Lab 5: Equipotentials [0NLINE) Contents: I. Introduction ............................................................................... 1 ll. Setup ...................................................................................... 2 III. Mapping Equipotential Lines ....................................................... 3 IV. Conclusions ............................................................................... 6 I. Introduction Purgse If you have a set of points that are all at the same potential these are called equipotentials and a line connecting a set of equipotential points is called an equipotential line. In this lab we will map these lines for different charge distributions. The following equations may be useful (5 is a dummy variable meaning it can be x, y. 2, etc): E = 5 Electric Field More accurately electric field is the gradient of the potential ( E = _W) meaning the three dimensional derivative that gives you the path of steepest descent. By the end of this lab you should be able to: . Have an intuitive understanding of electric potentials and fields for some basic charge distributions. 0 Determine the relationship between electric field and electric potential. Materialsr'Eguigment Charges and Fields Phet Simulation httpsphet.colorado.edufsimsfhtmllcharges-and-eldsllatestlcharges-and-fields en.html ll. Setup 1. 2. 3. Open the simulation. Uncheck all the options except gridlines. Know where the voltage meter and ruler are. lll. Map the equipotential lines and electric eld lines A. TWO LINES PROCEDURE 1. 2. 3. 4. Draw two straight lines out of charges on the grid spaced about 3 meters apart (see image). Check the voltages on the blue charge line and the red charge line. Use graph paper or a screenshot of your image to plot lines of equal voltage leguipotential lines] by using the voltage probe to trace a line where the voltage is the same along the line. Do this by moving the mobile probe along the grid until you find a point where the multimeter reads 0.0 V. The point will not necessarily be right at one ofthe grid markings. Use a screenshot or hand drawing of what you see on the screen (if not a screenshot I recommend using graph paper). It is important that you do this to scale. Draw a dot on the image or graph paper corresponding to this point (you may use a pencil to record the points). Then nd another point a few squares away which is at the same voltage. Repeat until you feel condent you have mapped out all the points on the grid that are at 0.0 V; then draw a line connecting these points. As the pattern develops, you may find it easier to anticipate where the points will fall. Be sure to check over the entire grid, however, including behind and to the side of the electrodes. Label the line "0.0 V." . O I I O O I Repeat the above procedure to map at least 6 more lines of varying voltages between the values you read off the blue and red charge lines. QUESTIONS 1 . Represent the electric field lin (NOT VECTORS) by drawing 8-10 equally spaced, continuous lines which are everywhere perpendicular to the equipotential lines. Draw arrows on the eld lines indicating the direction of the electric eld. Use a different color from the color used to map the equipotential lines. a. Where do the field lines begin and end? b. Describe the field line density. Where are the electric field lines closest together? Where are they farthest apart? Why? 2. What, approximately, is the potential midway between the two conductors? 1. What, approximately, is the strength of the electric field midway between the two conductors? Hint: You will need the voltage difference between two lines near the center and their distance apart. Calculate first, showing your work, then use a sensor to check.B. TWO CIRCLES Repeat the mapping for the sheet with two circles. Draw an evenly spaced positive and negative ring in your simulation and repeat the procedure from the previous section. QUESTIONS 2. Represent the electric field lines by drawing 8-10 equally spaced, continuous lines which are everywhere perpendicular to the equipotential lines. Draw arrows on the field lines indicating the direction of the electric field. Use a different color from the color used to map the equipotential lines. a. Where do the field lines begin and end? b. Describe the eld line density. Where are the electric field lines closest together? Where are they farthest apart? Why? 3. What, approximately, is the potential midway between the two conductors? 4. What, approximately, is the strength of the electric eld midway between the two conductors? You may nd it easier to answerthis question if youjust measure the potential at a few points near the center. Calculate rst, showing your work, then use a sensor to check. C. RANDOM SHAPE Repeat the mapping for a third, different pattern. Make two random shapes and repeat. QUESTIONS 1. Sketch in a set of electric field lines on your plot of equipotentials. Where is the electric field the strongest? What, approximately, is its magnitude? 2. Where is the electric field the most uniform? How can you tell?VI. Questions 1. What changes if you switch which side is red (positive) and which is blue (negative)? 2. If you wanted to push a charge along one of the eld lines from one conductor to the other, how does the choice of field line affect the amount of work required? (Think carefully about work and how it relates to potential and potential energy.) 3. The potential is everywhere the same on an equipotential line. Is the electric eld everywhere the same on an electric field line