Between the two lines which makes logical sense as

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between the two lines, which makes logical sense, as the existence of the two potentials will create an intense electrical field in between, and a mild electrical field elsewhere. This idea, that the equipotentials tend to follow curvature is supported by the concentric circle data as well, as their shape there matches the geometry of the electrodes, that is, of concentric circles. However, we see more interesting results with the other geometries. If we take a conducting, closed shape and put it in between electrodes, it will act as a sort of Faraday cage, blocking out any electrical potential differences generated by the electrodes. In addition, it will distort the electrical fields around it, bending the equipotentials with respect to its curvature. This tends to make sense with how we suspect a conductor to behave in the presence of charges. Further away from the closed shape, we see what we expect from a pair of parallel lines, indicating that this more complex case is simply building off of the simplistic case. Similarly, for the oddly curved shape, we see equipotentials that follow the curvature of the curved shape on one side, whereas on the other, we find the expected potentials for a line of charge. However, within the curved shape, the potentials behave oddly, being similar to a line of charge close to the other electrode, and then curving as the potentials re-interact with the curved shape. Lastly, the point does not make a sharp point in equipotentials as might be guessed, but rather, the potentials become extremely close together, telling us that the point has both a large gradient in electrical potential, and thus, an intense electrical field as compared to a side of the triangle. The rest of that test is similar to what we have seen for lines. Thus, in a qualitative sense, we may generalize this for all states of two potentials, that potentials will follow the curvature of the nearest conducting surface. As a corollary to that, if there is a surface that is enclosed and has no charge associated with it, there will be no difference in the electrical potential within the surface. The exception to this is a point; a point and other sharp
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Christopher Reinemann
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