Visual and Mathematical Representations of the Electric Field

Transcription

1 Visual and Mathematical Representations of the Electric Field 1.1 Represent and reason. For each situation pictured in the table that follows, represent gravitational force or the electric force that the object of source mass or source charge exerts on the object of test mass or test charge at the points shown. a) Use a field approach to explain in words how the source object can exert a force on test objects without directly touching them at each of these points. For the gravitational field, discuss how the magnitude of the force may depend on the properties of the field, on the mass of the source object, and on the distance away from the source object. Consider similar factors for the electric field. b) Discuss how the presence of a source mass or a source charge alters the space. How far do you think this alteration extends? c) Discuss whether a system that includes Earth and the test object possesses gravitational potential energy. Discuss whether a system that includes the source charged object and the test charged object possesses electric potential energy. Does each energy depend on the magnitude of the source mass or the test mass? On the source charge or the test charge? Lessons are modified from the Active Learning Guide, Etkina and Van Heuvelen 1

2 Did you know? We cannot see electric fields created by charged objects; we only know about the field s presence at different locations by placing other charged objects at these locations. The presence of the field is induced by how the motion of the charged object is changed. We call the objects that probe the field test charged objects (or simply test charges) and the objects causing the field source charged objects (source charges). The test charge has to be small so that it does not alter the location of the source charges creating the field. Physicists define two quantities to describe the field produced by a source electric charge in the space surrounding the charge. For a particular point in that space, one field quantity is related to the force that the field exerts on a test charge placed at that point. (This is a VECTOR quantity). The other field quantity is related to the electric potential energy that a test charge has at that point (this depends on the choice of zero level of potential and is a scalar quantity). We use the name, electric field intensity or simply, electric field for the first quantity and the name electric potential (V field) for the second. 1.2 E-Field Lab 1. Go to Once the simulation is open, a green box in the bottom right hand corner will appear. Click on grid and a grid will appear on the screen. Above the green box there is a box for E-field sensors, and 1 nc positive and negative source charges. (Remember: nc = 10-9 C) Place a positive source charge at any position on the grid. Then place the E-field sensor at various positions around the source charge, click on Show E-field and observe the arrow. Place the positive 1nC back into the red box and take out a negative source charge. Again, place the E-field sensor at various positions, click on Show E-field and observe the arrow. a) Discuss how the arrow is consistent with the process for finding the E-field at a point in space near a given source(s)? Why are the arrows part of the simulation? b) Place multiple sources on the screen; what happens to the arrow? What else can we conclude about the arrow? c) How does the magnitude of the E-field at any point A depend on the source charge? Test charge? The distance between the source charge and point A? Lessons are modified from the Active Learning Guide, Etkina and Van Heuvelen 2

3 1.3 Practice: There are three charged particles below. For each of the dots (A,B,C), represent the E field at that given point with labeled vectors. C A B Q=+q Q= -2q Q=+q 1.4 Diagram Jeopardy. E field vectors due to one or more electrically charged objects are shown below. Indicate with circles, including the + or signs, the charged source objects creating the field. a. b. Lessons are modified from the Active Learning Guide, Etkina and Van Heuvelen 3

4 Electric Field Lines An E field can be represented with E field lines. They have the following properties. The direction of the E field line at a point is in the same direction as the E field at that point. E field lines start on positively charged objects and end on negatively charged objects. The magnitude of the field at a point is represented by the density or concentration of the lines near that point. A corollary to this idea is that the number of lines leaving or termination on the charged object is proportional to the charge. 1.5 Reason. Examine the definition above and answer the following questions on E field lines. a) Can E field lines ever cross? b) What is the direction of the E field directly between two positive equal magnitude charged particles? Explain why this happens. Draw an example c) What is the direction of the E field directly between two negative equal magnitude charged particles? Explain why this happens. Draw an example. Lessons are modified from the Active Learning Guide, Etkina and Van Heuvelen 4

5 1.6 Electric field Hockey (Electric field hockey is a property of the University of Colorado) On the computers, go to. Answer the questions that follow. a) Set the difficulty to practice. When you drag a positive charge out of the bin on the top right and put it on the hockey table, which direction is there an arrow pointing from our black test charge? Why does it point in this direction? b) Drag a Negative charge out of the bin and place it on the field. You will notice the arrow that comes from the test charge points towards this new charge placed on the table. How does the arrow s length depend on the distance between the source charge and the test charge? Is the relationship linear? Why does it exhibit this pattern? c) Position the source charges so you can shoot the test charge into the goal. Press start and try it out. d) With a single positive and negative charge on the table separated by about an inch, click the box that says Field. Describe the direction the clear/white arrows on the table point. What do you think these Field arrows represent? e) Using a few combinations of charges, try to score goals on all three of the difficulty settings. (Don t let the puck leave the table). Take screenshots of your goals and them to me (msbuggescience@gmail.com). Lessons are modified from the Active Learning Guide, Etkina and Van Heuvelen 5