MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Physics 8.02 Spring 2005 Experiment 1: Using the TEAL Visualizations OBJECTIVES 1. To explore the types of visualizations available through the TEAL website. 2. To become familiar why they are there, which is to help you with geometry, mathematics, and physics. 3. To explore how electrostatic forces hold matter together. INTRODUCTION Electromagnetism is a subject that is highly complex and mathematical, and we hope to help you develop a better intuition about this subject through passive and interactive visualizations, without the use of advanced mathematics. These visualizations are for three purposes. 1. To help you with the geometric issues. Because electromagnetism involves vector cross products, the subject is innately three-dimensional, and many of our animations are built using 3D tools. 2. To help you with the math. We do a lot of different kinds of integrals in electromagnetism (line, surface, and volume), many of which you do not see until the end of 18.02, and we want to help you understand those using visualizations of the mathematical concepts 3. To help you with the physics. Electromagnet fields mediate the interaction of the material objects that produce them by transmitting energy and momentum between those objects. In particular, fields exert a tension parallel to field lines and a pressure perpendicular to field lines, and that is most obvious when you use an interactive applet demonstrating this phenomena. You will not have seen a lot of the materials we will discuss today, but don’t panic. We just want to get you familiar with why the visualizations exist and what you can use them for as we proceed in the course. PLATFORMS We have three different kinds of animations, which run on the following platforms. 1. Movie files, which should run on server, Windows PCs, and MACs with no additional software added to your computer. 2. Java 3D Applets, which run on server, Windows PCs, and MACs. If you want to run these on your own computer at home, you must download and install Java 3D E01-1source code. Directions for doing that are given at http://evangelion.mit.edu/802TEAL3D/visualizations/resources/download.htm. 3. Macromedia ShockWave files, which run only on Window’s PCs and MACs. You must download the free Shockwave player from Macromedia’s website. The first time you try to play one of our Shockwaves it is programmed to go to that website and download the player (assuming you want to of course). If your computing resources do not include one of these platforms, use the server PC Cluster. This Cluster is heavily used during the day for classes, but is available outside of scheduled classes. We now go through examples of each of these kinds of visualizations in each of the categories we mentioned above—i.e. geometry, mathematics, and physics. PART 1. GEOMETRY Navigation: Go to the 8.02 public web page at http://web.mit.edu/8.02t/www. The bottom link on the left will bring you to the Teal Visualization Page. Once there, select Vector Fields from the links on the right. Figure 1 The TEAL Visualization page at http://web.mit.edu/8.02T/www/802TEAL3D/ Coordinate Systems Select the Coordinate Systems Shockwave on the next to bottom left column of the Vector Fields page. Once it loads you will see the following page: E1-2The text on the right explains the purpose of the visualization. To get instructions for the interface, click in the instructions (popup window). To get a full screen version of the shockwave, click on the fullscreen version link. Exercise 1: Go to the full screen version of the shockwave do all of the following: 1. Explore all three of the coordinate systems contained in it. 2. Move your observation point around in all three directions. 3. Change your viewpoint by clicking and dragging in the window. 4. Move the viewpoint in and out using the keyboard controls. Question 1 (answer on the tear-sheet at the end): What is it about the coordinate axes in cylindrical and spherical coordinates that makes those axes very different from the axes in a Cartesian coordinate system? PART 2. MATHEMATICS Line Integrations Return to the TEAL visualization page, http://web.mit.edu/8.02T/www/802TEAL3D/ (see Figure 1 above). Now choose Electrostatics from the links on the right, and go to the Ring of Charge Shockwave (fifth visualization down on the column to the right). This is a visualization of the mathematical equation E01-3GE = ke ∫dq rˆ (1.1)2r applied to the situation where we have a ring of charge and the integration in Equation (1.1) is a line integral over the ring. In the visualization we have broken our integration up into a sum over 30 charge elements on the ring, and do a sum to calculate the electric field. That is, we have replaced (1.1) with GiE = ke ∑q rˆi (1.2)2 i ri Exercise 2: Look at the instructions on the pop-up menu and then go to the full screen version of the shockwave do all of the following: 1. Move your observation point around the two directions in the plane of the map. Be careful to first move “down”, as there is a bug that crashes the shockwave if you move sideways to begin with. 2. Turn the grass seeds map on and off. Note that the vector sum of our thirty individual electric fields due to each charge element is always parallel to the grass seeds correlation direction, as it should be. 3. Change your viewpoint by clicking and dragging in the window. 4. Move the viewpoint in and out using the keyboard controls. 5. Select one of the 30 “charge elements” as explained in the instructions, and note what electric field it produces. Question 2 (answer on the tear-sheet at the end): What is the magnitude of the electric field right at the center of the circle of charge? Why does it have that value? Grass seeds from analytic formulas Go to http://web.mit.edu/8.02t/www/802TEAL3D/visualizations/vectorfields/licapplet/licapplet .htm and bring up the applet at that link by left clicking on the picture. Exercise 3: G 1. The applet starts out with the vector function F(,xy) =−y ˆi + x ˆj in the boxes. Hit the Grass Seeds button near the bottom of the right panel of the applet to see what this vector function looks like in grass seeds. E1-4G 2. Try entering a new and different F(, (, (,xy) = gxy )ˆi + hxy )ˆj in the text boxes labeled by these functions. You must use the usual symbolic nomenclature, e.g.
View Full Document
Unlocking...