Each diagram in Fig 2 depicts a force field in a region of space. (c) For each c

Question

Each diagram in Fig 2 depicts a force field in a region of space.

(c) For each case, is it possible to draw a self-consistent set of equipotential contours for that situation? If so: Draw them! (Each drawing should clearly show the correct shape of the contour lines, the correct relative spacing of the contours, and label the regions that correspond to highest and lowest potential energy) If not: Explain why drawing such contours is impossible.

Each diagram in Fig 2 depicts a force field in a region of space. (a) For which force fields can you identify a closed path over which ? For each such case, clearly indicate an appropriate path on the diagram. (b) For each case indicate if gradient x F = 0 everywhere in the box? Also, for each case, could the force depicted in the diagram be conservative? Briefly, explain. (c) For each case, is it possible to draw a self-consistent set of equipotential contours for that situation? If so: Draw them! (Each drawing should clearly show the correct shape of the contour lines, the correct relative spacing of the contours, and label the regions that correspond to highest and lowest potential energy) If not: Explain why drawing such contours is impossible.

Explanation / Answer

A conservative force does equal work on an object as that object moves from some point a to another point b, independent of path taken. In other words,

if electric force were conservative, then no matter how a particle decides to move from a-->b, the same work is done on it by the electric force. And, indeed, the electric force is conservative.

If electric force weren't conservative, there really wouldn't be any such concept as "potential difference."

If you think about it, when we say that the potential difference between two points is x, that potential difference is INDEPENDENT of path.

If electric force weren't conservative, the potential at point b would depend on how you got there from point a (a zigzag versus a straight line, for example).
No work is done moving a charged particle perpendicular to a field (along equipotential surfaces)

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