Electric Field Mapping

Transcription

1 Name: Date: PC1143 Physics III Electric Field Mapping 5 Laboratory Worksheet Part A: Parallel Electrodes Distance between parallel electrodes: d = Attach your plots of equipotential lines and electric field here. Question A-1: (1) Draw the best smooth curves through the points at the same potential. These are the equipotential lines. (2) Draw the electric field lines. Starting at the positive electrode on your diagram, draw a line to the negative electrode in such a way that the line always crosses an equipotential line at right angles. Draw 6 9 field lines through the region between the electrodes and the regions above and below their ends. Use arrows on the lines to show the direction of the electric field. Page 1 of 6

2 Electric Field Mapping Laboratory Worksheet Page 2 of 6 Analysis A-1: Estimate an experimental value for the electric field strength E in the central region between the electrodes and its associated uncertainty with the appropriate number of significant figures. Show a sample calculation and be sure to attach a copy of the spreadsheet to your laboratory report. Experimental value: E = ± Part B: Concentric Electrodes Radius of the central cylindrical pole: a = Inner radius of the ring electrode: b = Attach your plots of equipotential lines and electric field here. Question B-1: (1) Draw the best smooth curve through the points at the same potential in the interior region. (2) Draw 8 electric field lines in the interior region. Use arrows on the lines to show the direction of the electric field.

3 Electric Field Mapping Laboratory Worksheet Page 3 of 6 Question B-2: Show that the electric potential in the interior region between a positively charged cylinder with radius a and a negatively charged cylindrical shell with inner radius b (b > a) is given by ( r V (r) = V a V m ln (1) a) where V a is the electric potential at r = a and V m is a constant. Analysis B-1: Determine the average radius for each equipotential line and tabulate the values of the potential with the average radii. Measure the radius from the center of the positive electrode, so that the outer radius of the positive electrode is at r = a and the inner radius of the ground electrode is at r = b. Show a sample calculation. Electric Potential V (V) Average Radius r (cm) #1 #2 #3 #4 #5

4 Electric Field Mapping Laboratory Worksheet Page 4 of 6 Analysis B-2: Perform a linear least squares fit to your data with the electric potential V as the vertical axis and ln(r/a) as the horizontal axis. Plot a graph of electric potential V against ln(r/a). Also show on the graph the straight line that was obtained by the linear least fit to the data as well as the error-bar of your data. Be sure to attach a copy of the graph (with the spreadsheet) to your laboratory report. Gradient: ± y-intercept: ± Correlation coefficient: Analysis B-3: The gradient of the plot V against ln(r/a) is V m. Determine a theoretical value for V m from the equation (1) directly using the fact that V (r = b) = 0. Also, determine the experimental value for the constant V m from your results of your linear least squares fit above. Compare it with the theoretical value using percentage discrepancy. Show your work. Theoretical value: Experimental value: ± % discrepancy = % Analysis B-4: Tabulate the electric field strength at the radii of the equipotentials. Show a sample calculation. Electric Field Strength E (V/cm) #1 #2 #3 #4 #5

5 Electric Field Mapping Laboratory Worksheet Page 5 of 6 Part C: Circular Electrodes Distance between two side poles from center to center: L = Attach your plots of equipotential lines and electric field here. Question C-1: (1) Draw the best smooth curve through the points at the same potential. (2) Draw 8 electric field lines, starting at 8 symmetric points on the positive electrode. Use arrows on the lines to show the direction of the electric field. Analysis C-1: Determine the distance of each equipotential line from the surface of the negative electrode along the central axis from the negative electrode to the positive. Tabulate the electric potential at the distance from the surface of the negative electrode. Electric Potential V (V) Distance x (cm) 0

6 Electric Field Mapping Laboratory Worksheet Page 6 of 6 Analysis C-2: Along the central axis from the negative electrode to the positive, the electric field should follow a straight line, although it is not constant in magnitude. We can find an approximate value for the field at points along this central axis by using E V/ x for closely spaced points. Determine the electric field strength at the midpoint for each pair of adjacent equipotential lines along the central axis from the negative electrode to the positive. Show your work. Midpoint Distance x (cm) Electric Field Strength E (V/cm) 6 Laboratory Report Submit a laboratory report within ONE week after your laboratory session. Important: Before leaving the laboratory, have a demonstrator initial on your data table(s)! Last updated: Wednesday 14 th January, :43pm (KHCM)