An electron is moved through a region with anelectric potential defined by the e

Question

An electron is moved through a region with anelectric potential defined by the equipotential lines shown(position is given in meters, time is given in seconds, andelectric potential is given in volts).   Rank the work done by the external force (smallest to greatest) forAnimations 1--5. Explain the basis for your ranking. The animation can be found at http://pages.towson.edu/jrsimpson/PhysletsCD/contents/electromagnetism/e_potential/default.htmlphyslet problem 25.3.
So far I think that the 0V one should be the smallest (soanimation 1) because it doesn't change to a different V but then Iam not sure about the others.   An electron is moved through a region with anelectric potential defined by the equipotential lines shown(position is given in meters, time is given in seconds, andelectric potential is given in volts).   Rank the work done by the external force (smallest to greatest) forAnimations 1--5. Explain the basis for your ranking. The animation can be found at http://pages.towson.edu/jrsimpson/PhysletsCD/contents/electromagnetism/e_potential/default.htmlphyslet problem 25.3.
So far I think that the 0V one should be the smallest (soanimation 1) because it doesn't change to a different V but then Iam not sure about the others.  

Explanation / Answer

There are two important points to remember: 1) an electron is negatively charged. This willmean that when moving to a higher potential ("voltage") it will be"rolling down hill" and the work done by en external force will benegative! 2) the physical "work" definition (which includes negative and zerowork) only cares about the difference in the beginning and finalpotential. 3) Since we are only ranking work for one specific charge we canuse Volt, without caring that it is actually a measure of potentialenergy per unit charge. (Work has the same unit as enrgyNm=J=Ws) If I move a positive charge from -3 Volts to +6 Volts, theextern force will have to do work corresponding to the 9 Voltdifference. If it were a negative charge the force could receiveenergy (do "negative work") as the negative charge was pulled bythe electric field. Figure out the work for all five cases and put them in order. (It'spossible that some might be equal!)

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