Phys 232 Lab 8 Ch 21 Interactions with Magnetic Fields 1
|
|
- Gabriel Robbins
- 7 years ago
- Views:
Transcription
1 Phys 3 Lab 8 Ch 1 Interations with Magneti Fields 1 Equipment: omputer with VPython, single e/m apparatus for qualitative experimenting: Fore on dipole: blak power supply, TeahSpin Magneti Fore apparatus, high-watt 1 resistor, digital Multi-meter, BNC ables Objetives In this lab you will: Simulate the fairly-uniform field of Helmholtz oils Simulate the motion of harged partiles in a uniform field Qualitatively experiment with eletrons moving in the fairly-uniform field of Helmholtz oils Qualitatively experiment with dipoles interating with the field of Helmholtz oils Simulate the smoothly-varying field of anti-helmholtz oils Qualitatively and quantitatively experiment with dipoles interating with field of anti- Helmholtz oils. Interation with a Uniform Magneti Field I. Produing a Uniform Magneti Field Helmholtz Coils a. Theory Before experimenting with or simulating a harged partile moving in a uniform magneti field, we ll digress and see how suh a field is typially produed for suh experiments. As you re familiar, a solenoid produes a very uniform magneti field; reall the simulation and measurements you made in Lab 5. In pratie though, a omplete solenoid is seldom used for one thing, it s awkward peering inside to see what the harged partiles are doing. With the right geometry, you an still have a fairly uniform field even if you remove all the oils from the mid-setion of the solenoid, leaving idential sets of oils only at the two ends. This right geometry is having the distane between the end oils equal to the radius of the oils. Pass the same urrent through the two sets of oils and you have the Helmholtz onfiguration. I I B R The field strength at the enter point should be R I, (1) R o Bmiddle 5 3/ 4 This follows from the Magneti Field of a Loop in setion 18.8, multiplied by sine there are two, equidistant sets of oils, and with z = ½R. What would be the field strength if you had a 1 amp urrent and a radius of 0.3 m? Note: In pratie, eah of the two remaining urrent loops is itself usually a set of N losely paked oils of wire; so the urrent through one loop would be N times the urrent flowing through just one wire.
2 Phys 3 Lab 8 Ch 1 Interations with Magneti Fields b. Simulation So you an visualize the field produed by a set of Helmholtz oils, you ll modify your Solenoid simulation to produe a HelmholtzCoils simulation. Download the opy of the Solenoid.py simulation available through WebAssign. As usual, open a fresh instane of VPython, paste the ode into it, add your names in a omment line near the top, and save as Helmholtz.py. For the sake of omparing the fields of a solenoid and of Helmholtz oils, before modifying the program to simulate Helmholtz oils, add a few lines so the existing program plots the strength of the magneti field aross two axes: lengthwise along the solenoid s entral axis, and perpendiularly aross its middle. It s been the better part of a semester sine you ve done anything like this, but you used similar lines of ode in Phys 31 when plotting things like the momentum of an alpha partile sattering from a gold nuleus. To be able to make rudimentary graphs, at the beginning of the program add the line from visual.graph import* To prepare the program to make the graphs, in the objets setion of the ode, add the lines Bygraph = gurve(olor = olor.yan) Bxgraph = gurve(olor = olor.red) To add points to these urves, at the bottom of the for obslo in obsloations: loop (below but outside of the for y and for theta loops), add if obslo.x ==0: #plots y omponent of B for points along x=0 axis, along solenoid Bygraph.plot(pos = (obslo.y,b.y)) if obslo.y == 0: #plots y omponent of B for points along y = 0 axis Bxgraph.plot(pos = (obslo.x,b.y)) Run the program and observe the width (in x, red plot) and length (in y, yan plot) of the entral region in whih the field remains fairly onstant. Now modify the ode to make a Helmholtz Coil set up. Given the way the program has already been oded, this requires two very minor hanges: Set the solenoid s length equal to its radius, Redue the number of oils to just. Run the program and again note over how wide (in x, red plot) and how long (in y, yan plot) the field remains fairly onstant. Whih devie, the solenoid or the Helmholtz Coils, has proportionally large region of uniform field in its enter? Aording to the plot, what is the strength of the field in this region (you re really just looking at the y omponent, but the other two are negligible)? This should agree well with the value you d alulated using the theoretial relation. When you re satisfied with your program (always helps to hek with a neighboring group) save and upload a opy of it.
3 Phys 3 Lab 8 Ch 1 Interations with Magneti Fields 3 II. Charged Partile Moving in a Uniform Magneti Field a. Theory At its simplest, the magneti interation is the attration of parallel urrents and repulsion of anti-parallel urrents. As with the eletri interation, it s onvenient to use the field onept to divide the interation into two steps: 1) soure urrent (moving harges) produes field, ) field transmits fore to sensor urrent (moving harges). The fore transmitted by a magneti field to a moving harged partile is F qv B. () For simpliity and onreteness, we ll onsider a onstant and uniform magneti field pointing in what we ll all the y diretion and a harged partile initially moving in the x- z plane (so, with no omponent parallel to B.) It s a mathematial fat that the vetor that results from a ross produt ( F, in this ase) is perpendiular to the two vetors that are rossed ( v and B ). That leads us to three useful onlusions (that are baked up mathematially in Phys 33): a) Sine the fore must be perpendiular to B, no omponent of fore ats parallel to B and so the omponent of v that s parallel to B, that is, in the y diretion, remains onstant. If it s initially 0, it remains 0. b) Sine the fore is perpendiular to v, it annot speed or slow the partile, just hange its diretion. ) It follows that, sine the fore an t hange the magnitude of v and it an t hange the omponent of v parallel to B, it then an t hange the magnitude of the ross produt of v and B from a onstant F qvb. So the fore is of onstant magnitude and always perpendiular to B and to v, and the partile has onstant speed. This should sound familiar from Phys 31 as leading to uniform irular motion. Based on this reasoning, we know the rate of hange of momentum must have magnitude dp dt v m. R By the momentum priniple, this must equal the net fore, so v m qvb R v m qb R Two important preditions follow. First, for a given speed (whih must remain onstant) and onstant magneti field (and harge and mass), the radius of the partile s irular orbit is set at mv mv R. (3) qb qb
4 Phys 3 Lab 8 Ch 1 Interations with Magneti Fields 4 Seond, for uniform irular motion the speed is related to the angular frequeny of orbit by v R, so the frequeny with whih the partile orbits is qb qb, m m whih is virtually independent of v for v<< (where 1.) The orresponding period would be m T. (4) qb b. Qualitative Experiment At the bak of the lass room, an apparatus is set up for seeing eletrons pass through a fairly uniform magneti field. - + B R - e I I V In brief, a filament is heated and some eletrons get boiled off. A pair of apaitor plates surrounds the filament so these freed eletrons get aelerated by the field within the apaitor. By onsidering potential and kineti energies, the resulting speed of the eletrons relates to the apaitor s voltage through 1 1m mv ev, assuming v<< and that the initial veloity is negligible. In WebAssign, rephrase this expression to give the speed in terms of the voltage. v = (5) The eletrons pass through a small hole in one of the plates and now fly freely. All of this is within a glass bulb with a low density of gas when an eletron rashes into a gas atom, the atom exites and de-exites, and so radiates violet light whih illuminates the
5 Phys 3 Lab 8 Ch 1 Interations with Magneti Fields 5 eletrons trail. All of this is between Helmholtz Coils whih provide a fairly uniform magneti field (aording to Eq n 1) thanks to the urrent flowing through the oils. Pause and onsider: Looking at the illustration of the set-up, Use the right-hand rule for field prodution to first hek that the diretion of the field is appropriate given the indiated diretion of the urrent in the oils. Use the right-hand rule for the fore transmitted by a field to a moving harged partile (remember, the harge of the eletron is negative ) to hek that the diretion of the harge s defletion is appropriate when it s moving rightward at the bottom, upward at the right, leftward at the top, and downward at the left. For example: an out-of-the-page field would deflet a right-bound positive harge downward, and so deflets the negatively-harged eletron upward. Similarly, hek that the defletion of the eletrons at these four points is onsistent with the rule that like urrents attrat and opposite urrents repel. For example, when the negatively-harged eletron is moving right, the rightbound urrent at the bottom of the loop repels it and the left-bound urrent at the top attrats it. In WebAssign, ombine equations 1, 3, and 5 (assuming v<< so 1) to give an equation for the radius of eletrons path in terms of the urrent through the Helmholtz oils and the voltage aross the apaitor plates (and other relevant fators like the oils radius, R ) rather than v or B. Note: the q in Eq n 3 would be e for our eletrons. R= (6) So the violet eletron trail should urve with a radius aording to Eq n 6. With the experimental apparatus at the bak of the room, Vary the aelerating voltage (dial on the power supply, keep in the 150V 300 V range) and see the radius vary in aordane with Eq n 6. Vary the urrent (dial at Helmholtz Coils base) through the Helmholtz oils (and thus the magneti field), and see the radius vary in aordane with Eq n 6.. Simulation You ll write a simulation to model an eletron s motion through a uniform magneti field. You ould modify your Helmholz.py program to inlude a moving eletron; however, the repeated realulation of magneti field everywhere the eletron goes would be unneessarily omputationally-intensive / slow. Sine your Helmholtz.py program has demonstrated that oils an produe a uniform field over a broad region, you ll simply write a program that takes a uniform field as a given. This is a good opportunity to refresh your memory of how to write a whole new program (rather than inrementally modifying an existing one). Create a new program in VPython, and name it EletronInB.py.
6 Phys 3 Lab 8 Ch 1 Interations with Magneti Fields 6 What follows will guide you through filling in the setions of the ode. Beginning As with all of your programs, you ll want to start off with the two from import lines (the exat same ones that start your Helmholtz.py program) and follow those with a omment line that inludes your names. Constants Define: the magneti field vetor (B) to be Tesla in the +y diretion a variable (Bsale) to sale the size of the arrows representing the magneti field (start with 500.0) 10 the time step (dt) to be 1 10 s the maximum time (tmax) to be s. Objets Create a sphere alled eletron to represent an eletron by filling in the definition eletron = sphere(...) with the following attributes o an initial position (pos) of 0,0,0 m. o a radius of 5 mm (muh larger than its atual size so it an be seen in your simulation). o a olor of olor.blue 31 o a mass of kg 19 o a harge of C o an initial veloity of v = vetor(0,0,1e6), units of m/s o and set it to leave a trail everywhere it goes by inluding, along with these other attributes, make_trail=true inside the definition of the eletron. At a few observation loations, reate arrows to represent the uniform magneti field. You an do this however you like, but here s one way: d = 0.1 #in meters, oordinates of observation loations obslos = [vetor(-d,0,-d), vetor(-d,0,d), vetor(d,0,-d), vetor(d,0,d)] #list of obslos for obslo in obslos: arrow(pos = obslo, axis = B*Bsale, olor = olor.yan) Initial Values Initialize the time at t = 0. Calulations It s been a while sine you ve written dynamis programs (ones that simulate the motion of partiles in response to fores), so here s a quik refresher: You have a while loop that steps through time, from t = 0 to some final time, tmax; inside that loop, you realulate the fore on the partile (aording to Eq n in this ase), then the partile s new veloity aording to the approximation F v v new old t m,
7 Phys 3 Lab 8 Ch 1 Interations with Magneti Fields 7 and then the partile s new position aording to r r vt Of ourse, you update the time too; new old. t new t old t I ll get you started, but you ll need to omplete eah line of ode (remember, A B in Python is ross(a,b)). While t < tmax: F = eletron.v = eletron.pos = t = rate(50000) Run the program and make sure the eletron behaves as you expet. Pause and onsider: How would you expet the harged partile to behave differently if it had a positive harge instead of a negative harge? Flip the sign of the harge and run the program again. How would you expet the harged partile to behave differently if it were initially going faster? Double its initial speed and run the program again. How would you expet the harged partile to behave differently if it initially had a omponent of veloity parallel to the field (remember, there an be no omponent of the fore parallel to the field)? Give the partile s veloity an initial y omponent of m/s and run the program again. Compare with Theory: Radius. Aording to Eq n (3), we expet a speifi radius of the partile s orbit for given mass, speed, harge, and magneti field. You ll have the program determine the theoretial and simulated radii. Theoretial Just before and outside the while loop, add a line to alulate the expeted radius, rtheory, based on the harge, mass, field, and speed (whih is mag(eletron.v)). Follow that with the print line print( the expeted orbital radius is, rtheory, m. ) What value do you get?
8 Phys 3 Lab 8 Ch 1 Interations with Magneti Fields 8 Simulated Assuming the eletron is indeed exeuting irular motion in the x-z plane, then the diameter of the orbit would the its maximum z oordinate minus its minimum z oordinate (and the radius would simply be half the diameter). So, To find the maximum and minimum x oordinates, add following lines o In the Initialization setion, define Zmax = eletron.z Zmin = eletron.z o o o At the bottom inside the while loop add if eletron.z > Zmax: Zmax = eletron.z Add some similar lines to determine Zmin. At the end of the program (outside the while loop), add (and omplete) the line rsimulate = #the radius of the simulated orbit, based on Zmin and Zmax print( the simulated orbital radius is, rsimulate, m. ) Run the program and see how the theoretial and simulated radii ompare. Period Aording to Eq n (4), we expet the period of the eletron s orbit to depend on the field strength, speed, mass, and harge in a speifi way. Theoretial Before and outside the while loop, add a line to alulate the expeted period, Ttheory, based on the harge, mass, and field strength. Then add a print statement to print out this value. What value do you get? Simulation As the partile goes bak and forth, the x-omponent of its veloity flips sign twie per orbit first swithing from heading left to heading right, and then swithing from heading right to heading left. So you an determine the period by ounting the time between these flips, and doubling it. In the initialization setion, define Fliptime = 0 #will keep trak of when the veloity flips diretion At the top inside the while loop add the line
9 Phys 3 Lab 8 Ch 1 Interations with Magneti Fields 9 Oldvx = eletron.v.x At the bottom inside the while loop add the lines if Oldvx/eletron.v.x <0: #true if veloity flipped diretion T = *(t Fliptime) Fliptime = t At the bottom of the program, add the print line print( the simulated orbital period is,t, s. ) Run the program and see how the theoretial and simulated periods ompare. When satisfied, save and upload the program. III. Dipole in a Uniform Magneti Field a. Theory A dis magnet is the most readily identifiable magneti dipole. As the name suggests, a magneti dipole has two poles North from whih magneti field lines emanate, and South into whih magneti field lines terminate. (In reality, magneti field lines are losed loops that ontinue on through the body of the magnet). The simplest magneti dipole to piture and understand is a single loop of urrent harged partiles speeding around in a irle. From Phys 31, you may reall that angular momentum an be defined for partiles moving around in a loop, and that property is useful for disussing the work and torque required to hange the partiles irular motion. As the angular momentum fouses on the motion of mass, the magneti moment fouses on the orresponding motion of harge. It is similarly useful for disussing the work and torque assoiated with the moving harges interations with a magneti field. Like angular momentum, the magneti moment vetor s diretion follows from a righthand rule: if the urrent flows ounter-lokwise about the y axis, then the magneti moment points in the +y diretion; if the urrent flows lokwise about the y axis, then the magneti moment points in the y diretion. The torque exerted via a magneti field on a magneti dipole is B. Applying a right-hand rule to this ross produt makes it lear that the torque must be perpendiular to both the magneti moment and the field. Of ourse, the diretion of the torque is the diretion of the axis about whih the dipole is getting twisted. An example of this situation is illustrated below. B
10 Phys 3 Lab 8 Ch 1 Interations with Magneti Fields 10 In this example, the magneti moment of the small oil points up and right while the field of the large oils points up; aordingly, the torque vetor points out of the page, meaning that the small oils is pushed so its right edge would rise and its left edge would fall. Though mathematially more omplex, a oneptually simpler argument is that the small oil experienes a torque to bring its urrent into better alignment with the urrent in the large oils beause parallel urrents attrat and anti-parallel urrents repel. b. Qualitative Experiment Experimental Setup A magneti dipole (dis magnet) hangs from a spring and is mounted so it an pivot in response to a torque transmitted by a magneti field. This hangs near the middle of a pair of Helmholtz Coils whose urrent, and thus field, you an ontrol with the power supply. (It s for a later experiment that the urrent is routed through a preision resistor.) Torque Experiment Make sure the magnet s dipole moment points at an angle off vertial (an arrow on its side marks its orientation.) If it isn t already, you an do this by lifting the plasti ap, (along with rod, spring and dipole) from the graduated ylinder, tipping the dipole, and then replaing the ap (rod, spring, and dipole.) Turn on the power supply (swith is on the bak) and observe the dipole s response. Turn off the power supply, unplug the ables form it and re-plug them reversed (red able to blak port and vie versa). This reverses the diretion of urrent flow through the Helmholtz oils, and thus the diretion of their magneti field. Turn the power supply bak on and observe the dipole s response. Fore Experiment Dial up the urrent flowing through the oils, thus the field strength, and observe the dipole s response. Though the intrinsi urrent in the dipole (in this ase, eletrons orbiting their atoms) is attrated to the parallel urrent flowing through the Helmholtz oils, the attration to the top oils is the same as that to the bottom oil, so the dipole experienes no net fore under the symmetri, onstant-field ondition.
11 Phys 3 Lab 8 Ch 1 Interations with Magneti Fields 11 Interation with a linearly-varying Magneti Field All of the preeding theory, simulations, and experiments have pertained to uniform magneti fields. Now you ll explore the simplest non-uniform magneti field one that points only along one axis with a strength (and diretion) that varies linearly along that diretion. I. Produing a linearly-varying Magneti Field a. Theory Before experimenting with or simulating a linearly-varying magneti field, we ll digress and onsider how one produes suh a field. As you might expet, this ould be ahieved by having a solenoid of linearly varying urrent (for example, the top rung aries 1 amp lokwise, the bottom rung aries 1 amp ounter-lokwise, and the urrent through the in-between rungs smoothly varies the one to the other as you move along the length.) However, that is both tehnially diffiult and unneessary. As a pair of Helmholtz oils an produe a rather uniform field between them, oils in an anti- Helmholtz onfiguration (opposite urrents in the two oils) produe a rather linearlyvarying field between them. The expression for the field along the axis between two oils in anti-helmholtz onfiguration (one entered at y = -R / and one entered at y = +R / with opposite urrent) is B y o y 1 R IR R 3/ o I R 1 y R R 3/. So this field varies along the axis like db 1 y IR y R o 3 5/ dy 1 y R R o 3 1 I R y R 1 y R R 5/ At a loation fairly near the midpoint, y << R, so the y in the denominator is negligible, and the y dependene in the numerator then anels out, leaving us with db dy y I I 3 (7) o R 5/ 4 5/ o R So the slope of the field vs. position along axis should be onstant, that is, the field should vary linearly along the axis (in the y<<r region.) b. Simulation To get a feel for this field, you an easily modify your Helmholtz.py program to simulate the anti-helmholtz onfiguration. Open your opy of Helmholtz.py In the line where Idl is defined, insert a fator of *y/l. This will simply equal 1 for the urrent loop up at above y = L/, but it will equal -1 for the urrent loop down at y = -L/, thus flipping the diretion of the urrent. (If you re interested in.
12 Phys 3 Lab 8 Ch 1 Interations with Magneti Fields 1 seeing what a linearly-varying solenoid would be like, just inrease the number of urrent loops to something large, like 50.) Run the program and observe the length of the region over whih B y varies linearly with y. II. Dipole Interating with a Linearly-Varying Magneti Field a. Theory Imagine a dipole built of a oil of urrent-arrying wire, and the oil has nonnegligible height. In a regular Helmholtz oil setup, the top loop of this dipole is just as strongly attrated to the urrent in the upper Helmholtz oil above it as the bottom loop of this dipole is attrated to the lower Helmholtz oil below it, so the dipole experienes no net fore. Equivalently, we an relate this to the assoiated uniform field (rather than diretly to the urrents that produe it) and say that in the uniform field of the Helmholtz oils, there is no net fore on a dipole. You ve already observed that a dipole will twist but not aelerate and translate due to a uniform field. However, in an anti-helmholtz setup, if the oil below attrats the dipole, the oil above repels it, so the dipole does feel a net fore. Equivalently, we an say that if the field varies along the length of the dipole, then the two faes feel unbalaned fores, and so there is a net fore. Mathematially, that is expressed as F B, In our ase, the dipole is free to (and will) align with the field that points along the y axis, so we an write more speifially and simply F y dby. (8) dy b. Qualitative Experiment Experimental Setup This is the same as for the Helmholtz onfiguration exept the power supply is onneted so the urrent flows in the opposite diretions in the two oils. Note the different wiring in the diagram.
13 Phys 3 Lab 8 Ch 1 Interations with Magneti Fields 13 Experiment Turn on the power supply and pass a urrent of about amps. In the plasti ap, loosen the set srew that holds the brass rod (to whih the spring and thus magnet are attahed) and raise it enough that the dipole goes above the top oil, then lower it until the dipole is below the midpoint. What does the dipole do as it rosses below the midpoint? Pause and onsider: Thinking of the field illustrated in your simulation, reason out why the dipole behaves as it does as you lower it. Here s a start: when the dipole is above the top oil, it s oriented so that it s aligned with and attrated to the urrent in the top ring. As you lower the dipole. Quantitative Experiment You ll determine the magneti moment of the dis magnet by varying the urrent, and thus derivative of the magneti field and observe the orresponding streth of the spring, and thus fore on the dipole. Together, the fore and derivative of the field determine the dipole moment (aording to Eq n 8.) If it s on, dial down the urrent and turn off the power supply. Adjust the height of the dipole so the top of its holder is aligned with the 0 mark on the plasti tube that surrounds it. Turn on the power supply. For urrent values from 0.5 amps to 3.0 amps, note the height of the top of the dipole s holder. Enter the urrent values and displaements into the table in WebAssign. o To get more preise measurements of the urrent, a multi-meter is monitoring the voltage aross a preision 1 resistor; by Ohm s law, the urrent in amps equals the voltage in volts. Given that our oils have a radius of 0.07m and are atually 168 loops of wire, Eq n 7 an be made more speifi to our set up as db y I T/(m A) dy. Use this to fill in the orresponding olumn of the table. The spring from whih the dipole hangs has a stiffness of k s = 0.01 N/m. Use this to fill in the fore olumn of the table. Plot fore as a funtion of the field s derivative, and from the slope, determine the magnet s magneti dipole.
14 Phys 3 Lab 8 Ch 1 Interations with Magneti Fields 14 Helmholtz.py
15 Phys 3 Lab 8 Ch 1 Interations with Magneti Fields 15 EletronInB.py The modifiation to Helmholtz.py to make it antihelmholt.py
10.1 The Lorentz force law
Sott Hughes 10 Marh 2005 Massahusetts Institute of Tehnology Department of Physis 8.022 Spring 2004 Leture 10: Magneti fore; Magneti fields; Ampere s law 10.1 The Lorentz fore law Until now, we have been
More information) ( )( ) ( ) ( )( ) ( ) ( ) (1)
OPEN CHANNEL FLOW Open hannel flow is haraterized by a surfae in ontat with a gas phase, allowing the fluid to take on shapes and undergo behavior that is impossible in a pipe or other filled onduit. Examples
More informationChapter 1 Microeconomics of Consumer Theory
Chapter 1 Miroeonomis of Consumer Theory The two broad ategories of deision-makers in an eonomy are onsumers and firms. Eah individual in eah of these groups makes its deisions in order to ahieve some
More informationarxiv:astro-ph/0304006v2 10 Jun 2003 Theory Group, MS 50A-5101 Lawrence Berkeley National Laboratory One Cyclotron Road Berkeley, CA 94720 USA
LBNL-52402 Marh 2003 On the Speed of Gravity and the v/ Corretions to the Shapiro Time Delay Stuart Samuel 1 arxiv:astro-ph/0304006v2 10 Jun 2003 Theory Group, MS 50A-5101 Lawrene Berkeley National Laboratory
More informationIn order to be able to design beams, we need both moments and shears. 1. Moment a) From direct design method or equivalent frame method
BEAM DESIGN In order to be able to design beams, we need both moments and shears. 1. Moment a) From diret design method or equivalent frame method b) From loads applied diretly to beams inluding beam weight
More informationRevista Brasileira de Ensino de Fsica, vol. 21, no. 4, Dezembro, 1999 469. Surface Charges and Electric Field in a Two-Wire
Revista Brasileira de Ensino de Fsia, vol., no. 4, Dezembro, 999 469 Surfae Charges and Eletri Field in a Two-Wire Resistive Transmission Line A. K. T.Assis and A. J. Mania Instituto de Fsia Gleb Wataghin'
More informationE/M Experiment: Electrons in a Magnetic Field.
E/M Experiment: Electrons in a Magnetic Field. PRE-LAB You will be doing this experiment before we cover the relevant material in class. But there are only two fundamental concepts that you need to understand.
More informationChapter 5 Single Phase Systems
Chapter 5 Single Phase Systems Chemial engineering alulations rely heavily on the availability of physial properties of materials. There are three ommon methods used to find these properties. These inlude
More informationRelativity in the Global Positioning System
Relativity in the Global Positioning System Neil Ashby Department of Physis,UCB 390 University of Colorado, Boulder, CO 80309-00390 NIST Affiliate Email: ashby@boulder.nist.gov July 0, 006 AAPT workshop
More informationSHAFTS: TORSION LOADING AND DEFORMATION
ECURE hird Edition SHAFS: ORSION OADING AND DEFORMAION A. J. Clark Shool of Engineering Department of Civil and Environmental Engineering 6 Chapter 3.1-3.5 by Dr. Ibrahim A. Assakkaf SPRING 2003 ENES 220
More information1.3 Complex Numbers; Quadratic Equations in the Complex Number System*
04 CHAPTER Equations and Inequalities Explaining Conepts: Disussion and Writing 7. Whih of the following pairs of equations are equivalent? Explain. x 2 9; x 3 (b) x 29; x 3 () x - 2x - 22 x - 2 2 ; x
More informationClassical Electromagnetic Doppler Effect Redefined. Copyright 2014 Joseph A. Rybczyk
Classial Eletromagneti Doppler Effet Redefined Copyright 04 Joseph A. Rybzyk Abstrat The lassial Doppler Effet formula for eletromagneti waves is redefined to agree with the fundamental sientifi priniples
More informationElectrician'sMathand BasicElectricalFormulas
Eletriian'sMathand BasiEletrialFormulas MikeHoltEnterprises,In. 1.888.NEC.CODE www.mikeholt.om Introdution Introdution This PDF is a free resoure from Mike Holt Enterprises, In. It s Unit 1 from the Eletrial
More informationExperiment 3: Magnetic Fields of a Bar Magnet and Helmholtz Coil
MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Physics 8.02 Spring 2006 Experiment 3: Magnetic Fields of a Bar Magnet and Helmholtz Coil OBJECTIVES 1. To learn how to visualize magnetic field lines
More informationExperiment 3: Magnetic Fields of a Bar Magnet and Helmholtz Coil
MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Physics 8.02 Spring 2009 Experiment 3: Magnetic Fields of a Bar Magnet and Helmholtz Coil OBJECTIVES 1. To learn how to visualize magnetic field lines
More informationSebastián Bravo López
Transfinite Turing mahines Sebastián Bravo López 1 Introdution With the rise of omputers with high omputational power the idea of developing more powerful models of omputation has appeared. Suppose that
More informationComay s Paradox: Do Magnetic Charges Conserve Energy?
Comay s Paradox: Do Magneti Charges Conserve Energy? 1 Problem Kirk T. MDonald Joseph Henry Laboratories, Prineton University, Prineton, NJ 08544 (June 1, 2015; updated July 16, 2015) The interation energy
More informationAnother Look at Gaussian CGS Units
Another Look at Gaussian CGS Units or, Why CGS Units Make You Cool Prashanth S. Venkataram February 24, 202 Abstrat In this paper, I ompare the merits of Gaussian CGS and SI units in a variety of different
More informationDSP-I DSP-I DSP-I DSP-I
DSP-I DSP-I DSP-I DSP-I Digital Signal Proessing I (8-79) Fall Semester, 005 IIR FILER DESIG EXAMPLE hese notes summarize the design proedure for IIR filters as disussed in lass on ovember. Introdution:
More informationMeasurement of Charge-to-Mass (e/m) Ratio for the Electron
Measurement of Charge-to-Mass (e/m) Ratio for the Electron Experiment objectives: measure the ratio of the electron charge-to-mass ratio e/m by studying the electron trajectories in a uniform magnetic
More information5.2 The Master Theorem
170 CHAPTER 5. RECURSION AND RECURRENCES 5.2 The Master Theorem Master Theorem In the last setion, we saw three different kinds of behavior for reurrenes of the form at (n/2) + n These behaviors depended
More informationUser s Guide VISFIT: a computer tool for the measurement of intrinsic viscosities
File:UserVisfit_2.do User s Guide VISFIT: a omputer tool for the measurement of intrinsi visosities Version 2.a, September 2003 From: Multiple Linear Least-Squares Fits with a Common Interept: Determination
More informationChannel Assignment Strategies for Cellular Phone Systems
Channel Assignment Strategies for Cellular Phone Systems Wei Liu Yiping Han Hang Yu Zhejiang University Hangzhou, P. R. China Contat: wliu5@ie.uhk.edu.hk 000 Mathematial Contest in Modeling (MCM) Meritorious
More informationA novel active mass damper for vibration control of bridges
IABMAS 08, International Conferene on Bridge Maintenane, Safety and Management, 3-7 July 008, Seoul, Korea A novel ative mass damper for vibration ontrol of bridges U. Starossek & J. Sheller Strutural
More informationForce on Moving Charges in a Magnetic Field
[ Assignment View ] [ Eðlisfræði 2, vor 2007 27. Magnetic Field and Magnetic Forces Assignment is due at 2:00am on Wednesday, February 28, 2007 Credit for problems submitted late will decrease to 0% after
More informationReview Questions PHYS 2426 Exam 2
Review Questions PHYS 2426 Exam 2 1. If 4.7 x 10 16 electrons pass a particular point in a wire every second, what is the current in the wire? A) 4.7 ma B) 7.5 A C) 2.9 A D) 7.5 ma E) 0.29 A Ans: D 2.
More informationCapacity at Unsignalized Two-Stage Priority Intersections
Capaity at Unsignalized Two-Stage Priority Intersetions by Werner Brilon and Ning Wu Abstrat The subjet of this paper is the apaity of minor-street traffi movements aross major divided four-lane roadways
More information3 Game Theory: Basic Concepts
3 Game Theory: Basi Conepts Eah disipline of the soial sienes rules omfortably ithin its on hosen domain: : : so long as it stays largely oblivious of the others. Edard O. Wilson (1998):191 3.1 and and
More informationTHE UNIVERSITY OF THE STATE OF NEW YORK THE STATE EDUCATION DEPARTMENT ALBANY, NY
P THE UNIVERSITY OF THE STATE OF NEW YORK THE STATE EDUCATION DEPARTMENT ALBANY, NY 4 Referene Tables for Physial Setting/PHYSICS 006 Edition List of Physial Constants Name Symbol Value Universal gravitational
More informationHow To Fator
CHAPTER hapter 4 > Make the Connetion 4 INTRODUCTION Developing seret odes is big business beause of the widespread use of omputers and the Internet. Corporations all over the world sell enryption systems
More informationChapter 21. Magnetic Forces and Magnetic Fields
Chapter 21 Magnetic Forces and Magnetic Fields 21.1 Magnetic Fields The needle of a compass is permanent magnet that has a north magnetic pole (N) at one end and a south magnetic pole (S) at the other.
More informationExperiment 7: Forces and Torques on Magnetic Dipoles
MASSACHUSETTS INSTITUTE OF TECHNOLOY Department of Physics 8. Spring 5 OBJECTIVES Experiment 7: Forces and Torques on Magnetic Dipoles 1. To measure the magnetic fields due to a pair of current-carrying
More informationExplanatory Examples on Indian Seismic Code IS 1893 (Part I)
Doument No. :: IITK-GSDMA-EQ1-V.0 inal Report :: A - Earthquake Codes IITK-GSDMA Projet on Building Codes Explanatory Examples on Indian Seismi Code IS 1893 (Part I) by Dr. Sudhir K Jain Department of
More information1. Units of a magnetic field might be: A. C m/s B. C s/m C. C/kg D. kg/c s E. N/C m ans: D
Chapter 28: MAGNETIC FIELDS 1 Units of a magnetic field might be: A C m/s B C s/m C C/kg D kg/c s E N/C m 2 In the formula F = q v B: A F must be perpendicular to v but not necessarily to B B F must be
More informationChapter 22 Magnetism
22.6 Electric Current, Magnetic Fields, and Ampere s Law Chapter 22 Magnetism 22.1 The Magnetic Field 22.2 The Magnetic Force on Moving Charges 22.3 The Motion of Charged particles in a Magnetic Field
More informationNeural network-based Load Balancing and Reactive Power Control by Static VAR Compensator
nternational Journal of Computer and Eletrial Engineering, Vol. 1, No. 1, April 2009 Neural network-based Load Balaning and Reative Power Control by Stati VAR Compensator smail K. Said and Marouf Pirouti
More informationMeasurement of Powder Flow Properties that relate to Gravity Flow Behaviour through Industrial Processing Lines
Measurement of Powder Flow Properties that relate to Gravity Flow ehaviour through Industrial Proessing Lines A typial industrial powder proessing line will inlude several storage vessels (e.g. bins, bunkers,
More informationSURFACE TENSION. Definition
SURFACE TENSION Definition In the fall a fisherman s boat is often surrounded by fallen leaves that are lying on the water. The boat floats, because it is partially immersed in the water and the resulting
More informationPre-lab Quiz/PHYS 224 Magnetic Force and Current Balance. Your name Lab section
Pre-lab Quiz/PHYS 224 Magnetic Force and Current Balance Your name Lab section 1. What do you investigate in this lab? 2. Two straight wires are in parallel and carry electric currents in opposite directions
More informationModern Physics Laboratory e/m with Teltron Deflection Tube
Modern Physics Laboratory e/m with Teltron Deflection Tube Josh Diamond & John Cummings Fall 2010 Abstract The deflection of an electron beam by electric and magnetic fields is observed, and the charge
More informationVOLTAGE CONTROL WITH SHUNT CAPACITANCE ON RADIAL DISTRIBUTION LINE WITH HIGH R/X FACTOR. A Thesis by. Hong-Tuan Nguyen Vu
VOLTAGE CONTROL WITH SHUNT CAPACITANCE ON RADIAL DISTRIBUTION LINE WITH HIGH R/X FACTOR A Thesis by Hong-Tuan Nguyen Vu Eletrial Engineer, Polytehni University of HCMC, 1993 Submitted to the College of
More informationOpen and Extensible Business Process Simulator
UNIVERSITY OF TARTU FACULTY OF MATHEMATICS AND COMPUTER SCIENCE Institute of Computer Siene Karl Blum Open and Extensible Business Proess Simulator Master Thesis (30 EAP) Supervisors: Luiano Garía-Bañuelos,
More informationDeadline-based Escalation in Process-Aware Information Systems
Deadline-based Esalation in Proess-Aware Information Systems Wil M.P. van der Aalst 1,2, Mihael Rosemann 2, Marlon Dumas 2 1 Department of Tehnology Management Eindhoven University of Tehnology, The Netherlands
More informationFORCE ON A CURRENT IN A MAGNETIC FIELD
7/16 Force current 1/8 FORCE ON A CURRENT IN A MAGNETIC FIELD PURPOSE: To study the force exerted on an electric current by a magnetic field. BACKGROUND: When an electric charge moves with a velocity v
More informationSession #3: Homework Solutions
Session #3: Homework s Problem #1 From a standard radio dial, determine the maximum and minimum wavelengths ( max and min ) for broadasts on the (a) AM band (b) FM band =, min = ; max = max min AM FM 3
More informationF220 Series. Installation Instructions. Photoelectric Smoke/Heat Detectors
F0 Series EN Installation Instrutions Photoeletri Smoke/Heat Detetors F0 Series Installation Instrutions.0 General Information EN.0 General Information. F0-B6 Series Bases Use with the F0 Series Heat and
More informationCHAPTER J DESIGN OF CONNECTIONS
J-1 CHAPTER J DESIGN OF CONNECTIONS INTRODUCTION Chapter J of the addresses the design and heking of onnetions. The hapter s primary fous is the design of welded and bolted onnetions. Design requirements
More informationAgile ALM White Paper: Redefining ALM with Five Key Practices
Agile ALM White Paper: Redefining ALM with Five Key Praties by Ethan Teng, Cyndi Mithell and Chad Wathington 2011 ThoughtWorks ln. All rights reserved www.studios.thoughtworks.om Introdution The pervasiveness
More informationEarthquake Loss for Reinforced Concrete Building Structures Before and After Fire damage
Earthquake Loss for Reinfored Conrete Building Strutures Before and After Fire damage Pai-Mei LIU, Yi-Hsuan Tu and Maw-Shyong SHEU 3 ABSTRACT The purpose of this paper is to propose a rational analytial
More informationHEAT CONDUCTION. q A q T
HEAT CONDUCTION When a temperature gradient eist in a material, heat flows from the high temperature region to the low temperature region. The heat transfer mehanism is referred to as ondution and the
More informationChapter 1: Introduction
Chapter 1: Introdution 1.1 Pratial olumn base details in steel strutures 1.1.1 Pratial olumn base details Every struture must transfer vertial and lateral loads to the supports. In some ases, beams or
More informationProgramming Basics - FORTRAN 77 http://www.physics.nau.edu/~bowman/phy520/f77tutor/tutorial_77.html
CWCS Workshop May 2005 Programming Basis - FORTRAN 77 http://www.physis.nau.edu/~bowman/phy520/f77tutor/tutorial_77.html Program Organization A FORTRAN program is just a sequene of lines of plain text.
More information1. The diagram below represents magnetic lines of force within a region of space.
1. The diagram below represents magnetic lines of force within a region of space. 4. In which diagram below is the magnetic flux density at point P greatest? (1) (3) (2) (4) The magnetic field is strongest
More informationA Holistic Method for Selecting Web Services in Design of Composite Applications
A Holisti Method for Seleting Web Servies in Design of Composite Appliations Mārtiņš Bonders, Jānis Grabis Institute of Information Tehnology, Riga Tehnial University, 1 Kalu Street, Riga, LV 1658, Latvia,
More information6/2016 E&M forces-1/8 ELECTRIC AND MAGNETIC FORCES. PURPOSE: To study the deflection of a beam of electrons by electric and magnetic fields.
6/016 E&M forces-1/8 ELECTRIC AND MAGNETIC FORCES PURPOSE: To study the deflection of a beam of electrons by electric and magnetic fields. APPARATUS: Electron beam tube, stand with coils, power supply,
More informationImpact Simulation of Extreme Wind Generated Missiles on Radioactive Waste Storage Facilities
Impat Simulation of Extreme Wind Generated issiles on Radioative Waste Storage Failities G. Barbella Sogin S.p.A. Via Torino 6 00184 Rome (Italy), barbella@sogin.it Abstrat: The strutural design of temporary
More informationSUBSTRUCTURE EXAMPLE. Full Height Abutment on Spread Footing
SUBSTRUCTURE EXAMPLE Full Height Abutment on Spread Footing This example illustrates the design of a full height abutment on spread footings for a single span ast-in-plae post-tensioned onrete box girder
More informationComputer Networks Framing
Computer Networks Framing Saad Mneimneh Computer Siene Hunter College of CUNY New York Introdution Who framed Roger rabbit? A detetive, a woman, and a rabbit in a network of trouble We will skip the physial
More informationPISTONLESS DUAL CHAMBER ROCKET FUEL PUMP
39 th AIAA/ASE/SAE/ASEE Joint Propulsion Conferene and Exhibit AIAA 2003-4479 20-23 July 2003, Huntsville Alabama PISTONLESS DUAL CHABER ROCKET FUEL PUP Steve Harrington, Ph.D. Flometris, In. Solana Beah,
More informationPhysical and mathematical postulates behind relativity
Physial and mathematial postulates behind relativity Tuomo Suntola Physis Foundations Soiety, Finland, www.physisfoundations.org In this presentation we look for answers to questions: What was the problem
More informationModelling and Simulation of Closed Loop Controlled Buck Converter Fed Pmbldc Drive System
Researh Journal of Applied Sienes, Engineering and Tehnology 3(4): 284-289, 2011 ISSN: 2040-7467 Maxwell Sientifi Organization, 2011 Reeived: Feruary 14, 2011 Aepted: Marh 15, 2011 Pulished: April 20,
More informationIsaac Newton. Translated into English by
THE MATHEMATICAL PRINCIPLES OF NATURAL PHILOSOPHY (BOOK 1, SECTION 1) By Isaa Newton Translated into English by Andrew Motte Edited by David R. Wilkins 2002 NOTE ON THE TEXT Setion I in Book I of Isaa
More informationDerivation of Einstein s Equation, E = mc 2, from the Classical Force Laws
Apeiron, Vol. 14, No. 4, Otober 7 435 Derivation of Einstein s Equation, E = m, from the Classial Fore Laws N. Hamdan, A.K. Hariri Department of Physis, University of Aleppo, Syria nhamdan59@hotmail.om,
More informationAmpere's Law. Introduction. times the current enclosed in that loop: Ampere's Law states that the line integral of B and dl over a closed path is 0
1 Ampere's Law Purpose: To investigate Ampere's Law by measuring how magnetic field varies over a closed path; to examine how magnetic field depends upon current. Apparatus: Solenoid and path integral
More informationThe purposes of this experiment are to test Faraday's Law qualitatively and to test Lenz's Law.
260 17-1 I. THEORY EXPERIMENT 17 QUALITATIVE STUDY OF INDUCED EMF Along the extended central axis of a bar magnet, the magnetic field vector B r, on the side nearer the North pole, points away from this
More informationPhysics 221 Experiment 5: Magnetic Fields
Physics 221 Experiment 5: Magnetic Fields August 25, 2007 ntroduction This experiment will examine the properties of magnetic fields. Magnetic fields can be created in a variety of ways, and are also found
More informationTHERMAL TO MECHANICAL ENERGY CONVERSION: ENGINES AND REQUIREMENTS Vol. I - Thermodynamic Cycles of Reciprocating and Rotary Engines - R.S.
THERMAL TO MECHANICAL ENERGY CONVERSION: ENGINES AND REQUIREMENTS Vol. I - Thermodynami Cyles of Reiproating and Rotary Engines - R.S.Kavtaradze THERMODYNAMIC CYCLES OF RECIPROCATING AND ROTARY ENGINES
More informationGeneral Physics (PHY 2140)
General Physics (PHY 2140) Lecture 12 Electricity and Magnetism Magnetism Magnetic fields and force Application of magnetic forces http://www.physics.wayne.edu/~apetrov/phy2140/ Chapter 19 1 Department
More informationElectroMagnetic Induction. AP Physics B
ElectroMagnetic Induction AP Physics B What is E/M Induction? Electromagnetic Induction is the process of using magnetic fields to produce voltage, and in a complete circuit, a current. Michael Faraday
More informationFig. 1.1 Rectangular foundation plan.
Footings Example 1 Design of a square spread footing of a seven-story uilding Design and detail a typial square spread footing of a six ay y five ay seven-story uilding, founded on stiff soil, supporting
More informationMagnetism. d. gives the direction of the force on a charge moving in a magnetic field. b. results in negative charges moving. clockwise.
Magnetism 1. An electron which moves with a speed of 3.0 10 4 m/s parallel to a uniform magnetic field of 0.40 T experiences a force of what magnitude? (e = 1.6 10 19 C) a. 4.8 10 14 N c. 2.2 10 24 N b.
More informationConversion of short optical pulses to terahertz radiation in a nonlinear medium: Experiment and theory
PHYSICAL REVIEW B 76, 35114 007 Conversion of short optial pulses to terahertz radiation in a nonlinear medium: Experiment and theory N. N. Zinov ev* Department of Physis, University of Durham, Durham
More informationPhysics 112 Homework 5 (solutions) (2004 Fall) Solutions to Homework Questions 5
Solutions to Homework Questions 5 Chapt19, Problem-2: (a) Find the direction of the force on a proton (a positively charged particle) moving through the magnetic fields in Figure P19.2, as shown. (b) Repeat
More informationMagnetic Field and Magnetic Forces
Chapter 27 Magnetic Field and Magnetic Forces PowerPoint Lectures for University Physics, Thirteenth Edition Hugh D. Young and Roger A. Freedman Lectures by Wayne Anderson Goals for Chapter 27 Magnets
More informationMotion of Charges in Combined Electric and Magnetic Fields; Measurement of the Ratio of the Electron Charge to the Electron Mass
Motion of Charges in Combined Electric and Magnetic Fields; Measurement of the Ratio of the Electron Charge to the Electron Mass Object: Understand the laws of force from electric and magnetic fields.
More informationIn this chapter, we ll see state diagrams, an example of a different way to use directed graphs.
Chapter 19 State Diagrams In this hapter, we ll see state diagrams, an example of a different way to use direted graphs. 19.1 Introdution State diagrams are a type of direted graph, in whih the graph nodes
More informationTHE PERFORMANCE OF TRANSIT TIME FLOWMETERS IN HEATED GAS MIXTURES
Proeedings of FEDSM 98 998 ASME Fluids Engineering Division Summer Meeting June 2-25, 998 Washington DC FEDSM98-529 THE PERFORMANCE OF TRANSIT TIME FLOWMETERS IN HEATED GAS MIXTURES John D. Wright Proess
More informationPhysics 2B. Lecture 29B
Physics 2B Lecture 29B "There is a magnet in your heart that will attract true friends. That magnet is unselfishness, thinking of others first. When you learn to live for others, they will live for you."
More informationIntelligent Measurement Processes in 3D Optical Metrology: Producing More Accurate Point Clouds
Intelligent Measurement Proesses in 3D Optial Metrology: Produing More Aurate Point Clouds Charles Mony, Ph.D. 1 President Creaform in. mony@reaform3d.om Daniel Brown, Eng. 1 Produt Manager Creaform in.
More informationImpedance Method for Leak Detection in Zigzag Pipelines
10.478/v10048-010-0036-0 MEASUREMENT SCIENCE REVIEW, Volume 10, No. 6, 010 Impedane Method for Leak Detetion in igzag Pipelines A. Lay-Ekuakille 1, P. Vergallo 1, A. Trotta 1 Dipartimento d Ingegneria
More informationFrom a strategic view to an engineering view in a digital enterprise
Digital Enterprise Design & Management 2013 February 11-12, 2013 Paris From a strategi view to an engineering view in a digital enterprise The ase of a multi-ountry Telo Hervé Paault Orange Abstrat In
More informationChapter 19: Magnetic Forces and Fields
Chapter 19: Magnetic Forces and Fields Magnetic Fields Magnetic Force on a Point Charge Motion of a Charged Particle in a Magnetic Field Crossed E and B fields Magnetic Forces on Current Carrying Wires
More informationComputational Analysis of Two Arrangements of a Central Ground-Source Heat Pump System for Residential Buildings
Computational Analysis of Two Arrangements of a Central Ground-Soure Heat Pump System for Residential Buildings Abstrat Ehab Foda, Ala Hasan, Kai Sirén Helsinki University of Tehnology, HVAC Tehnology,
More informationWaveguides. 8.14 Problems. 8.14. Problems 361
8.4. Problems 36 improving liquid rystal displays, and other produts, suh as various optoeletroni omponents, osmetis, and hot and old mirrors for arhitetural and automotive windows. 8.4 Problems 9 Waveguides
More informationMagnetic Field of a Circular Coil Lab 12
HB 11-26-07 Magnetic Field of a Circular Coil Lab 12 1 Magnetic Field of a Circular Coil Lab 12 Equipment- coil apparatus, BK Precision 2120B oscilloscope, Fluke multimeter, Wavetek FG3C function generator,
More informationLab 3 - DC Circuits and Ohm s Law
Lab 3 DC Circuits and Ohm s Law L3-1 Name Date Partners Lab 3 - DC Circuits and Ohm s Law OBJECTIES To learn to apply the concept of potential difference (voltage) to explain the action of a battery in
More informationREDUCTION FACTOR OF FEEDING LINES THAT HAVE A CABLE AND AN OVERHEAD SECTION
C I E 17 th International Conferene on Eletriity istriution Barelona, 1-15 May 003 EUCTION FACTO OF FEEING LINES THAT HAVE A CABLE AN AN OVEHEA SECTION Ljuivoje opovi J.. Elektrodistriuija - Belgrade -
More informationFixed-income Securities Lecture 2: Basic Terminology and Concepts. Present value (fixed interest rate) Present value (fixed interest rate): the arb
Fixed-inome Seurities Leture 2: Basi Terminology and Conepts Philip H. Dybvig Washington University in Saint Louis Various interest rates Present value (PV) and arbitrage Forward and spot interest rates
More information' R ATIONAL. :::~i:. :'.:::::: RETENTION ':: Compliance with the way you work PRODUCT BRIEF
' R :::i:. ATIONAL :'.:::::: RETENTION ':: Compliane with the way you work, PRODUCT BRIEF In-plae Management of Unstrutured Data The explosion of unstrutured data ombined with new laws and regulations
More informationPhysics 201 Homework 8
Physics 201 Homework 8 Feb 27, 2013 1. A ceiling fan is turned on and a net torque of 1.8 N-m is applied to the blades. 8.2 rad/s 2 The blades have a total moment of inertia of 0.22 kg-m 2. What is the
More informationConceptual: 1, 3, 5, 6, 8, 16, 18, 19. Problems: 4, 6, 8, 11, 16, 20, 23, 27, 34, 41, 45, 56, 60, 65. Conceptual Questions
Conceptual: 1, 3, 5, 6, 8, 16, 18, 19 Problems: 4, 6, 8, 11, 16, 20, 23, 27, 34, 41, 45, 56, 60, 65 Conceptual Questions 1. The magnetic field cannot be described as the magnetic force per unit charge
More informationFOOD FOR THOUGHT Topical Insights from our Subject Matter Experts
FOOD FOR THOUGHT Topial Insights from our Sujet Matter Experts DEGREE OF DIFFERENCE TESTING: AN ALTERNATIVE TO TRADITIONAL APPROACHES The NFL White Paper Series Volume 14, June 2014 Overview Differene
More informationAP2 Magnetism. (c) Explain why the magnetic field does no work on the particle as it moves in its circular path.
A charged particle is projected from point P with velocity v at a right angle to a uniform magnetic field directed out of the plane of the page as shown. The particle moves along a circle of radius R.
More informationStatic Fairness Criteria in Telecommunications
Teknillinen Korkeakoulu ERIKOISTYÖ Teknillisen fysiikan koulutusohjelma 92002 Mat-208 Sovelletun matematiikan erikoistyöt Stati Fairness Criteria in Teleommuniations Vesa Timonen, e-mail: vesatimonen@hutfi
More informationRelativistic Kinematics -a project in Analytical mechanics Karlstad University
Relativisti Kinematis -a projet in Analytial mehanis Karlstad University Carl Stigner 1th January 6 Abstrat The following text is a desription of some of the ontent in hapter 7 in the textbook Classial
More informationMagnetic Fields. I. Magnetic Field and Magnetic Field Lines
Magnetic Fields I. Magnetic Field and Magnetic Field Lines A. The concept of the magnetic field can be developed in a manner similar to the way we developed the electric field. The magnitude of the magnetic
More informationWeighting Methods in Survey Sampling
Setion on Survey Researh Methods JSM 01 Weighting Methods in Survey Sampling Chiao-hih Chang Ferry Butar Butar Abstrat It is said that a well-designed survey an best prevent nonresponse. However, no matter
More informationINCOME TAX WITHHOLDING GUIDE FOR EMPLOYERS
Virginia Department of Taxation INCOME TAX WITHHOLDING GUIDE FOR EMPLOYERS www.tax.virginia.gov 2614086 Rev. 07/14 * Table of Contents Introdution... 1 Important... 1 Where to Get Assistane... 1 Online
More informationCIS570 Lecture 4 Introduction to Data-flow Analysis 3
Introdution to Data-flow Analysis Last Time Control flow analysis BT disussion Today Introdue iterative data-flow analysis Liveness analysis Introdue other useful onepts CIS570 Leture 4 Introdution to
More informationChapter 30 - Magnetic Fields and Torque. A PowerPoint Presentation by Paul E. Tippens, Professor of Physics Southern Polytechnic State University
Chapter 30 - Magnetic Fields and Torque A PowerPoint Presentation by Paul E. Tippens, Professor of Physics Southern Polytechnic State University 2007 Objectives: After completing this module, you should
More information