Visualizing Gauss’s Law with Onions

Jen Kaelin is a longtime AP Physics reader.  Once when we were grading the same question, we competed to see how many hand turkeys we could find drawn on part (c)*.

* Not really, College Board Lawyers.  The competition was something I made up just now for humorous value.  The hand turkey was authentic, though.

The other night she told me about her frustration and then elation at her AP Physics C E&M class as they struggled to understand Gauss’s Law.  They simply couldn’t effectively visualize some Gaussian surfaces.

I’ve had good luck before bringing in physical items to help with more difficult visualizations in E&M.  My personal favorite* was the top of a sour cream container for visualizing magnetic flux. Know which way the magnetic field points, then place the sour cream top where the wire loop is.  This allows you to see, in three dimensions, whether the field lines penetrate the sour cream top, whether they point alongside the sour cream top and thus produce zero flux… or somewhere in between.  

* And my students’ favorite, as they walked into the exam and all told the proctor confidently and firmly, “Mr. Jacobs TOLD us all to bring these sour cream tops into the exam.  Yes, really. And the top to a butter container is acceptable too, he said, but not margarine because he hates margarine.”

I also used the sour cream top when the Gaussian surface required was the “pillbox”, as with a very large plane with two-dimensional charge distribution.  But a spherically symmetric charge distribution requires abstraction. I can show my class a sphere - a racquetball, e.g. - but they can’t open up the racquetball to see the charge distribution inside.

Unless you use an onion, like Jen did.

Jen brought in onions, peeling back layers to visualize how the volume and surface area get much smaller as the radius decreases.  She found plush onions online, and many of her students started carrying these around school. First as a joke, I’m sure, but the mnemonic stayed with them.  Jen finally felt comfortable with her class’s ability to use Gauss’s law under spherical symmetry.

You got a good physical manifestation of an abstract idea?  Post a comment…

Heresy: I don’t even mention the difference between speed and velocity

From John:

If a velocity is negative and the object is slowing down, do we say its velocity is decreasing since the magnitude is getting smaller, or do we say it is increasing since it is getting a higher value on the y-axis of a velocity/time graph?

Simplest answer: the question is not well posed.  Are we talking about the magnitude of the velocity vector, a.k.a. the speed?  Or are we talking the mathematical velocity function? The mathematical function is increasing; the speed is decreasing.

Better answer: This is a prime example why I avoid negative signs in first-year physics.  As soon as we talk about velocity as being positive or negative, we introduce an unnecessary abstraction that does nothing but impede comprehension.

Sure, you can try to resolve the conundrum by explicitly defining a positive direction, making a velocity-time graph, and explaining that while the velocity function increases, the absolute value of the function decreases, so the object slows down.  This is still too mathematical for first year students. Such folks do not have the intuitive understanding of functions that we physics teachers do. Don’t believe me? Give a quiz on which you ask them to define “magnitude” in their own words, without feeding them a canned textbook definition.  They will have no clue.

I know it is heresy of the highest order, and I will likely be stuck down by a bolt of lightning*.  But I recommend using the terms “speed” and “velocity” interchangeably, as synonyms. I try to say “speed” as a rule, but problem statements from external sources and students themselves use the word “velocity,” so I just translate to “speed.”

*Or a tornado… forty AP physics readers had to huddle in the lobby of the Crown Plaza last night as the local news blared with video of the apocalyptic storm which passed maybe a mile to our west.  Veteran AP readers have now lived through tornadoes in Nebraska, Colorado, and Missouri. Perhaps we could hold the reading in Vancouver?

Now there’s no conundrum!  In John’s case, the object is slowing down, so the speed is decreasing.  That’s, um, what “slowing down” means.

True, students have to work through some confusion on velocity-time graphs.  The fact sheet we use teaches students to memorize that speed is found by the vertical axis of a v-t graph; and the direction of motion is determined by whether the graph is above or below the horizontal axis. Above the axis represents motion “away from the detector,” while below the axis is motion “toward the detector.” (See, no use of the word “negative”!).  

The first time that someone organically encounters John’s graph, where (in mathematical language) the velocity function increases but speed decreases, some students are certainly confused.  Especially the mathematically astute folks want to tell me that the cart speeds up because the function increases, getting less negative. What do I do? I answer loudly, so the whole class hears, with one of the following lines of reasoning, both of which end in a wry smile:

* What’s the vertical axis value at the end of the cart’s motion?  (Zero.) How can a cart speed up to a stop?  :-)

* You are pulled over by a police officer, who writes you a ticket for going 100 mph.  In court you argue, “but your honor, I was traveling southbound, which is the negative direction… so my velocity was negative 100 mph.  That’s significantly less than the posted limit of +65 mph.” Good luck. :-)

How, then, would a student explain such a graph? Ideally, they’d say “The vertical axis values are getting closer to zero, so the cart’s speed is getting closer to zero.  That’s slowing down. Since the graph is below the horizontal axis, the cart is moving toward the detector.”

I know this method will be pooh-poohed by many physics teachers, especially those who spend two full lab periods trying to teach the rigorous mathematical difference between speed and velocity.  You don’t have to teach my way. Yet, please look at the results. My conceptual freshmen can interpret the physical meaning behind motion graphs - by year’s end, they can do AP-level motion graph problems.  In AP, I do mention months later that “velocity” means include direction, while “speed” means do not. My AP students average above 4 on the exam… so I’m not hurting their comprehension.

Point is, try it.  Eliminate technical mathematical terminology from your physics class wherever you can.  Speed and velocity is a great place to start.

And if you read “Physics Teacher Hospitalized with Lightning Burns” as a headline in the Kansas City Star, you’ll know what I did to bring on such divine wrath.  

Does a student who disrespects the AP exam "count against" the teacher?

On a physics teacher message board, someone asked:

If a student actually uses the Christmas Tree method or all Cs to answer all or part of the multiple choice questions.. 

Does this count against the teacher?

Just wondering... for a friend.... 

I'm not clear what you mean by "count against."  :-)

There is no College Board Secret Police.  You - and your administration - will see your students' scores on a 1-2-3-4-5 scale.  You may access a slightly more detailed report, indicating your students' overall performance broken down by topic.  That's it.  No one sees the multiple choice other than the computer who scores it.  

The readers see the free response.  I suppose that if the student writes "Kick Ms. Lipshutz in the butt for me" on the free response, one reader in one room in Kansas city will see that for approximately two seconds - that's how long it takes to write a zero and move on to the next problem.

The readers are not allowed, and not able, to track down teachers whose students give crap answers to the free response.  (We're not allowed or able to track down the ones whose students give awesome answers, either.)  The process is pretty danged anonymous.  

So, nothing to worry about.  If a student says (s)he made a christmas tree, consider that he or she is almost definitely exaggerating for the sake of playing misery poker with friends; or, they're trying to get a rise out of you.

Of course, the next step is to build your physics culture all year such that the student who says "I just bubbled christmas trees cause I don't understand anything" earns sneers from classmates.  You don't need to respond to such a student, other than to give them the same look you'd give a 14 year old who eats mashed potatoes with their fingers at a formal meal: not as much disapproving as disbelieving and pitying.  It's when the rest of the class gives that student a similar look that you know you've established the right tone.  That takes a few years.

2019 AP Physics 1 exam: Solutions

I've posted my solutions to the 2019 AP Physics 1 free response exam questions.  The questions themselves are available at this College Board link.  

My solutions are available via the "Pretty Good Physics" google group, using this teachers-only link.  If you are a teacher and would like to access these solutions, you must first sign up for the google group.  Gardner Friedlander runs the group - he will send an army of dagrons to utterly burninate you if you request access but are not a physics teacher.  He checks.  

Comments: I like the center of mass graphing question - the big deal is that the system center of mass doesn't change speed unless a net force acts.  

The experimental question can be done many different ways... Kristyn of Georgia noted that she set spring potential energy equal to gravitational potential energy rather than kinetic energy - that works just fine if you measure height rather than speed.  What a wonderful question.

The waves question had two(!) plug-and-chug calulational pieces.  Weird and unexpected, but certainly straightforward.  My students made the graph upside down... they had been talking about nodes in pressure rather than antinodes in particle displacement.  Who cares.  They'll get most credit.

Please let me know what I've missed... as always, I guarantee I would earn a 5, but not that I have gotten everything perfect.  

GCJ

Should I pay to get my students' AP exam booklets back?

On a physics message board, the question was asked: is it worth paying the College Board to get your students' AP exam booklets back?  Here's my answer...

It is SO not worth it.  They just give you the students' free response exam booklets - no other feedback.  Yes, you can look at the released rubrics and figure out their score on each question.  But that's trying to groom the horses long after they've escaped from the barn.  

You have access to so many officially released problems and rubrics from previous years!  Use those, especially during March and April.  You'll have a pretty danged good idea of what your students can do.  If one particular student over- or under- performs, don't worry about it.  If the whole class over- or under- performs compared to their scores on released rubrics in March and April, then look at the (free) score report to see if you can figure out what happened.  Your time is better spent preparing for and working with next year's students than trying to figure out the details of this year's class's performance.  

I suggest here thinking of a perspective integrated over multiple years, over multiple classes of students.  In that long term, any individual's exam, any individual's particular response, will be lost in the overall performance.  If you're consistently doing better on multiple choice than free response over many years, then it's worth taking action to improve free response.  If you're consistently bombing the circuits questions, then take action to improve the circuits portion of your class.  But these sorts of patterns can be gleaned from the information that the College Board gives you for free.