Electrostatic point charges ranking task poll -- Here's the answer!

Electric field is a vector -- that means that a sum of many electric fields requires vector addition, with arrows.  Just adding up the values of kQ/d^2 does not work.  (I don't care how many times you say this, someone in your class will forget on a test or quiz.)

The electric field created by a point charge points (hah!) away from a positive charge, and toward a negative charge.

Electric field vectors, like all vectors, are best added by placing them tip-to-tail.

Consider diagram 1 in the ranking task.  The top charge creates a field to the right (away from the charge); the bottom charge creates a field up and to the right.  The vector sum of these electric fields is in red below:

DIAGRAM 1



Now consider diagram 2.  The top charge still creates a field to the right, but the bottom charge now creates a field down and to the left (toward the negative charge).  The vector sum of these fields is in red below:

DIAGRAM 2

From the picture, it is apparent that the magnitude of the electric field in diagram 1 is bigger than the magnitude of the electric field in diagram 2 -- the arrow for Etotal is bigger.

Similar reasoning for diagrams 3 and 4 gives the same sized total electric field vectors, but pointing the opposite directions.  Since the *magnitude* of an electric field means the amount of electric field, regardless of direction, we can say that diagram 3's field has identical magnitude to diagram 1's field; and that diagram 2's field is equal in magnitude to diagram 4's field.

Thus the answer:  (1=3), (2=4).

You wanna rank the voltages at point P?  Go ahead, post a comment.

Multiple Choice questions may have more value than you think

It is common for teachers in other disciplines to view multiple choice questions as the lazy teacher's way of avoiding grading.  In physics, that could hardly be farther from the truth.

Even physics teachers often think of multiple choice questions merely as a useful way of evaluating student understanding broadly and quickly -- after all, it takes a student only about 1-2 minutes per question to respond, and a teacher 1-2 hundredths of a second to grade by machine.  A multiple choice question can be even more valuable.  Some ways to use multiple choice questions creatively:

* I've detailed many times the "test correction," in which students earn back half credit on a multiple choice item they miss by explaining the answer thoroughly.

* I've also explained my typical "clicker exercise," in which teams of two students each have a chance to respond to a multiple choice item on the classroom response system.  The ensuing discussions of each questions can be more valuable than the best-designed homework question.

* Multiple choice questions can be expanded into free response-style homework question with the addition of three words: "Justify Your Answer."  Just today I decided that my class had had enough AP free response review homework.  So I took three of the tougher magnetism questions off of the recently released 2009 AP multiple choice exam, printed them out on a page, and assigned the justifications for homework.

* Even after a question has been assigned and justified, you can develop a further quiz based on the situation presented.  For example, consider a typical multiple choice question in which two railroad carts bounce of each other.  Originally, students may have had to find the amount of mechanical energy dissipated in the collision.  For some reason, that calculation frequencly causes trouble.  So, after I've demanded a thorough justification, I give a quiz -- same question, only this time the carts stick together after collision.  If the student truly understood the concept and calculation on the original problem, the new one should be no trouble.

Condider the multiple choice question below:

A car collides with a mosquito.  Which experiences more acceleration in the collision?

(A) The car, by a factor of about 10⁶

(B) The mosquito, by a factor of about 10⁶

(C) The car, by a factor of about 10¹

(D) The mosquito, by a factor of about 10¹

(E) Both experience the same acceleration.

When correcting this problem, some students will obediently go through the Fnet=ma calculation, estimate the mass of the car to be a million or so times the mass of the mosquito, and correctly answer B.  But not everyone will truly recognize the underlying principle here: This reasoning depends on Newton's Third Law, which demands that the forces experienced by each object in the collision must be the same.

So I'll ask this follow up question on a quiz:

A car collides with a mosquito. The mosquito sticks to the car after the collision.

(a) Which experiences more acceleration during the collision, the mosquito or the car?

(b) Which experiences more impulse during the collision, the mosquito or the car?

(c) Which experiences more force during the collision, the mosquito or the car?

GCJ

Preparing for the AP exam -- Huge Equations Quiz

AP-level students need to memorize equations.

Why, you ask?  After all, many professors and teachers pooh-pooh rote memorization, citing the reasonable notion that physics is about the correct USE of fundamental principles, not about their instant recall. 

As a practical matter of teaching Advanced Placement physics, the AP multiple choice section does not provide an equation sheet; thus, a student who does not know that the energy of a capacitor is (1/2)CV² will not get a question right on that topic. (I've had it argued to me that it's better for a student just to know "energy is directly proportional to capacitance, and also to the square of the voltage." First of all, I dispute that a first or second year physics student understands what the word "proportional" means. Secondly, isn't it far easier to remember the equation than this long complex sentence?)

Beyond testing issues, I think it is pedagogically sound to insist that students know the equations that underlie the basic principles under study.  Physics problem solving requires making connections between topics, using multiple intellectual skills at the same time.  Students have a much easier time with multi-step problems if they have the confidence born of rote knowledge of the basic equations, if they DON'T have to spend two minutes of a 15 minute problem searching for the correct relationship on an equation sheet or in a textbook.

I make the memorization requirement clear all year in my AP class.  Equation sheets are never provided, except on the free response portions of tests; students are regularly quizzed on their recall of equations.  The "four minute drill," in which the class is prompted to take turns reciting as many equations as possible in four minutes, is a fun and effective rote review tool. 

I hammer home the need to memorize with a final, enormous equations quiz a couple of weeks before the exam.  The quiz consists of two parts:  20 prompts to which the student must write the correct equation (i.e. I say "net force" and the student replies "ma"), and 5 equations which the student must describe briefly (i.e. I say "ma" and the student says "net force").  The key is, this quiz is not graded on the square root curve -- 60% is the minimum passing score, and 90% is necessary for an A.  And, crucially, a passing score is required in order to pass the course.  I will have a percentage of the class get less than 60% on the first try -- these folks get to try again (with a slightly different quiz) on Monday.  And probably one or two will have to try again on Tuesday.  I've had seniors need four or five attempts to pass.  That's fine -- since they have to pass in order to graduate, they put in the minimal effort to memorize their equations.  Then they get a few more problems right on the AP exam than they otherwise would. 

If you're interested in using my huge equations quiz, check out the link on Scribd: http://www.scribd.com/doc/30391978/102-Huge-Equations-Quiz

GCJ

Summer Fun with Jacobs Physics

Okay, I kind of admit that this post is an advertisement.

I will be running four-- count 'em, FOUR-- Advanced Placement Summer Institutes.  The APSI is a week-long class designed, in principle, for new and experienced  teachers to learn and share ways to teach an AP course.  I would suggest that the APSI is useful professional development for ANY high school or college physics teacher, from conceptual physics all the way through the introductory undergraduate course.

At my APSI we spend a few hours discussing a physics program, specifically as it relates to the AP exam -- recruitment and selection of students, structure of the exam, topic coverage, selling the course to students, parents, and administrators, etc.  We then spend the vast majority of the week on the teaching of physics.  Specifically, I share a large number of my quantitative demonstrations on a wide variety of topics; I also run several laboratory exercises, and provide my entire lab sequence.  You will receive a 70-page packet of my teaching materials, a printed copy of some of the recent AP free response exams, and a CD with 30+ years of released free response and multiple choice AP physics tests, with solutions, corrections, fundamentals quizzes, and more.

Most importantly, the participants and I spend time getting to know one another.  We take ideas from each other; we make contacts which we draw upon during the school year.  I still remember and use all of the wonderful advice I received from experienced teachers at a summer institute I attended in 1997. 

Are you considering teaching AP in the future?  Come to an APSI.  Do you just want to improve your non-AP class?  Do you want to see the things we are doing in AP, with the intent of using what you like and discarding what you don't?  Do you want to just find out what AP physics is about before you make any kind of decision about the direction of your program?  Come to my APSI.

I will be offering five sessions this summer.  To sign up, contact the host univeristy; I can also give you personal contact information for the institute director if you email me.  The locations and dates of the Jacobs Physics institutes:

June 21-25, University of Georgia (Athens, GA, an hour north of Atlanta)
June 28-July 1, Kennesaw State University (near Atlanta)
July 19-23, North Carolina State University (Raleigh, NC)
Aug. 2-6, Manhattan College (in the North Bronx on a subway line)

Spread the word... if you can't yourself attend, see if a colleague or friend is interested.  The more the merrier.

GCJ

Physics Projects?

Greetings... been distracted the past week by some physics fights.  Oak Ridge (TN) High School and the Madeira School came to Woodberry on Saturday to discuss and debate the merits of the research projects we've all been working on this year.  Next year we will all get together at Oak Ridge Associated Universities in the first weekend of February. 

The four projects that will be discussed and debated next February are:

Dominos: "Numerous domino tiles are balanced on a table or floor with their long axis vertical with horizontal spaces that can be varied. When the first tile is knocked over a domino wave occurs. Predict and measure the speed of this wave and its dependence on various parameters."

Salt Water Oscillator: "Pour fresh water into tall container. Place a cup with a hole in its bottom surface on top of the fresh water. Prepare a solution of salt water and add some food coloring. Pour this solution into the cup on top of the fresh water and simultaneously push the cup down into the fresh water. Secure the cup so that the level of salt water is approximately the same as the level of fresh water. Observe the on-again and off-again flow of salt water into the fresh water. Predict the frequency of these oscillations from first principles, and compare to experiment. Investigate sizes of holes, salt concentrations, and other liquids."

Magic Motor: "Construct a DC motor without a commutator, using a single battery, a single permanent magnet, and a single loop of wire. Predict the frequency of rotation of this motor from first principles and compare to experiment."

Boiling Water: "Some people say it is important to put a lid on the pot when you want to boil water for tea to save energy and time. Investigate this phenomenon."

Need something to do after the AP exam?  Do you have a few students who are way ahead of the rest of the class and seem bored?  Give them these projects.  Next year, bring 2-4 of them to Tennessee, and let them show off what they've learned.  Want to add a research component to your class or to your science club?  Use these problems.  Do you have a second-year class who's done too many traditional laboratory exercises?  Replace standard lab work with these problems.

If you'd like more information about these problems or the tournament at Oak Ridge, please give a call -- 540-672-3900, or an email to greg_jacobs@woodberry.org. 

The difference between a tautology and a justification

Here's an optics homework question I asked the other day:

A concave mirror has a focal length of 10 cm.  It is desired that an image of an object be created that is upright and magnified three times.  (a) Should the object be placed greater or less than 10 cm from the mirror?  Justify your answer.

Now, in and out of class, we have reviewed this type of situation ad nauseum.  We have showed with equations, experiment, and ray diagrams that an object closer to the concave mirror than a focal length produces an enlarged virtual image; any object placed beyond a focal length from the mirror will produce a real image.  My students hopefully KNOW these mirror facts as well as they know that a field goal is worth three points.

Consider this justifcation, then:

The object should be placed less than 10 cm from the mirror, because that produces an enlarged, virtual image.

Such a justification earns no credit!  This response is a tautology, circular reasoning that essentially says "it is because it is."  I mean, *I* know that this student is reasoning from personal experience or memorized facts, but the student could just as easily be guessing and restating the conditions from the question stem.

A correct justification here must go beyond a restatement of the facts, no matter how simple the reasoning might be.  Possible correct justifications:

*... because an object placed inside the focal point of a concave mirror will *always* produce a virtual, enlarged image.  That's a property of concave mirrors.

*... look at my ray diagram here.  You see that the image is virtual and enlarged, and the object is inside the focal point.

* ... look at this calculation here.  I get an object distance of nearly 7 cm, which is clearly less than 10 cm.

* ... in my class we looked at images in concave mirrors, and we saw that only objects close to the mirror produced upright images.

Don't fall into the tautology trap.