team report. Experiment Session 2 Electrons and Solution Color Three hours of lab Complete E (Parts, 2, 3, 4, and 5B) Prepare discussion presentation Prepare team report. Course theme There are structure and property

More information

Three hours of lab Complete E1 (Parts 1, 2, 3, 4, and 5B) Prepare discussion presentation Prepare team report. Course theme

Three hours of lab Complete E1 (Parts 1, 2, 3, 4, and 5B) Prepare discussion presentation Prepare team report. Course theme Experiment 1 Session 2 Electrons and Solution Color Three hours of lab Complete E1 (Parts 1, 2, 3, 4, and 5B) Prepare discussion presentation Prepare team report. Course theme There are structure and property

More information

Analytical Study of Electromagnetic Wave Diffraction Through a Circular Aperture with Fringes on a Perfect Conducting Screen

Analytical Study of Electromagnetic Wave Diffraction Through a Circular Aperture with Fringes on a Perfect Conducting Screen International Journal of High Energy Physics 016; 3(5): 33-40 http://wwwsciencepublishinggroupcom/j/ijhep doi: 1011648/jijhep016030511 ISSN: 376-7405 (Print); ISSN: 376-7448 (Online) Analytical Study of

More information

Sheared Flow Stabilization in the Z-Pinch

Sheared Flow Stabilization in the Z-Pinch 1 IF/P7-28 Sheared Flow Stabilization in the Z-Pinch U. Shumlak, C.S. Adams, J.M. Blakely, B.J. Chan, R.P. Golingo, S.D. Knecht, B.A. Nelson, R.J. Oberto, M.R. Sybouts, and G.V. Vogman Aerospace & Energetics

More information

ECE 451 Advanced Microwave Measurements. Circular and Coaxial Waveguides

ECE 451 Advanced Microwave Measurements. Circular and Coaxial Waveguides ECE 451 Advanced Microwave Measurements Circular and Coaxial Waveguides Jose E. Schutt-Aine Electrical & Computer Engineering University of Illinois jesa@illinois.edu ECE 451 Jose Schutt Aine 1 Circular

More information

K E L LY T H O M P S O N

K E L LY T H O M P S O N K E L LY T H O M P S O N S E A O LO G Y C R E ATO R, F O U N D E R, A N D PA R T N E R K e l l y T h o m p s o n i s t h e c r e a t o r, f o u n d e r, a n d p a r t n e r o f S e a o l o g y, a n e x

More information

Solutions to PS 6 Physics 401a

Solutions to PS 6 Physics 401a Solutions to PS 6 Physics 401a 1. Let B point along the z axis. Then by circuar symmetry, we have B(r, t) =B(r, t)e z (1) Using Faraday s Law, we can find the electric field at radius r to be E(r, t) dl

More information

Cylindrical Dielectric Waveguides

Cylindrical Dielectric Waveguides 03/02/2017 Cylindrical Dielectric Waveguides Integrated Optics Prof. Elias N. Glytsis School of Electrical & Computer Engineering National Technical University of Athens Geometry of a Single Core Layer

More information

Physics 8.02 Exam Two Equation Sheet Spring 2004

Physics 8.02 Exam Two Equation Sheet Spring 2004 Physics 8.0 Exam Two Equation Sheet Spring 004 closed surface EdA Q inside da points from inside o to outside I dsrˆ db 4o r rˆ points from source to observer V moving from a to b E ds 0 V b V a b E ds

More information

PHY321 Homework Set 10

PHY321 Homework Set 10 PHY321 Homework Set 10 1. [5 pts] A small block of mass m slides without friction down a wedge-shaped block of mass M and of opening angle α. Thetriangular block itself slides along a horizontal floor,

More information

Bioscience, Biotechnology, and Biochemistry. Egg white hydrolysate inhibits oxidation in mayonnaise and a model system

Bioscience, Biotechnology, and Biochemistry. Egg white hydrolysate inhibits oxidation in mayonnaise and a model system Egg white hydrolysate inhibits oxidation in mayonnaise and a model system Journal: Manuscript ID BBB-00.R Manuscript Type: Regular Paper Date Submitted by the Author: -Jan-0 Complete List of Authors: Kobayashi,

More information

Modal Analysis and Cutoff Condition of a Doubly Clad Cardioidic Waveguide

Modal Analysis and Cutoff Condition of a Doubly Clad Cardioidic Waveguide Intl J ngg Sci Adv Research 5 Sep;():9-97 Modal Analysis and Cutoff Condition of a Doubly Clad Cardioidic Waveguide Ram Janma Department of Physics, University Institute of ngineering and Technology, Chhatrapati

More information

APPENDIX Z. USEFUL FORMULAS 1. Appendix Z. Useful Formulas. DRAFT 13:41 June 30, 2006 c J.D Callen, Fundamentals of Plasma Physics

APPENDIX Z. USEFUL FORMULAS 1. Appendix Z. Useful Formulas. DRAFT 13:41 June 30, 2006 c J.D Callen, Fundamentals of Plasma Physics APPENDIX Z. USEFUL FORMULAS 1 Appendix Z Useful Formulas APPENDIX Z. USEFUL FORMULAS 2 Key Vector Relations A B = B A, A B = B A, A A = 0, A B C) = A B) C A B C) = B A C) C A B), bac-cab rule A B) C D)

More information

Plasma heating in stellarators at the fundamental ion cyclotron frequency

Plasma heating in stellarators at the fundamental ion cyclotron frequency PHYSICS OF PLASMAS VOLUME 7, NUMBER FEBRUARY 000 Plasma heating in stellarators at the fundamental ion cyclotron frequency V. A. Svidzinski and D. G. Swanson Department of Physics, Auburn University, Auburn,

More information

-"l" also contributes ENERGY. Higher values for "l" mean the electron has higher energy.

-l also contributes ENERGY. Higher values for l mean the electron has higher energy. 170 - Giving the four parameters will uniquely identify an electron around an atom. No two electrons in the same atom can share all four. These parameters are called QUANTUM NUMBERS. PRINCIPAL QUANTUM

More information

For any use or distribution of this textbook, please cite as follows:

For any use or distribution of this textbook, please cite as follows: IT OpenCourseWare http://ocw.mit.edu Electromechanical Dynamics For any use or distribution of this textbook, please cite as follows: Woodson, Herbert H., and James R. elcher. Electromechanical Dynamics.

More information

PROPAGATION OF ELECTROMAGNETIC WAVES IN TOROIDAL STRUCTURES. by L.J. VAN DER PAUW. Philips Research Laboratories, P.O. Box 80.

PROPAGATION OF ELECTROMAGNETIC WAVES IN TOROIDAL STRUCTURES. by L.J. VAN DER PAUW. Philips Research Laboratories, P.O. Box 80. Philips J. Res. 43, 492-505, 1988 R 1197 PROPAGATION OF ELECTROMAGNETIC WAVES IN TOROIDAL STRUCTURES by L.J. VAN DER PAUW Philips Research Laboratories, P.O. Box 80.000, Eindhoven, 56007A, The Netherlands

More information

The Periodic Table. Periodic Properties. Can you explain this graph? Valence Electrons. Valence Electrons. Paramagnetism

The Periodic Table. Periodic Properties. Can you explain this graph? Valence Electrons. Valence Electrons. Paramagnetism Periodic Properties Atomic & Ionic Radius Energy Electron Affinity We want to understand the variations in these properties in terms of electron configurations. The Periodic Table Elements in a column

More information

7.6 Stress in symmetrical elastic beam transmitting both shear force and bending moment

7.6 Stress in symmetrical elastic beam transmitting both shear force and bending moment 7.6 Stress in symmetrical elastic beam transmitting both shear force and bending moment à It is more difficult to obtain an exact solution to this problem since the presence of the shear force means that

More information

Periodic orbits of continuous mappings of the circle without fixed points

Periodic orbits of continuous mappings of the circle without fixed points Ergod. Th. & Dynam. Sys. (1981), 1, 413^17 Printed in Great Britain Periodic orbits of continuous mappings of the circle without fixed points CHRIS BERNHARDT Mathematics Department, Southern Illinois University,

More information

Unit II Thermal Physics Introduction- Modes of Heat Transfer Normally there are three modes of transfer of heat from one place to another viz., conduction, convection and radiation. Conduction : Conduction

More information

ME 309 Fluid Mechanics Fall 2010 Exam 2 1A. 1B.

ME 309 Fluid Mechanics Fall 2010 Exam 2 1A. 1B. Fall 010 Exam 1A. 1B. Fall 010 Exam 1C. Water is flowing through a 180º bend. The inner and outer radii of the bend are 0.75 and 1.5 m, respectively. The velocity profile is approximated as C/r where C

More information

Properties of axial surface waves along dielectrically coated conducting cylinders

Properties of axial surface waves along dielectrically coated conducting cylinders Adv. Radio Sci., 10, 79 84, 2012 doi:10.5194/ars-10-79-2012 Author(s) 2012. CC Attribution 3.0 License. Advances in Radio Science Properties of axial surface waves along dielectrically coated conducting

More information

PhysicsAndMathsTutor.com 1

PhysicsAndMathsTutor.com 1 PhysicsndMathsTutor.com 1 Q1. Which line, to, correctly describes the trajectory of charged particles which enter, at right angles, (a) a uniform electric field, and (b) a uniform magnetic field? (a) uniform

More information

-"l" also contributes ENERGY. Higher values for "l" mean the electron has higher energy.

-l also contributes ENERGY. Higher values for l mean the electron has higher energy. 175 - Giving the four parameters will uniquely identify an electron around an atom. No two electrons in the same atom can share all four. These parameters are called QUANTUM NUMBERS. PRINCIPAL QUANTUM

More information

Solutions and Ions. Pure Substances

Solutions and Ions. Pure Substances Class #4 Solutions and Ions CHEM 107 L.S. Brown Texas A&M University Pure Substances Pure substance: described completely by a single chemical formula Fixed composition 1 Mixtures Combination of 2 or more

More information

A STUDY OF THE SOUND PROPAGATION IN THE ROUNDED SECTION OF A PIPE

A STUDY OF THE SOUND PROPAGATION IN THE ROUNDED SECTION OF A PIPE A STUDY OF THE SOUND PROPAGATION IN THE ROUNDED SECTION OF A PIPE Professor habil. dr. P. ILGAKOJIS, Lecturer dr. E. JOTAUTIENE - Lithuanian University of Agriculture Abstract: In this paper, the sound

More information

UHV - Technology. Oswald Gröbner

UHV - Technology. Oswald Gröbner School on Synchrotron Radiation UHV - Technology Trieste, 20-21 April 2004 1) Introduction and some basics 2) Building blocks of a vacuum system 3) How to get clean ultra high vacuum 4) Desorption phenomena

More information

ORBITAL DIAGRAM - A graphical representation of the quantum number "map" of electrons around an atom.

ORBITAL DIAGRAM - A graphical representation of the quantum number map of electrons around an atom. 160 ORBITAL DIAGRAM - A graphical representation of the quantum number "map" of electrons around an atom. 4p 3d 4s 3p 3s 2p 2s 1s Each blank represents an ORBITAL, and can hold two electrons. The 4s subshell

More information

Cyby TISIA E. Document No. - "/r ".. TECHNICAL LIBRARY /, Copy No. /- ' E. E. Secher. 2 uut15. No. EM JReport

Cyby TISIA E. Document No. - /r .. TECHNICAL LIBRARY /, Copy No. /- ' E. E. Secher. 2 uut15. No. EM JReport .All I( l-, ltc I+ / '" TECHNICAL LIBRARY /, Document No. - "/r ".. Copy No. /- ' Cyby E. E. Secher " ~~ ~ ~~ A I P"l +" ".i JReport No. EM 9-18 2 uut15 H.ARD MIfROFICHE COPY $o 6. - S PA CE 1NO TEC- LO.aQG3Y

More information

Circuits Capacitance of a parallel-plate capacitor : C = κ ε o A / d. (ρ = resistivity, L = length, A = cross-sectional area) Resistance : R = ρ L / A

Circuits Capacitance of a parallel-plate capacitor : C = κ ε o A / d. (ρ = resistivity, L = length, A = cross-sectional area) Resistance : R = ρ L / A k = 9.0 x 109 N m2 / C2 e = 1.60 x 10-19 C ε o = 8.85 x 10-12 C2 / N m2 Coulomb s law: F = k q Q / r2 (unlike charges attract, like charges repel) Electric field from a point charge : E = k q / r2 ( towards

More information

Torsion Stresses in Tubes and Rods

Torsion Stresses in Tubes and Rods Torsion Stresses in Tubes and Rods This initial analysis is valid only for a restricted range of problem for which the assumptions are: Rod is initially straight. Rod twists without bending. Material is

More information

THE SHEARED-FLOW STABILIZED Z-PINCH

THE SHEARED-FLOW STABILIZED Z-PINCH THE SHEARED-FLOW STABILIZED Z-PINCH U. Shumlak* J. Chadney R.P. Golingo D.J. Den Hartog M.C. Hughes S.D. Knecht W. Lowrie V.S. Lukin B.A. Nelson R.J. Oberto J.L. Rohrbach M.P. Ross and G.V. Vogman *University

More information

Electromagnetic waves in free space

Electromagnetic waves in free space Waveguide notes 018 Electromagnetic waves in free space We start with Maxwell s equations for an LIH medum in the case that the source terms are both zero. = =0 =0 = = Take the curl of Faraday s law, then

More information

NOTICE WARNING CONCERNING COPYRIGHT RESTRICTIONS: The copyright law of the United States (title 17, U.S. Code) governs the making of photocopies or

NOTICE WARNING CONCERNING COPYRIGHT RESTRICTIONS: The copyright law of the United States (title 17, U.S. Code) governs the making of photocopies or NOTICE WARNING CONCERNING COPYRIGHT RESTRICTIONS: The copyright law of the United States (title 17, U.S. Code) governs the making of photocopies or other reproductions of copyrighted material. Any copying

More information

Rocket Propulsion Prof. K. Ramamurthi Department of Mechanical Engineering Indian Institute of Technology, Madras

Rocket Propulsion Prof. K. Ramamurthi Department of Mechanical Engineering Indian Institute of Technology, Madras Rocket Propulsion Prof. K. Ramamurthi Department of Mechanical Engineering Indian Institute of Technology, Madras Lecture 24 Design Aspects of Solid Propellant Rockets We will continue with solid propellant

More information

The Q Machine. 60 cm 198 cm Oven. Plasma. 6 cm 30 cm. 50 cm. Axial. Probe. PUMP End Plate Magnet Coil. Filament Cathode. Radial. Hot Plate.

The Q Machine. 60 cm 198 cm Oven. Plasma. 6 cm 30 cm. 50 cm. Axial. Probe. PUMP End Plate Magnet Coil. Filament Cathode. Radial. Hot Plate. 1 The Q Machine 60 cm 198 cm Oven 50 cm Axial Probe Plasma 6 cm 30 cm PUMP End Plate Magnet Coil Radial Probe Hot Plate Filament Cathode 2 THE Q MACHINE 1. GENERAL CHARACTERISTICS OF A Q MACHINE A Q machine

More information

Wireless & Hybrid Fire Solutions

Wireless & Hybrid Fire Solutions ic b 8 c b u i N5 b 4o 25 ii p f i b p r p ri u o iv p i o c v p c i b A i r v Hri F N R L L T L RK N R L L rr F F r P o F i c b T F c c A vri r of op oc F r P, u icoc b ric, i fxib r i i ribi c c A K

More information

ORBITAL DIAGRAM - A graphical representation of the quantum number "map" of electrons around an atom.

ORBITAL DIAGRAM - A graphical representation of the quantum number map of electrons around an atom. 178 (MAGNETIC) SPIN QUANTUM NUMBER: "spin down" or "spin up" - An ORBITAL (region with fixed "n", "l" and "ml" values) can hold TWO electrons. ORBITAL DIAGRAM - A graphical representation of the quantum

More information

1. The figure shows two long parallel wires carrying currents I 1 = 15 A and I 2 = 32 A (notice the currents run in opposite directions).

1. The figure shows two long parallel wires carrying currents I 1 = 15 A and I 2 = 32 A (notice the currents run in opposite directions). Final Eam Physics 222 7/29/211 NAME Use o = 8.85 1-12 C 2 /N.m 2, o = 9 1 9 N.m 2 /C 2, o/= 1-7 T m/a There are additional formulas in the final page of this eam. 1. The figure shows two long parallel

More information

LA-UR SLL /PB/M TITLE: INTENSE ANNULAR RELATIVISTIC ELECTRON BEAM GENERATION IN FOILLESS DIODES. Michael E. Jones and Lester E.

LA-UR SLL /PB/M TITLE: INTENSE ANNULAR RELATIVISTIC ELECTRON BEAM GENERATION IN FOILLESS DIODES. Michael E. Jones and Lester E. LA-UR-79-3107 SLL 81 264/PB/M TITLE: INTENSE ANNULAR RELATIVISTIC ELECTRON BEAM GENERATION IN FOILLESS DIODES AUTHOR(S): Michael E. Jones and Lester E. Thode SUBMITTED TO: Physical Review Letters SOR 8?Ä1

More information

Magnetic Fields due to Currents

Magnetic Fields due to Currents Observation: a current of moving charged particles produces a magnetic field around the current. Chapter 29 Magnetic Fields due to Currents Magnetic field due to a current in a long straight wire a current

More information

ONE CENTURY LATER: REMARKS ON THE BARNETT EXPERIMENT

ONE CENTURY LATER: REMARKS ON THE BARNETT EXPERIMENT ONE CENTURY LATER: REMARKS ON THE BARNETT EXPERIMENT Alexander L. Kholmetskii Department of Physics Belarus State University 4, F. Skorina Avenue 220080 Minsk, Belarus E-mail: kholm@bsu.by Abstract The

More information

EIGENVALUE ANALYSIS OF SPHERICAL RESONANT CAVITY USING RADIAL BASIS FUNCTIONS

EIGENVALUE ANALYSIS OF SPHERICAL RESONANT CAVITY USING RADIAL BASIS FUNCTIONS Progress In Electromagnetics Research Letters, Vol. 24, 69 76, 2011 EIGENVALUE ANALYSIS OF SPHERICAL RESONANT CAVITY USING RADIAL BASIS FUNCTIONS S. J. Lai 1, *, B. Z. Wang 1, and Y. Duan 2 1 Institute

More information

Multiple Degree of Freedom Systems. The Millennium bridge required many degrees of freedom to model and design with.

Multiple Degree of Freedom Systems. The Millennium bridge required many degrees of freedom to model and design with. Multiple Degree of Freedom Systems The Millennium bridge required many degrees of freedom to model and design with. The first step in analyzing multiple degrees of freedom (DOF) is to look at DOF DOF:

More information

Graduate Diploma in Engineering Circuits and waves

Graduate Diploma in Engineering Circuits and waves 9210-112 Graduate Diploma in Engineering Circuits and waves You should have the following for this examination one answer book non-programmable calculator pen, pencil, ruler No additional data is attached

More information

Torsion of shafts with circular symmetry

Torsion of shafts with circular symmetry orsion of shafts with circular symmetry Introduction Consider a uniform bar which is subject to a torque, eg through the action of two forces F separated by distance d, hence Fd orsion is the resultant

More information

A DIVERTED PLASMA REVERSED FIELD PINCH. (U) JUL 80 W N MNHt*EINER DOE-EX-7-A UJNCLASSIFIED NRL-W DAO804 NVAIESECELOE E E E EEO

A DIVERTED PLASMA REVERSED FIELD PINCH. (U) JUL 80 W N MNHt*EINER DOE-EX-7-A UJNCLASSIFIED NRL-W DAO804 NVAIESECELOE E E E EEO A DIVERTED PLASMA REVERSED FIELD PINCH. (U) JUL 80 W N MNHt*EINER DOE-EX-7-A-39-1006 UJNCLASSIFIED NRL-W-495 14. 7 DAO804 NVAIESECELOE E E E EEO O Fe 0 HU- J11111L _ Jil. IIII1 III 'I D 1.6 lii 6 MICROCOPY

More information

CAMBRIDGE INTERNATIONAL EXAMINATIONS General Certificate of Education Advanced Subsidiary Level General Certificate of Education Advanced Level

CAMBRIDGE INTERNATIONAL EXAMINATIONS General Certificate of Education Advanced Subsidiary Level General Certificate of Education Advanced Level CAMBRIDGE INTERNATIONAL EXAMINATIONS General Certificate of Education Advanced Subsidiary Level General Certificate of Education Advanced Level MATHEMATICS 9709/1 PAPER 1 Pure Mathematics 1 (P1) Additional

More information

Physics GRE: Electromagnetism. G. J. Loges 1. University of Rochester Dept. of Physics & Astronomy. xkcd.com/567/

Physics GRE: Electromagnetism. G. J. Loges 1. University of Rochester Dept. of Physics & Astronomy. xkcd.com/567/ Physics GRE: Electromagnetism G. J. Loges University of Rochester Dept. of Physics & stronomy xkcd.com/567/ c Gregory Loges, 206 Contents Electrostatics 2 Magnetostatics 2 3 Method of Images 3 4 Lorentz

More information

TOPOLOGICAL AND MEASURE THEORETIC PROPERTIES OF ANALYTIC SETS

TOPOLOGICAL AND MEASURE THEORETIC PROPERTIES OF ANALYTIC SETS TOPOLOGICAL AND MEASURE THEORETIC PROPERTIES OF ANALYTIC SETS MAURICE SION 1. Introduction. G. Choquet's definition [l] of an analytic set in a topological space as the continuous image of a Kc has proved

More information

Sound Propagation in Ducts

Sound Propagation in Ducts Sound Propagation in Ducts Hongbin Ju Department of Mathematics Florida State Universit, Tallahassee, FL.3306 www.aeroacoustics.info Please send comments to: hju@math.fsu.edu In this section we will discuss

More information

Conducting rod on the axis of a charged ring: The Kelvin water drop generator

Conducting rod on the axis of a charged ring: The Kelvin water drop generator Conducting rod on the axis of a charged ring: The Kelvin water drop generator Gorazd Planinšič and Tomaž Prosen Physics Department, University of Ljubljana, Jadranska 19, 1111 Ljubljana, Slovenia Received

More information

Formulas and Constants (you may remove this page)

Formulas and Constants (you may remove this page) Formulas and Constants (you may remove this page) NA = 6.0x0 3 mol - h = 6.66x0-34 J s c =.99x0 m s - e =.60x0-9 C me = 9.09x0-3 kg Å = x0-0 m = 00 pm atm = 760 torr R = 0.006 L atm K - mol - =.34 J K

More information

a) (4 pts) What is the magnitude and direction of the acceleration of the electron?

a) (4 pts) What is the magnitude and direction of the acceleration of the electron? PHYSCS 22 Fall 2010 - MDTERM #3 SHOW ALL WORK & REASONNG FOR FULL PONTS Question 1. (5 pts): Accurately show or state the direction of the force that is felt by the following charges or currents. +q -q

More information

17th World Conference on Nondestructive Testing, Oct 2008, Shanghai, China AC CONDUCTIVITY OF NON MAGNETIC METALLIC ALLOYS

17th World Conference on Nondestructive Testing, Oct 2008, Shanghai, China AC CONDUCTIVITY OF NON MAGNETIC METALLIC ALLOYS 17th World Conference on Nondestructive Testing, 5- Oct, Shanghai, China AC CONDUCTIVITY OF NON MAGNETIC METALLIC ALLOYS F. Fraudita, Gallipoli, Audry, C. González Facultad de Ingeniería, Universidad Central

More information

Louisiana State University Physics 2102, Exam 2, March 5th, 2009.

Louisiana State University Physics 2102, Exam 2, March 5th, 2009. PRINT Your Name: Instructor: Louisiana State University Physics 2102, Exam 2, March 5th, 2009. Please be sure to PRINT your name and class instructor above. The test consists of 4 questions (multiple choice),

More information

of Arbitrary Length Microwave Breakdown of a Gas in a Cylindrical Cavity 0,&5 _ 8, '', _ MELVIN A. HERLIN, SANBORN C. BROWN TECHNICAL REPORT NO.

of Arbitrary Length Microwave Breakdown of a Gas in a Cylindrical Cavity 0,&5 _ 8, '', _ MELVIN A. HERLIN, SANBORN C. BROWN TECHNICAL REPORT NO. 0,&5 _ 8, '', _ Microwave Breakdown of a Gas in a Cylindrical of Arbitrary Length Cavity MELVIN A. HERLIN, SANBORN C. BROWN TECHNICAL REPORT NO. 77 JULY 30, 1948 RESEARCH LABORATORY OF ELECTRONICS MASSACHUSETTS

More information

Dynamics of Drift and Flute Modes in Linear Cylindrical ECR Plasma

Dynamics of Drift and Flute Modes in Linear Cylindrical ECR Plasma J. Plasma Fusion Res. SERIES, Vol. 8 (2009) Dynamics of Drift and Flute Modes in Linear Cylindrical ECR Plasma Kunihiro KAMATAKI 1), Sanae I. ITOH 2), Yoshihiko NAGASHIMA 3), Shigeru INAGAKI 2), Shunjiro

More information

MWP MODELING AND SIMULATION OF ELECTROMAGNETIC EFFECTS IN CAPACITIVE DISCHARGES

MWP MODELING AND SIMULATION OF ELECTROMAGNETIC EFFECTS IN CAPACITIVE DISCHARGES MWP 1.9 MODELING AND SIMULATION OF ELECTROMAGNETIC EFFECTS IN CAPACITIVE DISCHARGES Insook Lee, D.B. Graves, and M.A. Lieberman University of California Berkeley, CA 9472 LiebermanGEC7 1 STANDING WAVES

More information

Massachusetts Institute of Technology Department of Electrical Engineering and Computer Science Electric Machines

Massachusetts Institute of Technology Department of Electrical Engineering and Computer Science Electric Machines Massachusetts Institute of Technology Department of Electrical Engineering and Computer Science 6.685 Electric Machines Problem Set 1 Solutions September 1, 5 Problem 1: If we assume, as suggested in the

More information

(3 pts) 2. In which gas sample do the molecules have a lower average kinetic energy? (A) Gas A (B) Gas B (C) Neither

(3 pts) 2. In which gas sample do the molecules have a lower average kinetic energy? (A) Gas A (B) Gas B (C) Neither Consider two samples of gas, A and B, as shown in the figure below. Both containers are at the same temperature and pressure. Gas A 1.0 L 0.32 g Gas B 1.0 L 0.48 g (3 pts) 1. Which gas sample contains

More information

Mechanical Engineering Journal

Mechanical Engineering Journal 0123456789 Bulletin of the JSME Mechanical Engineering Journal Vol.2, No.5, 2015 3D MHD simulation of pressure drop and fluctuation in electromagnetic pump flow Takatoshi ASADA*, Rie AIZAWA**, Tetsu SUZUKI**,

More information

This idea had also occurred to us quite independently and for largely the. by Heisenberg4 that the multiplet separation is due to the difference

This idea had also occurred to us quite independently and for largely the. by Heisenberg4 that the multiplet separation is due to the difference 80 PHYSICS: BICHOWSK Y AND URE Y PROC. N. A. S. 1700, the variation depending mainly on the other atoms in the molecule. I am particularly indebted to Dr. W. W. Coblentz for his suggestions and personal

More information

For any use or distribution of this textbook, please cite as follows:

For any use or distribution of this textbook, please cite as follows: IT OpenCourseWare http://ocw.mit.edu Electromechanical Dynamics For any use or distribution of this textbook, please cite as follows: Woodson, Herbert H., and James R. elcher. Electromechanical Dynamics.

More information

On the Equation of the Parabolic Cylinder Functions.

On the Equation of the Parabolic Cylinder Functions. On the Equation of the Parabolic Cylinder Functions. By AKCH. MILNE, Research Student, Edinburgh University Mathematical Laboratory. (Bead 9th January 1914- Beceived 29th January 191 Jj). 1. Introductory.

More information

CBSE Sample Paper-05 (Solved) SUMMATIVE ASSESSMENT I MATHEMATICS Class IX. Time allowed: 3 hours Maximum Marks: 90. Section A.

CBSE Sample Paper-05 (Solved) SUMMATIVE ASSESSMENT I MATHEMATICS Class IX. Time allowed: 3 hours Maximum Marks: 90. Section A. CBSE Sample Paper-05 (Solved) SUMMATIVE ASSESSMENT I MATHEMATICS Class IX Time allowed: hours Maximum Marks: 90 General Instructions: a) All questions are compulsory. b) The question paper consists of

More information

Chapter 5 Three phase induction machine (1) Shengnan Li

Chapter 5 Three phase induction machine (1) Shengnan Li Chapter 5 Three phase induction machine (1) Shengnan Li Main content Structure of three phase induction motor Operating principle of three phase induction motor Rotating magnetic field Graphical representation

More information

Homework 6 solutions PHYS 212 Dr. Amir

Homework 6 solutions PHYS 212 Dr. Amir Homework 6 solutions PHYS 1 Dr. Amir Chapter 8 18. (II) A rectangular loop of wire is placed next to a straight wire, as shown in Fig. 8 7. There is a current of.5 A in both wires. Determine the magnitude

More information

Louisiana State University Physics 2102, Exam 3 April 2nd, 2009.

Louisiana State University Physics 2102, Exam 3 April 2nd, 2009. PRINT Your Name: Instructor: Louisiana State University Physics 2102, Exam 3 April 2nd, 2009. Please be sure to PRINT your name and class instructor above. The test consists of 4 questions (multiple choice),

More information

Solution Set Eight. 1 Problem #1: Toroidal Electromagnet with Gap Problem #4: Self-Inductance of a Long Solenoid. 9

Solution Set Eight. 1 Problem #1: Toroidal Electromagnet with Gap Problem #4: Self-Inductance of a Long Solenoid. 9 : Solution Set Eight Northwestern University, Electrodynamics I Wednesday, March 9, 6 Contents Problem #: Toroidal Electromagnet with Gap. Problem #: Electromagnetic Momentum. 3 3 Problem #3: Type I Superconductor.

More information

Title Number of Particles at Zero-Tempera. 琉球大学理工学部紀要. 理学編 = Bulletin of Scien. natural sciences(26):

Title Number of Particles at Zero-Tempera. 琉球大学理工学部紀要. 理学編 = Bulletin of Scien. natural sciences(26): Title The Pressure of a Non-interacting E Number of Particles at Zero-Tempera Author(s) Kamizato, Tsuneo 琉球大学理工学部紀要. 理学編 = Bulletin of Scien Citation Engineering Division, University of natural sciences(26):

More information

ECE357H1F ELECTROMAGNETIC FIELDS FINAL EXAM. 28 April Examiner: Prof. Sean V. Hum. Duration: hours

ECE357H1F ELECTROMAGNETIC FIELDS FINAL EXAM. 28 April Examiner: Prof. Sean V. Hum. Duration: hours UNIVERSITY OF TORONTO FACULTY OF APPLIED SCIENCE AND ENGINEERING The Edward S. Rogers Sr. Department of Electrical and Computer Engineering ECE357H1F ELECTROMAGNETIC FIELDS FINAL EXAM 28 April 15 Examiner:

More information

THE HEAVISIDE OPERATIONAL CALCULUS* BY H. W. MARCH

THE HEAVISIDE OPERATIONAL CALCULUS* BY H. W. MARCH 1927.I HEAVISIDE OPERATIONAL CALCULUS 311 Again, generally fit^f. Under what condition will /i /'? From (2) and (3) we see that the dual of a function is the same as the negative of the function if each

More information

Some Thoughts on A High Power, Radiation Cooled, Rotating Toroidal Target for Neutrino Production

Some Thoughts on A High Power, Radiation Cooled, Rotating Toroidal Target for Neutrino Production Some Thoughts on A High Power, Radiation Cooled, Rotating Toroidal Target for Neutrino Production J.R.J. Bennett Rutherford Appleton Laboratory, Didcot, UK 1 Introduction This note considers the power

More information

Physics 504, Lecture 9 Feb. 21, 2011

Physics 504, Lecture 9 Feb. 21, 2011 Last Latexed: February 17, 011 at 15:8 1 1 Ionosphere, Redux Physics 504, Lecture 9 Feb. 1, 011 Let us return to the resonant cavity formed by the surface of the Earth a spherical shell of radius r = R

More information

Physics 2B Winter 2012 Final Exam Practice

Physics 2B Winter 2012 Final Exam Practice Physics 2B Winter 2012 Final Exam Practice 1) When the distance between two charges is increased, the force between the charges A) increases directly with the square of the distance. B) increases directly

More information

For any use or distribution of this textbook, please cite as follows:

For any use or distribution of this textbook, please cite as follows: MIT OpenCourseWare http://ocw.mit.edu Electromechanical Dynamics For any use or distribution of this textbook, please cite as follows: Woodson, Herbert H., and James R. Melcher. Electromechanical Dynamics.

More information

Radial heat flow in two coaxial cylindrical discs

Radial heat flow in two coaxial cylindrical discs Radial heat flow in two coaxial cylindrical discs Daalder, J.E. Published: 0/0/977 Document Version Publisher s PDF, also known as Version of Record (includes final page, issue and volume numbers) Please

More information

J10M.1 - Rod on a Rail (M93M.2)

J10M.1 - Rod on a Rail (M93M.2) Part I - Mechanics J10M.1 - Rod on a Rail (M93M.2) J10M.1 - Rod on a Rail (M93M.2) s α l θ g z x A uniform rod of length l and mass m moves in the x-z plane. One end of the rod is suspended from a straight

More information

Chapter 4: Magnetic Field

Chapter 4: Magnetic Field Chapter 4: Magnetic Field 4.1 Magnetic Field 4.1.1 Define magnetic field Magnetic field is defined as the region around a magnet where a magnetic force can be experienced. Magnetic field has two poles,

More information