Induced EMF caused by a falling magnet, and a qualitative demonstration

Helmholtz coils of the type useful for demonstrating
the answer to today's question.

I've seen the multiple-choice question from at least two different sources:  a bar magnet is dropped through a circular wire coil from above.  The north end of the magnet points down.  What will a graph of induced EMF (or current) in the coil vs. time look like?

Answer:

This question requires use of Lenz's Law.  I teach an approach to Lenz's law described here.  Let's consider first the time while the magnet approaches the wire loop, and then separately the time when the magnet recedes toward the ground.

As the magnet approaches, the magnetic field is down toward the ground because the B field due to a bar magnet points out of the north end.  The magnetic flux is increasing because the bar magnet approaches the coil, increasing the magnetic field at the location of the coil.  Becuase flux increases, I flip my right thumb opposite the magnetic field, and curl my fingers -- the current in the coil is counter-clockwise when viewed from above.

After the magnet passes through the coil and is receding, the magnetic field still points down toward the ground!  This is because the B field due to a bar magnet points into the south end.  The magnetic flux is now decreasing because the bar magnet recedes from the coil, producing an ever-smaller magnetic field at the location of the coil.  Becuase the flux decreases, I keep my right thumb pointing in the direction of the magnetic field, curl my fingers, and find the current in the coil is the other way -- clockwise as viewed from above.

I asked my AP classes this question as a "check your neighbor" exercise today in class.  At first, when working alone, most of the class (~2/3) didn't recognize that the current switches direction when the magnet passes through the coil.  Upon discussion, I found that the key misconception was the direction of the magnetic field when the magnet receded.  Either they thought that the magnetic field must have a different direction near the other pole, or they thought that since the field was decreasing, the field itself must switch directions.  Good arguments among the class changed some views, such that after discussion about 2/3 of the class had the correct answer.

Setting up the demonstration:

Long time blog readers know that I don't think it good enough to explain something like this conceptually and/or mathematically without doing the experiment.  Nature is the ultimate arbiter of arguments.  So I set up the problem.

I used a 10-cm diameter wire coil with a gazillion loops.  I've on other occasions used a bigger diameter set of coils scavenged from a 20 year old broken q/m device.  You'll get the best results if you use a coil with enormous numbers of loops, like one designed to produce strong, uniform magnetic fields -- a Helmholtz coil, like those shown at the top of the post.

I hooked a Vernier voltage probe to my labpro, and set the labpro to take 1000 data points per second for 2 seconds.  A student clicked "collect;"  When data collection began, I dropped a small (~5 cm length) bar magnet through the coil.

A bit of zooming produced the graph shown above.  As expected, the voltage switched polarity (i.e. the current switched directions) as the magnet passed through the coil. 

Though it's not brutally obvious, the right-hand hump is not as wide on the graph as the left-hand hump.  Why not?  Because the magnet speeds up in free fall, and so recedes from the coil faster than it approached the coil.  I dropped the magnet from about shoulder height.  The ~0.10 s duration of the voltage spikes are substantially less than the ~0.5 s time I calculate for the magnet to fall to the ground, as it should be. 

Any more follow up thoughts?  This demonstration can produce a wealth of interesting calculations and experiments suitable for an end-of-year independent laboratory investigation.

How I "conduct" a laboratory session -- NO HANDOUTS!

But Mr. Lipshutz, you didn't tell us
 which graduated cylinder to use!

At my AP summer institutes, I offer attendees my entire general and AP physics laboratory program.  I describe each experiment briefly in writing; I include the "lab report" evaluative exercise that is assigned for homework; and we even actually conduct three of the labs I use.

Confusion generally reigns, though, until teachers actually try out a couple of my experiments.  The issue?  "What do you give to the students so they'll know what to do?  Do you have the lab handout?"

My answer is, I give the students nothing.  I demonstrate the use of the equipment -- moreso early in the year than later in the year.  I tell the class what to measure and how to measure it.  On the board, I draw the graph (always a graph) that they should make.  That's it.*

But how will the class know what to do? 

First of all, they LISTEN to me.  If they know a handout is coming, why should they listen actively to anything I say?  "I'll just read the handout," they'll think.

Secondly, I don't want students blindly following directions.  Figuring out how to measure something is an experimental physics skill, even at the most basic level of "how are we going to find the volume of this water?"  Recognizing that they need a graduated cylinder rather than a beaker, then selecting an appropriate cylinder from the shelf, then realizing that the one they chose was too big -- all that is a learning experience.  My placing the proper-sized cylinder on the lab table and writing "pour the water into the graduated cylinder and read from the bottom of the meniscus" teaches the class to follow directions, nothing more.

And finally... how many times have you handed out a carefully-prepared lab sheet, then had ten students ask a question to which the response is, "Look at the handout here."?  Students DON'T READ LAB HANDOUTS CAREFULLY.  We all know this.  So instead of wasting time preparing a handout, then getting frustrated, then complaining about how these dang kids today don't read anything... just don't give a handout.  Laboratory isn't the time to be teaching the skill of following written directions, I don't think -- that's for homework, tests, and home ec class.

I know you're skeptical.  After all, your teachers all through high school and college probably never failed to hand out a lab sheet with complete instructions.  It's not easy to let go of this crutch.  But flying by the seat of your students' pants in lab does work beautifully.  Joshua Beck, who attended my workshop at NC State University last summer, says not giving a procedural handout on lab days "has been great, for me and them."  He's right.  Try it.

* Sure, early in the year I make sure everyone is acquainted with my lab requirements, as shown here.  These aren't on a handout, they're just oft-repeated guidelines. 

Magnetic force on a wire demonstration

The force on a current-carrying wire is given by F = ILB, where I is the current, L is the length of the wire in the magnetic field, and B is the value of the magnetic field.  The direction of that force is given by a right-hand rule.

This seems like an easy enough concept to demonstrate in a classroom setting:  set up a horseshoe magnet, connect a wire to a battery, run the wire between the magnet poles, and watch the wire jump.  (Or, watch the wire hug the desktop, if you set the magnet poles the wrong way.)

Here's a seven-second youtube video of someone doing this very demonstration:

Now, I didn't do this demonstration at all for the first 14 years I taught.  Why not?  It seems so easy...

To get this to work, the magnetic force has to be bigger than (approximately) the weight of the wire.  Even with some big-butt magnets, this still requires a current through the wire in the neighborhood of 5-30 A.  The variable-voltage power supplies I use for circuit labs won't give out that current -- for safety reasons, they're fused somehow so that the max current they can provide is in the neighborhood of a few hundred mA.  I could use a car battery, but I don't have one around, and I don't really *want* one around... the last thing I need is to shock myself or a careless student.

But last year, when I was cleaning out part of a sputnik-era storeroom, I found this classroom-use variable-voltage power supply from 1960 or 1970.  It even had a two-pronged, non-polarized plug.  Sure enough, the current-limiting feature was absent.  I can get 10-12 amps through a single alligator-clipped wire. 

I'm less concerned about frying myself with this than I am with a car battery, for two reasons -- (1) the car battery has enormous electrodes intended for contact with jumper cables, while the power supply has 1 cm diameter poles intended for alligator or banana plugs; it's hard to make accidental contact with the power supply.  (2) The power supply is plugged in to a fused power strip, and so can be easily shut off manually or automatically.  The battery keeps on rollin' no matter what.

Perfect!  I clipped two alligator wires to a long, thin piece of aluminum foil -- this reduces the weight of the wire, so the wire should "jump" more easily.  The aluminum foil wire was strung between the poles of a strong magnet.  I asked the class which way I should connect the other end of the alligator clips to the power supply.  They had to use the right hand rule to figure out what direction of current we wanted to provide an upward force on the wire.  Then I connected the wires to the power supply, flipped the switch... and the wire jumped, just like in the video.

I used the same power supply and a compass the next day to show the direction of the magnetic field created by a current-carrying wire.  Since the current in the wire is ~10 A, the magnetic field generated 1 cm away from the wire is about 10^-3 T. That's 100 times the earth's magnetic field, so the compass "ignores" the earth's field and just points in the direction of the wire's field.

GCJ

My Rant: "When are we ever gonna use this?"

9th grade physics student: Mr. Lipshutz, graphing is pointless and we are never going to need this.

Mr. Lipshutz:  You're gonna need it on the exam, so shut up and start studying.

The student who whines about "when are we gonna need this" is really saying "I need an excuse for why I won't learn what you ask me to learn. Here's one excuse that has consistently gotten me sympathy from my parents and teachers outside the science department: If I fail, it's not because I'm a lazy bum, it's because the material isn't useful to me right this instant."

Never mind that American history has no immediate use outside the classroom, never mind that conjugations of être are useless except in the unlikely event I go to Paris, never mind that I'm never going to make a dime just because I understand Hamlet's motivations. I'm going to complain that physics is useless because some adult somewhere in my life (and most of my friends) will validate my intransigence by saying, "That's okay, honey, no one is really expected to understand that stuff, you're right, you're never going to need it. Everyone gets a D in that class."

When are we gonna use this, you ask? Right now, on this pop quiz.

 

GCJ

How much justification is enough for Right Hand Rules?

An electron moves to the right into a uniform magnetic field, as shown in the diagram.  The question: What is the direction of the force on the electron?  Justify your answer.

The student reasonably asks, how much justification is enough? 

"The electron is moving right, so I point the fingers of my right hand to the right.  The magnetic field is down the page, so I put my right palm toward the bottom of the page and curl my fingers.  I extend my thumb, which now points into the page - that would be the direction of the force on a positive charge.  Since this is an electron, I flip the direction of the force, so the electron is forced out of the page."  -- Too much.  We don't need a dissertation.  On a test, one might have just a minute or so to solve this kind of problem.  It's unreasonable to expect a student to provide this level of detail about such a simple problem, especially as the student becomes so proficient that this problem is easy.

"Out of the page -- first right hand rule."  -- Not enough.  There are three right hand rules, which are all taught differently in different physics classes.  And even then, saying that a right hand rule applies isn't much beyond stating a bare answer.  Of COURSE a right hand rule applies -- it's a magnetism question!

"Out of the page.  Use the RHR for the force on a moving charge.  Point right, curl down the page, flip the thumb because the charge is negative." -- Just right.  The right hand rule in use is identified unambiguously.  ("The right hand rule associated with F = qvB would have been good, too.)  The mechanics of the rule are stated clearly but in a shorthand.  Anyone reading this justification would recognize that this student understands why the force on this charge is out of the page.

All I need is a box of donuts...

Picture credit:  Paul Vickers

Hi, folks.  The picture to the right shows me in sector 7G, er, at Oak Ridge National Lab's original graphite reactor.  The facility was taken offline in (I think) 1962, and has not been disturbed since.  All controls, dials, seats, labels, everything is just as it was on the last day the reactor was active.  So I entered the control room, sat in the swivel chair, and attempted to cause a Homer Simpson-style meltdown.  I failed.

I haven't posted in weeks 'cause I've been arranging the US Invitational Young Physicists Tournament.  The Harker School of San Jose, California took first place; Woodberry Forest (my school) came in first in the preliminary rounds, but was upset in the playoffs by Rye Country Day School of New York. 

Now I'm desperately trying to catch up with the pile of work I ignored in order to go to the tournament in Oak Ridge.  I'll get back to posting here in a while.  Until then, try to figure out what each of those dials does.

GCJ

Finding an appropriate digital multimeter

Extech MN36 digital multimeter

I'm introducing my general physics class to electric circuits with an experiment.  I generally find that the idea of voltage and current doesn't really sink in until students have had a chance to measure these quantities in circuits with which they can play.  (I also find that there is little correlation between my best problem solvers and my best circuit hooker-uppers.  Circuits experiments give an opportunity for success to some otherwise weak students.)  So this week, my class will do the simplest circuit experiment one could ever devise:  keeping a constant battery voltage, graph the current through a variable resistor as a function of the resistance. 

For years, though, I could not do this experiment effectively.  The ammeters -- really multimeters -- in my classroom wouldn't measure a wide range of currents, and would blow a fuse if they measured too much current.  You can certainly trust introductory students to blow an ammeter's fuse, no matter how much preventitive instruction and warning you give.

I really wanted a meter which would measure currents as small as a few microamps, and as large as a few milliamps.  Then we can use the standard available power supplies that provide 5-15V with tens of kilohms of resistance.

Why are these values important?  Most cheap resistors are rated at about 1/4 watt... so to keep the resistor from getting hot and ruined, the voltage squared divided by the resistance for any individual resistor must be less than 0.25 watt.  Even with as much as 15 V across as small as a 1 k resistor, the power is acceptable.  That calculates to a maximum current of 15 milliamps... and my preference isn't to come too close to this maximum. 

The meters I bought 10-15 years ago weren't this sensitive to current.  Their sensitivity was in the 1 mA range.  But last summer I searched google shopping under "digital multimeter."  I found a number of reasonably priced meters that would measure currents as small as 1 μA!  I've pictured one, the Extech MN36, which was listed at $17 on Amazon.  No price guarantees, and I've never used this particular meter -- I'm just showing an example of what I found.  Look around, there are gazillions of meters, many of which will serve your needs.

When you're looking for a class set of multimeters, DON'T look at science supply stores!  Their prices are inflated, and they don't necessarily give you a good selection.  Look around at electronics retailers.  Make sure to check the specs to see that the resolution for DC current is in the 1-10 microamp range.  If you have to, buy four this year, and four more next year, etc. 

Once you have the meter, all you need is a huge pile of 5-200 kilohm resistors -- which can be found from electronics stores in bulk for 1-2 cents apiece -- and some battery holders.  You can add more expensive power supplies, breadboards, or "resistance substitution boxes" later if you want.  But don't let cost or procurement be an obstacle to simple and fun electronics experiments.