PHGN-361 Spring
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4) The Electric Field of Dreams does not account for magnetic fields produced by a changing electric field. This is evident in the description of the applet and the behavior of charges within the applet. The explicit description of the applet states that the learning goals are to explain "the relation between the size and direction of the blue electric field lines to the sign and magnitude of the charge of a particle," "the interactions between two charged particles and explain why they move as they do," and "what happens when you apply different external electric fields." Within the applet we find that the only term accounted for in the Lorentz force law is the electric term. There must not be any magnetic force because there is no behavior exhibited by the particles indicative of the term containing the cross product between the velocity of the particles and a magnetic field. There is a discontinuity any time a charge is added. | 4) The Electric Field of Dreams does not account for magnetic fields produced by a changing electric field. This is evident in the description of the applet and the behavior of charges within the applet. The explicit description of the applet states that the learning goals are to explain "the relation between the size and direction of the blue electric field lines to the sign and magnitude of the charge of a particle," "the interactions between two charged particles and explain why they move as they do," and "what happens when you apply different external electric fields." Within the applet we find that the only term accounted for in the Lorentz force law is the electric term. There must not be any magnetic force because there is no behavior exhibited by the particles indicative of the term containing the cross product between the velocity of the particles and a magnetic field. There is a discontinuity any time a charge is added. | ||
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| + | 5) I think to provide an approximation for a plasma would a far more complex setup than the applet can provide. Even as high as 20-30 different "atoms" in the simulation start producing some weird results (particles jumping from one side of the box to the other almost instantaneously). I'm currently trying to get a system to "settle" into an equilibrium state with ~50 of +/-1 charges of mass 1, and nothing seems to be changing. I think we would need on the order of hundreds, if not thousands, of particles to successfully approximate a plasma, and certainly in a larger container. The "boundary" conditions of not being able to go outside the box seem to be messing with any good approximation that we could get from this applet. | ||
===Critical comments on the answers === | ===Critical comments on the answers === | ||
Revision as of 06:51, 29 April 2011
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Instructor information
Professor: Dr. Frank Kowalski
Office: Meyer 438
Office Hours:
Monday 12-2 and Tuesday 12-3.
Extra Credit Group Exam Problem Due May 2 at 10 AM
Please go to this site [1] (electric field of dreams) and play with the applet. Edit the following subsections iterating questions with answers. Generate both critical and positive comments on the questions and answers and come up with experiments to answer questions. All those participating will receive 20 extra points on exam 4 (there are 10 points per problem and about 5 problems on the exam) if the group draws insightful conclusions. Less credit will be given for less productive effort. You must log in on this wiki to participate. Please make your name apparent in the log in to receive credit.
Formal Q&A
Let's use this to make a formal question and answer section that follows "one question, one answer" format, and use the sections below as a workspace to iron out the details.
Q: Is energy conserved in this applet?
A: Energy seems to be conserved for a static electric field. Changing the electric field can introduce energy to the system. It is possible that when opposite charges get close together, the total energy is no longer conserved, though this needs to be looked into further.
Q: Does this model incorporate quantum mechanical effects and, if so, does the behavior of charges in the applet violet the Pauli Exclusion Principle?
A: This is a purely classical view of point charge interactions. Therefore, the effects of quantum mechanics and the stipulations of the Pauli Exclusion Principles are not applicable.
Questions
1) Energy Conservation: This reminds me of the fourth numerical assignment in Intermediate Mechanics. Do you think the total energy is conserved?
2) Chaos Theory: It appears that the location of where the particles are initially placed are not the same. So then does this system exhibit chaos? or is the boundary/walls of this system enough to predict the eventual outcome?
3) Electrons and Protons are fermions, but are neutrons (I'd hope so)? If yes then doesn't the applet violate the Pauli exclusion principle by allowing a neutron(assuming no charge in the sim is a neutron) to occupy the same space as the protons and electrons in the simulation?
4) Does this applet account for the fact that a changing electric field produces a magnetic field?
5) If we place tens of positive and tens of negative particles in this applet, could it act as a reasonable approximation for a confined plasma?
6) In the vein of 5), could we simulate the polarization of a material using positive and negative charges? Could a lattice structure of any stability be set up?
Answers
1a) Energy conservation: I let the applet run for a few minutes, and no, energy is definitely not conserved. With three charges, it didn't take long before they were flying around the box with an obviously higher energy than they started with. The time resolution for the simulation must not be good enough...
1b) I believe Energy is conserved, setting the charge higher than the mass you can observe coulomb repulsion. Also I have not been able to observe the runaway effect stated above. I am curious however about how the collisions with the walls of the system effects this.
1c) After the applet had run continuously without intervention for about fifteen minutes, I couldn't detect any difference in the speed of the balls. As the balls interact with each other, their individual speeds change, sometimes resulting in one of them moving surprisingly quickly. However, it doesn't appear that the overall energy of the system changes over time and energy does appear to be conserved.
2) Recalling some information on Chaos from IM, the system can be completely "random" or settle into chaos. It is also difficult to distinguish between chaos and random noise contributions through numerical errors. Further analysis of this system is needed to determine if it shows chaotic behaviour or just random bouncing ball behaviour. Although at first glance, one could say that this system is chaotic. There is no long term pattern and the system is not predictable, thus satisfying the condition of chaos.
3) This applet doesn't seem to apply anything related to quantum mechanics. It wouldn't make sense to simulate electrons, protons, and neutrons as point particles if we were interested in things relating to quantum mechanics; we would need to use wave functions. With that said, the Pauli Exclusion Principle states that no two fermions can exist in the same quantum state i.e. have the same quantum numbers. This doesn’t mean that there is no probability that the two can’t be in the same position. So even if the applet used wave functions and showed a probability that the two had the same position, it wouldn’t be violating the Pauli Exclusion Principle as long as the two still had different quantum numbers.
4) The Electric Field of Dreams does not account for magnetic fields produced by a changing electric field. This is evident in the description of the applet and the behavior of charges within the applet. The explicit description of the applet states that the learning goals are to explain "the relation between the size and direction of the blue electric field lines to the sign and magnitude of the charge of a particle," "the interactions between two charged particles and explain why they move as they do," and "what happens when you apply different external electric fields." Within the applet we find that the only term accounted for in the Lorentz force law is the electric term. There must not be any magnetic force because there is no behavior exhibited by the particles indicative of the term containing the cross product between the velocity of the particles and a magnetic field. There is a discontinuity any time a charge is added.
5) I think to provide an approximation for a plasma would a far more complex setup than the applet can provide. Even as high as 20-30 different "atoms" in the simulation start producing some weird results (particles jumping from one side of the box to the other almost instantaneously). I'm currently trying to get a system to "settle" into an equilibrium state with ~50 of +/-1 charges of mass 1, and nothing seems to be changing. I think we would need on the order of hundreds, if not thousands, of particles to successfully approximate a plasma, and certainly in a larger container. The "boundary" conditions of not being able to go outside the box seem to be messing with any good approximation that we could get from this applet.
Critical comments on the answers
1a and 1b) It's worth noting when talking about energy conservation that we can apply an external electric field to the box. An electric field can add energy to the system. Thinking about the scenario where there is just one charge in the box at rest, when you add an external field the e-field does work on the charge and moves it. This could be how the system gains energy with time.
1c) The fact that there was no visible change in energy in a system with multiple balls does not necessarily mean that the applet obeys conservation of energy. It is difficult to detect a change in energy in a system with multiple particles as all forms of energy for each particle have to be determined.
Q: 2) I found that it was easy to deliberately add or subtract energy to or from the system by altering the direction of the 'external' electric field, but without making any alterations to the field, it didn't appear that the energy of the system was changing with time.
Positive comments on the answers
1) 1b seems to mirror the situation I encountered with the applet as opposed to 1a, that is if energy conservation is defined as initial energy equals final energy. As long as the electric field is constant (such that no external force acts upon the system) then the energy should be conserved.
2) From looking at my app for a good ten minutes now, I can say that it seems to be a chaotic system. I think the amount of balls may play into whether the system becomes chaotic or not (12 balls result in a chaotic system).
Experiments to test questions
1) An easy experiment to test conservation of energy is to start the system with 2 particles and no external electric field so there is motion and then remove one. We now have one particle bouncing around all alone that should have no external forces acting on it. If we let it run for 15 minutes or so and return, it is traveling at a noticeably different speed. This would indicate energy is not conserved.
2) To see if the system exhibit chaotic behaviour, we can run calculations and analysis through Mathematica (as in IM Numerical Assignment 5?). Also we can run multiple simulations simultaneously and watch to see if the system runs in the same path at some point.
2) A specific experiment to test if this simulation can exhibit chaotic motion would be to set up two nearly identical situations differing only by a tiny preturbation in the initial conditions and start them at the same time. If they follow very similar patterns of motion then the system is not chaotic. If, however, the slight difference in initial conditions causes a huge difference in motion later on then the system is chaotic. Exe: Two situations were set up with charges of mass 1.0 and charge -1.0 in the top left and bottom right corners with no external electric field. The initial positions of the charges varied by only a few pixels from one set up to the other. These simulations were started at the same time. Around 5 minutes into the simulations, the charges in one simulation were clearly moving in very different manners than the charges in the other simulation. This would imply that a system with this set up does indeed exhibit chaotic motion. However, by an hour into the experiment, both applets exhibited the same pattern of motion: the charges move back and forth horizontally with very little vertical motion. It would be interesting to test if this final pattern of motion holds true for all two charge systems.
Other comments
1) Energy Conservation: Something just occurred to me, which I didn't think of when I was working on the fourth numerical. Total energy could be maintained (even though there were obvious spikes in the total energy when the three masses approached one another) by normalizing the energy at each timestep, just like we do in quantum and thermal. That is to say, reduce each objects kinetic and potential energy by a factor such that their relative energies remain the same, and the total energy is constant. The only issue with this is that divvying up the energy into kinetic and potential for each particle might be a little tricky (especially because the potential depends on where each particle actually is. This would be a cool feature to go back and add to that three-body simulation, though.
2) The details of this simulation is limited, ie. we don't know the accuracy of each calculation made and we don't know how many decimal places the calculations keep track of. All we know is that there is repulsion between the two balls, we can set the amount of repulsion/mass through the preferences button, and the total amount of particles in the box.
3) I found it interesting that when I added a particle with no electrical charge, the other (charged) particles didn't interact with it at all. It's clear that the charged particles interact with each other only due to their charge (since they don't actually impact each other), but I thought that the program might allow collisions between particles in the absence of electrostatic repulsion.
4a) Along the same lines as collisions, I am pretty sure that this applet does not account for magnetic fields as well. Assuming only two dimensional motion, the "currents" created by the moving charges would produce a B-Field that would either attract or repel the other charges. Just an interesting note.
4b) It is tough to gauge the presence of a magnetic field in an applet that works with two dimensions. Think about the cross products involved in finding the magnetic force using the Lorentz force law and the magnetic and electric fields using Faraday's law and Ampere's law.
Creativity Links
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Course Information
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Course videos, applets, and links
Video Lectures for March 7 through March 11 are
Here is the InkSurvey link Kowalski InkSurvey site
Homework assignment 7 has for problem 1 this link applet
and for problem 2 this link cell phone
Homework assignment 10 uses the following link [2]
Applet links:
Harmonic oscillator applet [3]
E from a moving charge [4]
Charge and field distribution on conductors and in dielectrics [5]
metal sphere inside a capacitor where the voltage across the capacitor can be varied [6]
Applet link for Faraday's Law used in the April 13 lecture [7]
Applet link for Faraday's law with a rectangular wire near a long wire [8]
Applet to calculate inductance [9]
Plinko link [10]
Lectures
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Homework Assignments:
See the syllabus for the first homework assignment.
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Homework Solutions:
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HAARP problem in assignment 12.
A part of rhetoric [11] is to manipulate the facts to sway the viewers’ opinion. You need to recognize this manipulation in the context of science and engineering (not only in politics). One example in this video is that interruptions of communications in a nuclear war are the primary objective of HAARP.
Indeed nuclear explosions generating an electromagnetic pulse (EMP) do disrupt communications by creating gamma rays whose Compton electrons spiral around the Earth’s field lines thereby producing a huge EMP (large enough to fuse 300 street lights 1300 km away). Please see the following references [12] and [13]
However, HAARP is not a nuclear weapon. Yet that doesn’t stop the authors of the video from making that false connection. Here are more reliable descriptions of HAARP along with a discussion of conspiracy theories associated with it.
Other manipulations of the facts are that the Earth’s rotation rate will be dramatically affected. It is easy to calculate the energy required to do this and compare it with the electromagnetic energy that can be generated.
Just like in the applets you need to think critically about the information you find. Here are some resources
-the effects of HAARP [14]
-HAARP on wikipedia [15]
Exams with solutions and Rubrics
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Old Exams with solutions and Rubrics
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Problem solving strategies and sample problems:
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Volume and surface integrals in cylindrical coords [16]
Line integrals
Delta functions
