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16 January 2014

Quiz question: What is the electric potential at points A and B?

An electron gains kinetic energy in moving 7 cm from point A to point B.  The potential difference between A and B is 21,000 V.  
(a)   What is the electric potential at point A?
(b)  What is the electric potential at point B?

This is in the classic style of my quiz questions -- the student who can recite and use facts of physics jumps straight to an answer, while the student who is "thinking too much" ties his brain in knots.  I frequently ask simple questions in all sorts of different contexts.  Part of Bill Belichick's* genius is running similar plays but out of completely different formations, confusing all but the best-prepared defenses.  I try to do for physics what he does for football offense -- same ideas, different formations.

* Bill Belichick is the head coach of the New England Patriots football team.  He and his public persona provoke a huge variety of emotions in football fans, the positiveness of which usually correlates to a fan's distance from Boston.  No one doubts, though, that he is a football genius, the most successful head coach since Vince Lombardi.  Based on his success, his public demeanor, and his looks, he is often compared to the Galactic Emperor.

After a few days my students can all tell me that a negative charge is forced from low-to-high potential.  But soon we get in to sources of potential, the equation for potential due to a point charge, and don't forget all the stuff with electric fields.  So it's worth asking a basic question in a new context.

The answer to the question above is straightforward from the facts:  Since the electron "gains KE," it experienced a net force toward point B.  Since an electron is forced from low to high potential, point B must be at a higher potential than point A.  Since the potential difference between the two points is 21,000 V, point B must be 21,000 V higher than point A.*  

* Point A can be at any potential, any at all.  All that matters for problems with electric potential is the potential difference between two points.  There's no such thing as an "absolute" potential, only a potential compared to some other reference point.

What's so confusing, then?  The window dressing in the wording is confusing.  How many students will see "7 cm" and immediately convert to meters and try to plug into kQQ/d?  How many will just give up when they can't figure out the electric potential at point A, when that doesn't really matter?

Now, some lawyers would whine that this is not a "fair" question.  "Part (a) is a trick!  And you gave irrelevant information.  That's not nice."  

Oh, baloney.  A student who truly understands electric potential recognizes what "potential difference" means in any context, not just when he's asked to spit back a definition.  A student who becomes confused by these questions does not understand physics as well as a student who sees the correct approach; this question becomes an important mechanism toward internalizing a deeper understanding of "potential difference."  The student who gets this wrong and learns from the mistake will likely do well on the AP exam (or on the class final); the student who just gets pissy about fairness will not likely do well when faced with AP-style problems that similarly pose questions in new contexts.  Physics class isn't about how many answers we can get right to pad our grades, it's about discovering how the universe works.

You have a simple question in an unusual context?  Let me know in the comments or by email.

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