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3. Physics 202 Lab 2 Plotting Electric Field Lines

Lab #2 Plotting Electric Field Lines

1. Is there a physical principle that requires that electric field lines are drawn starting on positive charges and ending on negative charges? If your answer is yes, what is that principle? If your answer is no, why are they always drawn that way?

The electric field is defined as the force upon a positive test charge at the location around another defined charge. Because the test charge is assumed to be positive it makes sense that when drawing these lines they should follow the path that a positive test charge would follow, so starting at the positive side and moving towards the negative charge is justifiable.

2. Is the equipotential pattern what you expected for your electrode configuration? Justify your answer by comparing and contrasting your experimental results to the theoretical patterns provided in class or in the textbook. Answer this question separately for each graph you completed.

The equipotential pattern is very similar to that found online. For the parallel plate configuration, for the region between the two plates the equipotential lines are evenly spread out and remain for the most part parallel between the plates with a slight curving beyond the length of the two plates.

For a dipole the data found matches that of theoretical equipotential lines, with small circular regions very close to each charge and with growing radii until the middle in which the middle, at roughly 5 V, the equipotential line is vertical. This relationship can be seen in the graphs formed from the data collected.

3. Is the electric field pattern what you expected for your electrode configuration? Justify your answer by comparing and contrasting your experimental results to the theoretical patterns provided in class or in the textbook. Answer this question separately for each graph you completed.

The electric field pattern was almost exactly similar to theoretical models for that of the parallel plate configuration. This is because between the heights of the parallel plates the E-field lines are all basically straight lines from the positive plate to the negative plate. Towards the outer region there were also slight curves outwards but for most of the portion of these E-field lines in this region they still remain parallel to the other lines.

As for the field lines for the dipole, in the center they are almost a straight shot from the positive end to the negative end. For the other lines, they bend outwards but always loop back towards the negative dipole just as seen in theoretical models.

4. How did your equipotentials behave behind the electrodes (toward the edges of the page) as compared to between the electrodes (near the center of the page)? How do you explain this behavior? Answer this question separately for each graph you completed.

For the parallel plates, behind the electrodes the voltage remained around 9V and clear cut equipotential lines were very difficult to line out.

For the dipole the equipotential lines were more spaced out than the area between the electrodes. This is because they were at an area where they were less impacted by the pulling force of the negative electrode so the strength was only dependent on the positive electrode.

5. What is the relationship between the density (spacing) of electric field lines and the strength of the electric field?

The denser the spacing of the electric field lines are the stronger the electric field is, the stronger the electric field is between.

6. Did the areas of greatest electric field line density correspond to where they should be theoretically? Explain your answer. Answer this question separately for each graph you completed.

For the dipole between the two plates the spacing was very evenly spaced out showing the same strength of electric field throughout, which is theoretically correct. The only extra spacing was towards the outside of the two electric plates, which in theory should be a weaker electric field as shown in our graph.

For the dipole configuration the E-field lines were clustered close together in the region between the two electrodes and, just as theory shows, more spread out through the regions higher and lower than the line directly through the electrode, showing that the E-field in those regions was weaker than directly in between.

7. If you were to move a proton along one of your equipotential lines, a. would there be any work done and b. how would the energy of the proton change?
   1. There would be no work done.
   2. The energy of the proton would be the same.

8. Similarly, if you moved a proton following one of your electric field lines, a. would there be any work done and b. how would the energy of the proton change?
   1. If the proton is moved in the direction of the field lines the work would be positive and if moved in the opposite direction of the field lines, the work would be negative.
   2. Moving along the lines of the E-field lines, the potential energy would become less and less and moving it against the lines of the E-field the potential energy would rise.

9. Type an error analysis following the information in the back of the lab manual. You must list and classify all the errors that you encountered in this experiment. Remember, if you made a mistake but corrected it, this is not an error in the experiment.

One of our errors stems from the fact that we took each equipotential line to the tenth place. To diminish this source of error we could have taken much more careful readings, but this would have cost us a lot of time that we could not afford.

By using our best drawing skills to draw in the electric field lines, the field lines may be slightly skewed. Using a ruler would not fix this situation due to the fact that the E-field needs to cross every equipotential at perpendicular angles. Perhaps by going back and taking 20 equipotential lines instead of only 10 we would be able to have much more clear cut E-field lines.

Another source of error could have stemmed from the translation of the points of equipotential on the actual source conductive graph paper to the recorded paper graph paper. A way to minimize this would be to perhaps have a graph paper with a grid array that was more tightly spaced.

One last source of error may have come from faulty readings from the actual source conductive graph paper itself. The only way to remedy this would be to use a fresh conductive paper for every lab, but as the materials are expensive and require preparations to get the electrodes painted on this may be improbable.