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Transcript
Sierzega: Electric Fields 1 Electric Fields Did You Know? 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 (a vector quantity). The other field quantity is related to the electric potential energy that a test charge has at that point (this one depends on the choice of the zero level of potential energy and is a scalar quantity). We use the name electric field intensity or simply electric field ( E field) for the first quantity and the name electric potential (V field) for the second. E field: To determine the physical quantity called E field at a point, you need to place a small positive test charge qtest at that point. Then measure or calculate the electric forces that other electrically charged objects exert on it, find the sum of these electric forces, and divide it by the magnitude of the test charge: Felectrically charged objects on qtest E= qtest If the E field at a point is due to only a single source charge qsource, then the E field equals the electric force exerted on a test charge qtest by the source charge qsource at that point divided by the test charge: Fq source on qtest E = qtest 1.1 E-Field Lab http://phet.colorado.edu/en/simulation/charges-and-fields 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. 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? Sierzega: Electric Fields 1 1.2 A small aluminum ball is charged with +1.0 x 10-9 C. Determine the magnitude of the E field due to this source charge at the four points shown below. Represent the E field at each point using an arrow. Use the simulation to predict the magnitude and direction of the E field at each point. 5 cm to the right of the ball + 7 cm to the left of the ball + 1 cm above the ball 10 cm below the ball + + 1.3 Reason Place two +1 nC sources at one position on the grid. Three meters away place three -1 nC sources. Predict the magnitude and direction of the E-field vector 1 m to the left of the negative sources and then 1 m to the right of the negative sources. 1.4 Reason Place a +1 nC source at one position on the grid, move down 2 meters and to the right 2 meters and place a -1 nC source there. Predict the E-field at one of the corners of the 2 m x 2 m square. 1.5 Reason Place three positive charges around a 2 m x 2 m square and predict what the E-field will be in the empty corner and again in the middle of the square. Sierzega: Electric Fields 1 1.6 There is a 1.24 g object near Earth that has an excess of charge on it. There is a uniform E field directed downwards of magnitude 475 N/C. What must the excess charge (sign and magnitude) be in order for the object to remain stationary? 1.7 A charged object with charge -6 nC remains at rest at position x = +1.0 m. a) Find the magnitude and direction of the E -field at x = +0.6 m. b) At what location(s) does the E -field have a magnitude of 4 N/C? 1.8 A charge, q1 = 5.0 µC, is at the origin, and a second charge, q2 = -3.0 µC, is on the x-axis 0.80 m from the origin. a) Find the electric field at a point on the x-axis 0.400 m from the origin. b) Find the electric field at a point on the y-axis 0.400 m from the origin. 1.9 Two charged objects of +5q and -q are placed at positions y = +0.0 m and y = +0.5 m, respectively. a) Determine the E -field at position y = +0.25 m. b) Find the location at which the E -field is zero. 1.10 A -2.5µC and a +6.0 µC charged objects are 1.0 m apart from each other. Determine the point (other than an infinite distance away) at which the total electric field is zero. Did You Know? Electric field lines: An E field can be represented with E field lines. They have the following properties: E field vector at a point is tangent to the direction of the E field line. 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 terminating on a charged object is proportional to the magnitude of its electric charge. Sierzega: Electric Fields 1 1.11 Represent and Reason Draw E field vectors and E field lines for the electric field created by the source charged objects described in the table that follows. Explain the difference between vector and line representation and how the vectors help you draw the lines. (a) A point-like positively charged object. (b) A point-like positively charged object with twice the magnitude of charge as in (a). (c) A point-like negatively charged object. (d) A point-like negatively charged object with twice the magnitude of charge as in (c). (g) A small positively charged object and a small negatively charged object of equal magnitude charge separated by a distance s. (h) A small positively charged object and a small negatively charged object with twice the magnitude electric charge separated by a distance s. + + (e) Two positively charged point-like objects of equal magnitude charge and separated by a distance s. (f) Two negatively charged point-like objects of equal magnitude charge and separated by a distance s.