The condition for maximum intensity by the transmitted light in a plane parallel air film is. For an air film, μ = 1. (2-1)

Size: px
Start display at page:

Download "The condition for maximum intensity by the transmitted light in a plane parallel air film is. For an air film, μ = 1. (2-1)"

Transcription

1 hapte Two Faby--Peot ntefeomete A Faby-Peot intefeomete consists of two plane paallel glass plates A and B, sepaated by a distance d. The inne sufaces of these plates ae optically plane and thinly silveed so that they can eflect 70% of the incident light. The oute faces of these plates ae also paallel to each othe but inclined to thei espective inne sufaces to avoid intefeence effect due to multiple eflection and efaction. With this intefeomete, finges of constant inclination ae obtained by tansmitted light afte multiple eflections between the glass plates. [Fig. 1] Fig. 1 Light fom an extended souce S 1 of monochomatic souce is endeed paallel by the collimating lens L 1. Each of the paallel ays suffes multiple eflections in the ai film enclosed between the plates A and B and emeges fom the plate B. A ay oiginating fom the point souce S on S 1 afte suffeing intenal eflection issues fom B in the fom of a paallel beam which intefee and ae bought to focus at P by the lens L. The finges fomed in the focal plane of L ae cicula. The condition fo imum intensity by the tansmitted light in a plane paallel ai film is Fo an ai film, μ 1. μdcosφ nλ dcosφ nλ (-1) whee n 0, 1,, 3, etc. is the intege giving the ode of intefeence fo a paticula finge. This condition is satisfied fo all the points on a cicle though P with cente at O. The value of the path diffeence depends upon the angle φ, so that we have a seies of

2 - - hapte Two concentic cicles with O as the cente on the sceen o eyepiece. Finges of constant inclination ae called Haidinge Finges. n this intefeomete, the two plates ae invaiably kept paallel. One of the plates is fixed and the othe plate is moved with a ack and pinion aangement. f the distance between the two plates is deceased, the value of φ deceases fo a given λ and n. t means with a decease in d, the ings shink and disappea at the cente. Wheneve t is deceased by λ, one ing disappeas at the cente. Also, the ode of the ings deceases fom cente outwads. The ing patten of a Faby-Peot intefeomete is extemely shap in compaison to the ing patten obtained with a Michelson intefeomete. Hence, Faby-Peot intefeomete is vey useful fo esolving vey small wavelength diffeences. ntensity of the tansmitted beam n a Faby-Peot intefeomete, the shapness of the finges depends on the eflection coefficient of the silveed sufaces. Let the Faby-Peot plates be sepaated by t. 6 Suppose the tansmitted amplitudes ae,,,,... etc. is the eflection X A B Fig. coefficient and is the poduct of the oiginal amplitude and the tansmission coefficient at the two plates [Fig. ]. The tansmitted beams have a constant phase diffeence whee Y π λ ( t cos φ) Applying the law of polygon of vectos, the intensity is popotional to the squae of the esultant amplitude. 6 p.d φ φ...jj...raoo { t cosφ t (Path diffeence p.d) t cosφ. p.d t cosφ. On the othe side, p.d t cosφ. Total p.d

3 Faby-Peot ntefeomete ( + cos + cos +...) + ( ) 1 3 X component 1 3 Y component [ ] O, ( cos + cos +...) + ( ) (-) Mathematically, i i 6 i e + e + e +... i e whee i 1. i Multiply the numeato and the denominato of the ight hand side by 1 e. e i + e i + e 6 i e i i i ( e + e ) + (-3) Also, e ± i cos ± i. Substituting its value in Eq. (-3), ( cos + i ) + ( cos + i ) Sepaating the eal and imaginay tems, +... ( cos i ) [ ] cos + i + cos i cos + i ( 1 cos + cos +...) + i( ) + (-) cos + Equating the eal and imaginay tems, and cos ( 1 cos + cos +...) + + (-5) cos + ( ) (-6) cos + As < 1, < 1. Substituting the values fom (-5) and (- 6) in (-), ( cos ) ( cos + ) ( ) ( ) cos JJ...Raoo

4 - - ( ) ( ) O, ( ) cos + cos + hapte Two i.e. cos + cos + ( ) cos + i.e. cos + ( ) cos + O, cos + i.e. ( ) + O, k ( ) + (-7) Special ases (i) When 0, π, π,..., 0, π, π,... and 0. n this case, the denominato in Eq. (-7) will have a minimum value. Hence, the intensity of the finges will be a imum. O, (-8) k ( ) ( ) π 3π 5π (ii) When π, 3π, 5π,...,,,,... and 1. n this case, the denominato in Eq. (-7) has a imum value. Hence, intensity of the finge will be a minimum....jj...raoo min ( ) +

5 Faby-Peot ntefeomete O, min ( ) (-9) O, min k ( ) Visibility of finges The visibility of finges is Substituting the values of and min, V V min (-10) k + min ( ) ( ) k + k k ( ) ( ) ( ) ( ) i.e. V ( ) + ( ) O, V (-11) Eq. (-11) shows that the visibility of the finges is a function of the eflection coefficient only. The visibility of the finges inceases with incease in the value of. Shapness of the finges The esultant intensity at the point of inteface in the focal plane is k ( ) ( ) + (-7) and the imum intensity is...jj...raoo k ( ) (-8) Following Faby, the intensity distibution within the finges may be witten as follows:

6 - 6 - k ( ) ( ) ( ) [ ] hapte Two o, F (-1) ( ) whee F is the coefficient of finesse. ( ) Half-width A measue of shapness of finges, i.e. how apidly the intensity diminishes on eithe side of the imum, is the finge half width. The finge half width is the total width of a finge at points whee the intensity falls to half the intensity imum. Fo a given value of, if a gaph is plotted between and, the half-width is quite small [Fig. 3]. ntensity of the peak at half width is. Fom Eq. (-7) and (-8), ( ) Half Width Fig.3 k k + ( ) ( ) o, ( ) + o, (-13) ( )...JJ...Raoo

7 Faby-Peot ntefeomete At half-width, and ( ) 1 O, { phase diffeence (-1) Fom Eq. (-1), when 1, 0. That is, the visibility is imum. at half-width deceases with incease in the value of. Accoding to Eq. (-1), 1 F Fo values of geate than ½, 1 F is so small that the appoximation adian can be made without any seious eo. Then, F. But, the phase diffeence between two successive ima is π. The total half width, measued in ode numbes is, theefoe, W (-15) π π F π The half width and theefoe, the shapness of the intefeence finges depends upon the coefficient of finesse F. Fo Michelson intefeomete, the intensity of the finges is given by cos At half-width,....jj...raoo

8 - 8 - hapte Two cos 1 1 π 1.57 adian. Fo a Faby-Peot intefeomete with 0. 9 at half-width, 0.11adian [fom Eq. (-7)]. This shows that the finges obtained with a Faby-Peot intefeomete ae compaatively much shape than those obtained with a Michelson intefeomete. Resolving powe of a Faby Peot intefeomete Altenative fom of Rayleigh s citeion of esolution Rayleigh s citeion can be expessed in an altenative fom, if the spectal lines have equal intensities (i.e. thee ae no seconday ima and minima), which will be applicable to the esolution of Faby Peot finges. The intensity distibution in the finges of gating specta is given by α Nβ R o (-16) α β whee N is the numbe of lines on the gating suface and R o is the esultant amplitude, α is the phase diffeence between the exteme ays fom the fist slit and β is the phase A B 1 λ D λ+δλ n n n + 1N Fig. : Gating finges at the limit of esolution diffeence between the exteme ays fom the second slit. The fist facto R ( α α ) o gives the intensity distibution in the diffaction by a gle slit. The second facto Nβ β gives the intefeence patten fo N slits. Neglecting the diffaction tem in equation (-16), the intensity distibution in the finges of gating specta is given by Nβ β (-17) Pincipal imum occu when β ± n π whee n is an intege and N. The fist minimum on eithe side of the pincipal imum occus when N β nnπ ± π....jj...raoo

9 Faby-Peot ntefeomete As shown in Fig, the point, the intesection of intensity cuves of two spectal lines when just esolved, is midway between thei centes. Hence at (half width), 1 N β nnπ ± π o, β nπ ± π N (-18) The intensity at,, fo each line is given by ( nnπ ± π ) 1 N ( nπ ± π N) ( ± π N) π π 0.05 (-19) Hence, ( ) and 0.81 (-0) D Thus, Rayleigh s citeion of esolution implies that the two spectal lines of equal intensity may be said to be just esolved if midway between thei ima the esultant intensity due to ovelap is 0.81 of the imum in the combined intensity patten, i.e (o 8π ) of the height of the two peaks in the esultant intensity patten. Resolving powe of Faby Peot intefeomete: Definition At any point in the patten due to ai spaced Faby Peot instument, the ode of intefeence is expessed as n λ e cos θ (-1) whee n is not necessaily an intege. Fo small angles of incidence, equation (-1) becomes n λ e (-) The change in the ode coesponding to the change in the wavelength is obtained by diffeentiating equation (-). n Δλ + λ Δn 0 Hence, λ n R.P (-3) Δλ Δn ntepetation of equation (-3) n measuing the shift of one spectal line λ Δλ in tems of the ode numbe n of the othe line λ, thee should be a shift of at least Δ n n R. P to obtain the limit of esolution. The negative sign indicates that a positive incease in λ coesponds to a negative change (decease) in n....jj...raoo

10 An expession fo esolving powe λ λ+δλ At half width hapte Two 0 Suppose, that two wavelengths λ and λ + Δλ ae emitted by a souce with equal intensities. The bight finges of each wavelength will be fomed alongside one anothe as shown in Fig 5. Accoding to Aiy s fomula, the intensity is given by (-1) ( ) whee is the phase diffeence between the tansmitted (emegent) beams. Fo just esolution, Fig (this occus at half width. Ode fo λ ). Theefoe, 0.05 ( ) o, ( ) 0.05( ) i.e ( ) i.e. 1 1 ( 0.05)( ) JJ...Raoo

11 Faby-Peot ntefeomete ( ) o, ( ) ( ) (-) hange in ode by 1 coesponds to a phase change of π. hange in ode by Δn coesponds to a phase change of π ( Δn). Now, accoding to Taylo s citeion, thee is a just detectable dop in intensity between two finges so that they can be esolved, if the sepaate intensity cuves intesect at, i.e. if the sepaation of the ima is equal to the half value width. Theefoe, phase change between two ima. Fom equations (-) and (-5), ( Δn) π π Δn (-5) o, ( ) Δn π π ( ) (-6) n view of equation (-6), equation (-3) becomes λ Δλ Δn n 1 πn [ ( ) ] o, λ Δλ πn [ ( )]...JJ...Raoo πn.595n R.P (-7) ( ) ( ) Theefoe, in a Faby Peot intefeomete, the esolving powe inceases with an incease in the eflecting powe.

12 - 1 - Application of Faby-Peot ntefeomete hapte Two To detemine the diffeence between two closely spaced wavelengths f a souce of light consisting of two wavelengths λ 1 and λ which diffe slightly is used, then two sets of finges coesponding to the two wavelengths λ 1 and λ ae poduced. These finges on supeimposition give ise to positions of imum and minimum intensity. A position of imum intensity is poduced when a bight finge of one wavelength coincides with the bight finge of the othe wavelength (consonance). A position of minimum intensity is poduced when the bight finge of one wavelength coincides with the dak finge of the othe wavelength (dissonance). The distance between the two plates is adjusted so that a imum intensity position is obtained. The eading of the micomete scew is noted. The movable plate is futhe moved till again a imum position is obtained. The eading of the micomete scew is again noted. Let λ 1 > λ. f l is the distance though which the plate has been moved, then ( n + ) l nλ λ 1 1 l l o, 1 λ λ λ1λ i.e. λ 1 λ l Taking λ as the mean wavelength, the diffeence in wavelengths λ is Questions 1 λ λ (-8) l 1. Discuss the constuction and woking of a Faby-Peot intefeomete.. Descibe the fomation of finges by Faby-Peot intefeomete and discuss the intensity distibution. 3. Define visibility V of finges. alculate the same fo finges obtained by Faby-Peot intefeomete.. Show that the finges obtained with a Faby-Peot intefeomete ae compaatively much shape than those obtained with a Michelson intefeomete. 5. Deive an expession fo the esolving powe of a Faby-Peot intefeomete. 6. State the altenative fom of Rayleigh s citeion of esolution....jj...raoo

13 Faby-Peot ntefeomete Explain the use of Faby-Peot intefeomete to detemine the diffeence between two closely spaced wavelengths. Poblems 1. White light is incident nomally on a Faby Peot intefeomete with a plate sepaation of x 10-6 m. alculate the wavelengths fo which thee ae intefeence ima tansmitted beam in the ange of 000 to 5000 Å?. White light is incident nomally on a Faby Peot intefeomete with a plate sepaation of x 10 - cm. alculate the wavelengths fo which thee ae intefeence ima in the tansmitted beam in the ange 000 to 500 Å. 3. n a spectomete, one half of the slit is illuminated with mecuy light and the second half is illuminated with white light though a Faby Peot intefeomete. n the wavelength ange of 000 to 5000Å, 0 finges ae obseved in the continuous spectum. alculate the plate sepaation of the Faby Peot intefeomete.. Fo a Faby-Peot intefeomete, the eflection coefficient is 0.9 and What is the esolving powe of the instument at λ 500 Å? What is the minimum sepaation in wavelength that can be seen with the instument? Sepaation of the plates is 3 mm. 5. Fo a Faby-Peot intefeomete, find the half width of the finges, given the coefficient of eflection Two Faby-Peot intefeometes have equal plate sepaation and thei coefficients of eflection ae 0.8 and 0.9. Find the atio of half-width of ima in the two cases....jj...raoo

The geometric construction of Ewald sphere and Bragg condition:

The geometric construction of Ewald sphere and Bragg condition: The geometic constuction of Ewald sphee and Bagg condition: The constuction of Ewald sphee must be done such that the Bagg condition is satisfied. This can be done as follows: i) Daw a wave vecto k in

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

Class XII - Physics Wave Optics Chapter-wise Problems. Chapter 10

Class XII - Physics Wave Optics Chapter-wise Problems. Chapter 10 Class XII - Physics Wave Optics Chapte-wise Poblems Answes Chapte (c) (a) 3 (a) 4 (c) 5 (d) 6 (a), (b), (d) 7 (b), (d) 8 (a), (b) 9 (a), (b) Yes Spheical Spheical with huge adius as compaed to the eath

More information

Lecture 04: HFK Propagation Physical Optics II (Optical Sciences 330) (Updated: Friday, April 29, 2005, 8:05 PM) W.J. Dallas

Lecture 04: HFK Propagation Physical Optics II (Optical Sciences 330) (Updated: Friday, April 29, 2005, 8:05 PM) W.J. Dallas C:\Dallas\0_Couses\0_OpSci_330\0 Lectue Notes\04 HfkPopagation.doc: Page of 9 Lectue 04: HFK Popagation Physical Optics II (Optical Sciences 330) (Updated: Fiday, Apil 9, 005, 8:05 PM) W.J. Dallas The

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

Electrostatics (Electric Charges and Field) #2 2010

Electrostatics (Electric Charges and Field) #2 2010 Electic Field: The concept of electic field explains the action at a distance foce between two chaged paticles. Evey chage poduces a field aound it so that any othe chaged paticle expeiences a foce when

More information

Black Body Radiation and Radiometric Parameters:

Black Body Radiation and Radiometric Parameters: Black Body Radiation and Radiometic Paametes: All mateials absob and emit adiation to some extent. A blackbody is an idealization of how mateials emit and absob adiation. It can be used as a efeence fo

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

Solution Set #3

Solution Set #3 05-733-009 Solution Set #3. Assume that the esolution limit of the eye is acminute. At what distance can the eye see a black cicle of diamete 6" on a white backgound? One acminute is, so conside a tiangle

More information

SAMPLE PAPER I. Time Allowed : 3 hours Maximum Marks : 70

SAMPLE PAPER I. Time Allowed : 3 hours Maximum Marks : 70 SAMPL PAPR I Time Allowed : 3 hous Maximum Maks : 70 Note : Attempt All questions. Maks allotted to each question ae indicated against it. 1. The magnetic field lines fom closed cuves. Why? 1 2. What is

More information

Chapter 16. Fraunhofer Diffraction

Chapter 16. Fraunhofer Diffraction Chapte 6. Faunhofe Diffaction Faunhofe Appoimation Faunhofe Appoimation ( ) ( ) ( ) ( ) ( ) λ d d jk U j U ep,, Hugens-Fesnel Pinciple Faunhofe Appoimation : ( ) ( ) ( ) λ π λ d d j U j e e U k j jk ep,,

More information

This brief note explains why the Michel-Levy colour chart for birefringence looks like this...

This brief note explains why the Michel-Levy colour chart for birefringence looks like this... This bief note explains why the Michel-Levy colou chat fo biefingence looks like this... Theoy of Levy Colou Chat fo Biefingent Mateials Between Cossed Polas Biefingence = n n, the diffeence of the efactive

More information

Mathematisch-Naturwissenschaftliche Fakultät I Humboldt-Universität zu Berlin Institut für Physik Physikalisches Grundpraktikum.

Mathematisch-Naturwissenschaftliche Fakultät I Humboldt-Universität zu Berlin Institut für Physik Physikalisches Grundpraktikum. Mathematisch-Natuwissenschaftliche Fakultät I Humboldt-Univesität zu Belin Institut fü Physik Physikalisches Gundpaktikum Vesuchspotokoll Polaisation duch Reflexion (O11) duchgefüht am 10.11.2009 mit Vesuchspatne

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

1) Emits radiation at the maximum intensity possible for every wavelength. 2) Completely absorbs all incident radiation (hence the term black ).

1) Emits radiation at the maximum intensity possible for every wavelength. 2) Completely absorbs all incident radiation (hence the term black ). Radiation laws Blackbody adiation Planck s Law Any substance (solid, liquid o gas) emits adiation accoding to its absolute tempeatue, measued in units of Kelvin (K = o C + 73.5). The efficiency at which

More information

Physics 2212 GH Quiz #2 Solutions Spring 2016

Physics 2212 GH Quiz #2 Solutions Spring 2016 Physics 2212 GH Quiz #2 Solutions Sping 216 I. 17 points) Thee point chages, each caying a chage Q = +6. nc, ae placed on an equilateal tiangle of side length = 3. mm. An additional point chage, caying

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

Introduction to Arrays

Introduction to Arrays Intoduction to Aays Page 1 Intoduction to Aays The antennas we have studied so fa have vey low diectivity / gain. While this is good fo boadcast applications (whee we want unifom coveage), thee ae cases

More information

Σk=1. g r 3/2 z. 2 3-z. g 3 ( 3/2 ) g r 2. = 1 r = 0. () z = ( a ) + Σ. c n () a = ( a) 3-z -a. 3-z. z - + Σ. z 3, 5, 7, z ! = !

Σk=1. g r 3/2 z. 2 3-z. g 3 ( 3/2 ) g r 2. = 1 r = 0. () z = ( a ) + Σ. c n () a = ( a) 3-z -a. 3-z. z - + Σ. z 3, 5, 7, z ! = ! 09 Maclauin Seies of Completed Riemann Zeta 9. Maclauin Seies of Lemma 9.. ( Maclauin seies of gamma function ) When is the gamma function, n is the polygamma function and B n,kf, f, ae Bell polynomials,

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

SEE LAST PAGE FOR SOME POTENTIALLY USEFUL FORMULAE AND CONSTANTS

SEE LAST PAGE FOR SOME POTENTIALLY USEFUL FORMULAE AND CONSTANTS Cicle instucto: Moow o Yethiaj Name: MEMORIL UNIVERSITY OF NEWFOUNDLND DEPRTMENT OF PHYSICS ND PHYSICL OCENOGRPHY Final Eam Phsics 5 Winte 3:-5: pil, INSTRUCTIONS:. Do all SIX (6) questions in section

More information

OSCILLATIONS AND GRAVITATION

OSCILLATIONS AND GRAVITATION 1. SIMPLE HARMONIC MOTION Simple hamonic motion is any motion that is equivalent to a single component of unifom cicula motion. In this situation the velocity is always geatest in the middle of the motion,

More information

Homework 7 Solutions

Homework 7 Solutions Homewok 7 olutions Phys 4 Octobe 3, 208. Let s talk about a space monkey. As the space monkey is oiginally obiting in a cicula obit and is massive, its tajectoy satisfies m mon 2 G m mon + L 2 2m mon 2

More information

TheWaveandHelmholtzEquations

TheWaveandHelmholtzEquations TheWaveandHelmholtzEquations Ramani Duaiswami The Univesity of Mayland, College Pak Febuay 3, 2006 Abstact CMSC828D notes (adapted fom mateial witten with Nail Gumeov). Wok in pogess 1 Acoustic Waves 1.1

More information

Supplementary Figure 1. Circular parallel lamellae grain size as a function of annealing time at 250 C. Error bars represent the 2σ uncertainty in

Supplementary Figure 1. Circular parallel lamellae grain size as a function of annealing time at 250 C. Error bars represent the 2σ uncertainty in Supplementay Figue 1. Cicula paallel lamellae gain size as a function of annealing time at 50 C. Eo bas epesent the σ uncetainty in the measued adii based on image pixilation and analysis uncetainty contibutions

More information

Between any two masses, there exists a mutual attractive force.

Between any two masses, there exists a mutual attractive force. YEAR 12 PHYSICS: GRAVITATION PAST EXAM QUESTIONS Name: QUESTION 1 (1995 EXAM) (a) State Newton s Univesal Law of Gavitation in wods Between any two masses, thee exists a mutual attactive foce. This foce

More information

MASSACHUSETTS INSTITUTE OF TECHNOLOGY Physics Department. Problem Set 10 Solutions. r s

MASSACHUSETTS INSTITUTE OF TECHNOLOGY Physics Department. Problem Set 10 Solutions. r s MASSACHUSETTS INSTITUTE OF TECHNOLOGY Physics Depatment Physics 8.033 Decembe 5, 003 Poblem Set 10 Solutions Poblem 1 M s y x test paticle The figue above depicts the geomety of the poblem. The position

More information

Experiment I Voltage Variation and Control

Experiment I Voltage Variation and Control ELE303 Electicity Netwoks Expeiment I oltage aiation and ontol Objective To demonstate that the voltage diffeence between the sending end of a tansmission line and the load o eceiving end depends mainly

More information

Velocimetry Techniques and Instrumentation

Velocimetry Techniques and Instrumentation AeE 344 Lectue Notes Lectue # 05: elocimety Techniques and Instumentation D. Hui Hu Depatment of Aeospace Engineeing Iowa State Univesity Ames, Iowa 500, U.S.A Methods to Measue Local Flow elocity - Mechanical

More information

Light Time Delay and Apparent Position

Light Time Delay and Apparent Position Light Time Delay and ppaent Position nalytical Gaphics, Inc. www.agi.com info@agi.com 610.981.8000 800.220.4785 Contents Intoduction... 3 Computing Light Time Delay... 3 Tansmission fom to... 4 Reception

More information

Absorption Rate into a Small Sphere for a Diffusing Particle Confined in a Large Sphere

Absorption Rate into a Small Sphere for a Diffusing Particle Confined in a Large Sphere Applied Mathematics, 06, 7, 709-70 Published Online Apil 06 in SciRes. http://www.scip.og/jounal/am http://dx.doi.og/0.46/am.06.77065 Absoption Rate into a Small Sphee fo a Diffusing Paticle Confined in

More information

Inverse Square Law and Polarization

Inverse Square Law and Polarization Invese Squae Law and Polaization Objectives: To show that light intensity is invesely popotional to the squae of the distance fom a point light souce and to show that the intensity of the light tansmitted

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

Our Universe: GRAVITATION

Our Universe: GRAVITATION Ou Univese: GRAVITATION Fom Ancient times many scientists had shown geat inteest towads the sky. Most of the scientist studied the motion of celestial bodies. One of the most influential geek astonomes

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

Chapter 7-8 Rotational Motion

Chapter 7-8 Rotational Motion Chapte 7-8 Rotational Motion What is a Rigid Body? Rotational Kinematics Angula Velocity ω and Acceleation α Unifom Rotational Motion: Kinematics Unifom Cicula Motion: Kinematics and Dynamics The Toque,

More information

Single Particle State AB AB

Single Particle State AB AB LECTURE 3 Maxwell Boltzmann, Femi, and Bose Statistics Suppose we have a gas of N identical point paticles in a box of volume V. When we say gas, we mean that the paticles ae not inteacting with one anothe.

More information

Chapter 1. Introduction. 1.1 The scanning optical microscope

Chapter 1. Introduction. 1.1 The scanning optical microscope Chapte 1 This thesis descibes the fomulation of a mathematical model descibing the signal geneation pocess in both the eflectance and magneto-optic, Type 1 and Type 2, scanning optical micoscopes. The

More information

Galilean Transformation vs E&M y. Historical Perspective. Chapter 2 Lecture 2 PHYS Special Relativity. Sep. 1, y K K O.

Galilean Transformation vs E&M y. Historical Perspective. Chapter 2 Lecture 2 PHYS Special Relativity. Sep. 1, y K K O. PHYS-2402 Chapte 2 Lectue 2 Special Relativity 1. Basic Ideas Sep. 1, 2016 Galilean Tansfomation vs E&M y K O z z y K In 1873, Maxwell fomulated Equations of Electomagnetism. v Maxwell s equations descibe

More information

Auchmuty High School Mathematics Department Advanced Higher Notes Teacher Version

Auchmuty High School Mathematics Department Advanced Higher Notes Teacher Version The Binomial Theoem Factoials Auchmuty High School Mathematics Depatment The calculations,, 6 etc. often appea in mathematics. They ae called factoials and have been given the notation n!. e.g. 6! 6!!!!!

More information

V 16: X-ray Diffraction

V 16: X-ray Diffraction Matin-Luthe-Univesity Halle-Wittenbeg Institute of Physics Advanced Pactical Lab Couse V 16: X-ay Diffaction 1) Recod the chaacteistic of an x-ay counte filled with agon and halogen as a function of the

More information

Phys101 Lectures 30, 31. Wave Motion

Phys101 Lectures 30, 31. Wave Motion Phys0 Lectues 30, 3 Wave Motion Key points: Types of Waves: Tansvese and Longitudinal Mathematical Repesentation of a Taveling Wave The Pinciple of Supeposition Standing Waves; Resonance Ref: -7,8,9,0,,6,,3,6.

More information

F g. = G mm. m 1. = 7.0 kg m 2. = 5.5 kg r = 0.60 m G = N m 2 kg 2 = = N

F g. = G mm. m 1. = 7.0 kg m 2. = 5.5 kg r = 0.60 m G = N m 2 kg 2 = = N Chapte answes Heinemann Physics 4e Section. Woked example: Ty youself.. GRAVITATIONAL ATTRACTION BETWEEN SMALL OBJECTS Two bowling balls ae sitting next to each othe on a shelf so that the centes of the

More information

Page 1 of 6 Physics II Exam 1 155 points Name Discussion day/time Pat I. Questions 110. 8 points each. Multiple choice: Fo full cedit, cicle only the coect answe. Fo half cedit, cicle the coect answe and

More information

2.5 The Quarter-Wave Transformer

2.5 The Quarter-Wave Transformer /3/5 _5 The Quate Wave Tansfome /.5 The Quate-Wave Tansfome Reading Assignment: pp. 73-76 By now you ve noticed that a quate-wave length of tansmission line ( λ 4, β π ) appeas often in micowave engineeing

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

Ch 30 - Sources of Magnetic Field! The Biot-Savart Law! = k m. r 2. Example 1! Example 2!

Ch 30 - Sources of Magnetic Field! The Biot-Savart Law! = k m. r 2. Example 1! Example 2! Ch 30 - Souces of Magnetic Field 1.) Example 1 Detemine the magnitude and diection of the magnetic field at the point O in the diagam. (Cuent flows fom top to bottom, adius of cuvatue.) Fo staight segments,

More information

AST 121S: The origin and evolution of the Universe. Introduction to Mathematical Handout 1

AST 121S: The origin and evolution of the Universe. Introduction to Mathematical Handout 1 Please ead this fist... AST S: The oigin and evolution of the Univese Intoduction to Mathematical Handout This is an unusually long hand-out and one which uses in places mathematics that you may not be

More information

Scattering in Three Dimensions

Scattering in Three Dimensions Scatteing in Thee Dimensions Scatteing expeiments ae an impotant souce of infomation about quantum systems, anging in enegy fom vey low enegy chemical eactions to the highest possible enegies at the LHC.

More information

Markscheme May 2017 Calculus Higher level Paper 3

Markscheme May 2017 Calculus Higher level Paper 3 M7/5/MATHL/HP3/ENG/TZ0/SE/M Makscheme May 07 Calculus Highe level Pape 3 pages M7/5/MATHL/HP3/ENG/TZ0/SE/M This makscheme is the popety of the Intenational Baccalaueate and must not be epoduced o distibuted

More information

ASTR415: Problem Set #6

ASTR415: Problem Set #6 ASTR45: Poblem Set #6 Cuan D. Muhlbege Univesity of Mayland (Dated: May 7, 27) Using existing implementations of the leapfog and Runge-Kutta methods fo solving coupled odinay diffeential equations, seveal

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

3.6 Applied Optimization

3.6 Applied Optimization .6 Applied Optimization Section.6 Notes Page In this section we will be looking at wod poblems whee it asks us to maimize o minimize something. Fo all the poblems in this section you will be taking the

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

Analysis of simple branching trees with TI-92

Analysis of simple branching trees with TI-92 Analysis of simple banching tees with TI-9 Dušan Pagon, Univesity of Maibo, Slovenia Abstact. In the complex plane we stat at the cente of the coodinate system with a vetical segment of the length one

More information

Euclidean Figures and Solids without Incircles or Inspheres

Euclidean Figures and Solids without Incircles or Inspheres Foum Geometicoum Volume 16 (2016) 291 298. FOUM GEOM ISSN 1534-1178 Euclidean Figues and Solids without Incicles o Insphees Dimitis M. Chistodoulou bstact. ll classical convex plana Euclidean figues that

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

To Feel a Force Chapter 7 Static equilibrium - torque and friction

To Feel a Force Chapter 7 Static equilibrium - torque and friction To eel a oce Chapte 7 Chapte 7: Static fiction, toque and static equilibium A. Review of foce vectos Between the eath and a small mass, gavitational foces of equal magnitude and opposite diection act on

More information

Phys 774: Ellipsometry

Phys 774: Ellipsometry Dielectic function Phys 774: Ellipsomety Optical vibations (phonons) Fee electons (plasma) Electonic tansitions (valence conduction band) Dielectic function and efactive index ae geneally complex: ε ε

More information

763620SS STATISTICAL PHYSICS Solutions 2 Autumn 2012

763620SS STATISTICAL PHYSICS Solutions 2 Autumn 2012 763620SS STATISTICAL PHYSICS Solutions 2 Autumn 2012 1. Continuous Random Walk Conside a continuous one-dimensional andom walk. Let w(s i ds i be the pobability that the length of the i th displacement

More information

Surveillance Points in High Dimensional Spaces

Surveillance Points in High Dimensional Spaces Société de Calcul Mathématique SA Tools fo decision help since 995 Suveillance Points in High Dimensional Spaces by Benad Beauzamy Januay 06 Abstact Let us conside any compute softwae, elying upon a lage

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

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

Lecture 8 - Gauss s Law

Lecture 8 - Gauss s Law Lectue 8 - Gauss s Law A Puzzle... Example Calculate the potential enegy, pe ion, fo an infinite 1D ionic cystal with sepaation a; that is, a ow of equally spaced chages of magnitude e and altenating sign.

More information

Stanford University CS259Q: Quantum Computing Handout 8 Luca Trevisan October 18, 2012

Stanford University CS259Q: Quantum Computing Handout 8 Luca Trevisan October 18, 2012 Stanfod Univesity CS59Q: Quantum Computing Handout 8 Luca Tevisan Octobe 8, 0 Lectue 8 In which we use the quantum Fouie tansfom to solve the peiod-finding poblem. The Peiod Finding Poblem Let f : {0,...,

More information

Outline. Basics of interference Types of interferometers. Finite impulse response Infinite impulse response Conservation of energy in beam splitters

Outline. Basics of interference Types of interferometers. Finite impulse response Infinite impulse response Conservation of energy in beam splitters ntefeometes lectue C 566 Adv. Optics Lab Outline Basics of intefeence Tpes of intefeometes Amplitude division Finite impulse esponse nfinite impulse esponse Consevation of eneg in beam splittes Wavefont

More information

21 MAGNETIC FORCES AND MAGNETIC FIELDS

21 MAGNETIC FORCES AND MAGNETIC FIELDS CHAPTER 1 MAGNETIC ORCES AND MAGNETIC IELDS ANSWERS TO OCUS ON CONCEPTS QUESTIONS 1. (d) Right-Hand Rule No. 1 gives the diection of the magnetic foce as x fo both dawings A and. In dawing C, the velocity

More information

1. THINK Ampere is the SI unit for current. An ampere is one coulomb per second.

1. THINK Ampere is the SI unit for current. An ampere is one coulomb per second. Chapte 4 THINK Ampee is the SI unit fo cuent An ampee is one coulomb pe second EXPRESS To calculate the total chage though the cicuit, we note that A C/s and h 6 s ANALYZE (a) Thus, F I HG K J F H G I

More information

Centripetal Force OBJECTIVE INTRODUCTION APPARATUS THEORY

Centripetal Force OBJECTIVE INTRODUCTION APPARATUS THEORY Centipetal Foce OBJECTIVE To veify that a mass moving in cicula motion expeiences a foce diected towad the cente of its cicula path. To detemine how the mass, velocity, and adius affect a paticle's centipetal

More information

2 x 8 2 x 2 SKILLS Determine whether the given value is a solution of the. equation. (a) x 2 (b) x 4. (a) x 2 (b) x 4 (a) x 4 (b) x 8

2 x 8 2 x 2 SKILLS Determine whether the given value is a solution of the. equation. (a) x 2 (b) x 4. (a) x 2 (b) x 4 (a) x 4 (b) x 8 5 CHAPTER Fundamentals When solving equations that involve absolute values, we usually take cases. EXAMPLE An Absolute Value Equation Solve the equation 0 x 5 0 3. SOLUTION By the definition of absolute

More information

F-IF Logistic Growth Model, Abstract Version

F-IF Logistic Growth Model, Abstract Version F-IF Logistic Gowth Model, Abstact Vesion Alignments to Content Standads: F-IFB4 Task An impotant example of a model often used in biology o ecology to model population gowth is called the logistic gowth

More information

3.1 Random variables

3.1 Random variables 3 Chapte III Random Vaiables 3 Random vaiables A sample space S may be difficult to descibe if the elements of S ae not numbes discuss how we can use a ule by which an element s of S may be associated

More information

1 Spherical multipole moments

1 Spherical multipole moments Jackson notes 9 Spheical multipole moments Suppose we have a chage distibution ρ (x) wheeallofthechageiscontained within a spheical egion of adius R, as shown in the diagam. Then thee is no chage 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

PROBLEM SET #1 SOLUTIONS by Robert A. DiStasio Jr.

PROBLEM SET #1 SOLUTIONS by Robert A. DiStasio Jr. POBLM S # SOLUIONS by obet A. DiStasio J. Q. he Bon-Oppenheime appoximation is the standad way of appoximating the gound state of a molecula system. Wite down the conditions that detemine the tonic and

More information

Chapter 2: Introduction to Implicit Equations

Chapter 2: Introduction to Implicit Equations Habeman MTH 11 Section V: Paametic and Implicit Equations Chapte : Intoduction to Implicit Equations When we descibe cuves on the coodinate plane with algebaic equations, we can define the elationship

More information

Prepared by: M. S. KumarSwamy, TGT(Maths) Page - 1 -

Prepared by: M. S. KumarSwamy, TGT(Maths) Page - 1 - Pepaed by: M. S. KumaSwamy, TGT(Maths) Page - - ELECTROSTATICS MARKS WEIGHTAGE 8 maks QUICK REVISION (Impotant Concepts & Fomulas) Chage Quantization: Chage is always in the fom of an integal multiple

More information

! E da = 4πkQ enc, has E under the integral sign, so it is not ordinarily an

! E da = 4πkQ enc, has E under the integral sign, so it is not ordinarily an Physics 142 Electostatics 2 Page 1 Electostatics 2 Electicity is just oganized lightning. Geoge Calin A tick that sometimes woks: calculating E fom Gauss s law Gauss s law,! E da = 4πkQ enc, has E unde

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

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

ELECTROSTATICS::BHSEC MCQ 1. A. B. C. D.

ELECTROSTATICS::BHSEC MCQ 1. A. B. C. D. ELETROSTATIS::BHSE 9-4 MQ. A moving electic chage poduces A. electic field only. B. magnetic field only.. both electic field and magnetic field. D. neithe of these two fields.. both electic field and magnetic

More information

working pages for Paul Richards class notes; do not copy or circulate without permission from PGR 2004/11/3 10:50

working pages for Paul Richards class notes; do not copy or circulate without permission from PGR 2004/11/3 10:50 woking pages fo Paul Richads class notes; do not copy o ciculate without pemission fom PGR 2004/11/3 10:50 CHAPTER7 Solid angle, 3D integals, Gauss s Theoem, and a Delta Function We define the solid angle,

More information

Magnetic Field. Conference 6. Physics 102 General Physics II

Magnetic Field. Conference 6. Physics 102 General Physics II Physics 102 Confeence 6 Magnetic Field Confeence 6 Physics 102 Geneal Physics II Monday, Mach 3d, 2014 6.1 Quiz Poblem 6.1 Think about the magnetic field associated with an infinite, cuent caying wie.

More information

THE LAPLACE EQUATION. The Laplace (or potential) equation is the equation. u = 0. = 2 x 2. x y 2 in R 2

THE LAPLACE EQUATION. The Laplace (or potential) equation is the equation. u = 0. = 2 x 2. x y 2 in R 2 THE LAPLACE EQUATION The Laplace (o potential) equation is the equation whee is the Laplace opeato = 2 x 2 u = 0. in R = 2 x 2 + 2 y 2 in R 2 = 2 x 2 + 2 y 2 + 2 z 2 in R 3 The solutions u of the Laplace

More information

= e2. = 2e2. = 3e2. V = Ze2. where Z is the atomic numnber. Thus, we take as the Hamiltonian for a hydrogenic. H = p2 r. (19.4)

= e2. = 2e2. = 3e2. V = Ze2. where Z is the atomic numnber. Thus, we take as the Hamiltonian for a hydrogenic. H = p2 r. (19.4) Chapte 9 Hydogen Atom I What is H int? That depends on the physical system and the accuacy with which it is descibed. A natual stating point is the fom H int = p + V, (9.) µ which descibes a two-paticle

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

EXAM NMR (8N090) November , am

EXAM NMR (8N090) November , am EXA NR (8N9) Novembe 5 9, 9. 1. am Remaks: 1. The exam consists of 8 questions, each with 3 pats.. Each question yields the same amount of points. 3. You ae allowed to use the fomula sheet which has been

More information

Related Rates - the Basics

Related Rates - the Basics Related Rates - the Basics In this section we exploe the way we can use deivatives to find the velocity at which things ae changing ove time. Up to now we have been finding the deivative to compae the

More information

Tutorial Exercises: Central Forces

Tutorial Exercises: Central Forces Tutoial Execises: Cental Foces. Tuning Points fo the Keple potential (a) Wite down the two fist integals fo cental motion in the Keple potential V () = µm/ using J fo the angula momentum and E fo the total

More information

Basic Interference and. Classes of of Interferometers

Basic Interference and. Classes of of Interferometers Basic Intefeence and Classes of Intefeometes Basic Intefeence Two plane waves Two spheical waves Plane wave and and spheical wave Classes of of Intefeometes Division of of wavefont Division of of amplitude

More information

C/CS/Phys C191 Shor s order (period) finding algorithm and factoring 11/12/14 Fall 2014 Lecture 22

C/CS/Phys C191 Shor s order (period) finding algorithm and factoring 11/12/14 Fall 2014 Lecture 22 C/CS/Phys C9 Sho s ode (peiod) finding algoithm and factoing /2/4 Fall 204 Lectue 22 With a fast algoithm fo the uantum Fouie Tansfom in hand, it is clea that many useful applications should be possible.

More information

4.3 Area of a Sector. Area of a Sector Section

4.3 Area of a Sector. Area of a Sector Section ea of a Secto Section 4. 9 4. ea of a Secto In geomety you leaned that the aea of a cicle of adius is π 2. We will now lean how to find the aea of a secto of a cicle. secto is the egion bounded by a cental

More information

ac p Answers to questions for The New Introduction to Geographical Economics, 2 nd edition Chapter 3 The core model of geographical economics

ac p Answers to questions for The New Introduction to Geographical Economics, 2 nd edition Chapter 3 The core model of geographical economics Answes to questions fo The New ntoduction to Geogaphical Economics, nd edition Chapte 3 The coe model of geogaphical economics Question 3. Fom intoductoy mico-economics we know that the condition fo pofit

More information

Construction Figure 10.1: Jaw clutches

Construction Figure 10.1: Jaw clutches CHAPTER TEN FRICTION CLUTCHES The wod clutch is a geneic tem descibing any one wide vaiety of devices that is capable of causing a machine o mechanism to become engaged o disengaged. Clutches ae of thee

More information

, the tangent line is an approximation of the curve (and easier to deal with than the curve).

, the tangent line is an approximation of the curve (and easier to deal with than the curve). 114 Tangent Planes and Linea Appoimations Back in-dimensions, what was the equation of the tangent line of f ( ) at point (, ) f ( )? (, ) ( )( ) = f Linea Appoimation (Tangent Line Appoimation) of f at

More information

Determining solar characteristics using planetary data

Determining solar characteristics using planetary data Detemining sola chaacteistics using planetay data Intoduction The Sun is a G-type main sequence sta at the cente of the Sola System aound which the planets, including ou Eath, obit. In this investigation

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

AH Mechanics Checklist (Unit 2) AH Mechanics Checklist (Unit 2) Circular Motion

AH Mechanics Checklist (Unit 2) AH Mechanics Checklist (Unit 2) Circular Motion AH Mechanics Checklist (Unit ) AH Mechanics Checklist (Unit ) Cicula Motion No. kill Done 1 Know that cicula motion efes to motion in a cicle of constant adius Know that cicula motion is conveniently descibed

More information

QUALITATIVE AND QUANTITATIVE ANALYSIS OF MUSCLE POWER

QUALITATIVE AND QUANTITATIVE ANALYSIS OF MUSCLE POWER QUALITATIVE AND QUANTITATIVE ANALYSIS OF MUSCLE POWER Jey N. Baham Anand B. Shetty Mechanical Kinesiology Laboatoy Depatment of Kinesiology Univesity of Nothen Coloado Geeley, Coloado Muscle powe is one

More information

Gauss Law. Physics 231 Lecture 2-1

Gauss Law. Physics 231 Lecture 2-1 Gauss Law Physics 31 Lectue -1 lectic Field Lines The numbe of field lines, also known as lines of foce, ae elated to stength of the electic field Moe appopiately it is the numbe of field lines cossing

More information