In the diagram below, a large metal plate with a uniform charge density - sigma
ID: 2019576 • Letter: I
Question
In the diagram below, a large metal plate with a uniform charge density - sigma is a distance d above two positive terminals that are a distance L apart. Charge q1 moved from point A to point B along path 1, and q2 moved from point B to point A along path 2. Point C is equidistant from A and B. and q2 = q1. Which charge had the largest change of potential? Justify your answer. (Note: The grade for this question is based entirely on your justification. No credit will be given for an answer without a justification, even if it is correct.)Explanation / Answer
The change in potential is proportional to the amount of work done,
W = qV
So think about the work done. Work is done by the particle moving through the force field. There are two kinds of forces relevant to work: conservative and non-conservative. Conservative forces perform work independent of the path taken, but only due to the total displacement. Recall that the Coulomb force is conservative (a consequenc of the fact that a force is conservative is that it can be described with a potential energy, and the Coulomb force has a potential energy associated with it). Since the Coulomb force is conservative, then the path taken by the particle doesn't change the amount of work done, since theyre both the same charge. So, since q1 = q2 and the two works are the same, they both undergo the same change in potential energy.