Goldfish

I just finished out a four-day physics institute at Dunwoody High School near Atlanta.  I love running these institutes because I meet fun and interesting physics teachers,* and I always learn something new to bring back to my class for next year.

*Is there any other kind?

This year I have been showing off Wayne Mullins' electrostatics demonstration in water, in which I attach 20 V AC across two metal blocks in a shallow container of water.  We use a multimeter to map the voltage at different spots within the water.  The advantages of the water over the more traditional "conductive paper" for this experiment are twofold:  (1) You can feel the voltage viscerally by sticking two fingers of the same hand in the water -- the fingers tingle more with bigger voltage across them -- and (2) Tap water is much cheaper than conductive paper.

Dallas Turner, of Rockford, Illinois, noted that he had seen this very demonstration decades ago.  A college professor he knew had set up the electrodes in a slightly deeper tank than I use, and with dechlorinated water.  

Then the professor dumped in a bunch of little goldfish.

Aha!  The goldfish will align themselves along the lines of equipotential!  Just as you can spread your fingers as far as you want without a tingle as long as you spread them perpendicular to the electric field, so the goldfish can sit comfortably in the water as long as there's no potential difference between head and tail.  

In response to the obvious question from the animal lovers in our group, neither Dallas nor anyone thought that the goldfish were or could be harmed by this demonstration.  For humanitarian reasons,* when I do this demo I will be sure that the fish have a tank and caretaker** awaiting them after they perform for my class and for science.  We'll be sure to videotape the event.

*Defined as "avoiding the wrath of my wife, Burrito Girl"

**my nine-year-old son, who will name each individual goldfish

Index of refraction magic trick, I mean, demonstration

Light traveling from material 1 to material 2 is incident on material 2’s surface at an angle q_i, as shown above.  If materials 1 and 2 have the same index of refraction, which path will the light take upon refraction?

(A)  I

(B)  II

(C)  III

(D)  IV

I used this question, adapted from an AP-style question in the newest edition of Serway, on a recent quiz.  I don't think anyone in my class missed it.  Most folks answered it conceptually:  they know that light bends toward the normal when slowing down at an interface, away from normal when speeding up.  They correctly split the difference, recognizing that without a speed change there's no refraction.  A few used Snell's law, knowing that with equal n's, equal thetas are required.

Then I asked, what is the physical manifestation of this quiz?  

                                       

Consider a beaker of water, as shown above.  If I were to put a clear (not cloudy) ice cube in the water, how would we know that the ice cube was there?  Well, the water would look distorted at the location of the ice, because ice has a different index of refraction than water.  The bending of light at each face of ice would provide visual cues that something is inside the water.*

* Well, that and the fact that the ice would float on top of the water.  But still.

  

But what if I were to dunk an object with the same index of refraction as water?  What would I see?

Based on the quiz, the class reasons through the question:  rays of light would not bend at any interface.  Even a laser would pass straight through the object undeflected.  So we would see nothing.

A few years back, chemistry professor Pam Kerrigan of the College of Mount St. Vincent introduced me to Ghost Crystals.  (Follow the link for one place to purchase them, or ask your chem department.)  You place them gently in distilled water overnight, and they grow by absorbing water.  In their fully engorged state, they are solid, but have the same index of refraction as water.  Thus, when you place them in a beaker of water, they disappear -- just like we predicted on the quiz.

Now, the trick is, I've showed the students the "empty" beakers with a discussion of what would happen "if" I were to place a ghost crystal inside one and wait a day.  But after I do so, I reach in... and remove the engorged ghost crystal that no one noticed was already inside.  See -- there it is, now, out of the beaker on the desk.

I've seen (and done) this demo with Pyrex and mineral oil.  I think it's actually more impressive that way, especially if you throw a broken test tube into the beaker and remove the (already prepared) intact test tube that was previously invisible.  But mineral oil is messy messy messy, and I don't feel like paying for dry cleaning every time I do this demo.  So I went to ghost crystals.

GCJ

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

Mail Time: Waves on a snakey demonstration

Deidre Higgins, of Corbin Kentucky and veteran of my 2009 APSI at Morehead State University, writes:

I was trying to do some lesson planning over the break to get caught up & I was wondering if you could help me with a wave demo. I have in my notes from this summer something about showing interference using paper cups set up two "tiles" away and starting with an amplitude of one "tile," but that's about all I have. (Apparently I need to improve my note-taking skills!) I was wondering if you could give me a brief description of how to do this demo--I remember it being really good to show interference, I just don't remember the details.

Happy to help, Deidre. After I’ve shown the class all the relevant definitions for waves (i.e. amplitude, transverse wave, longitudinal wave, etc.), the class takes a field trip to the tiled floor of the hallway. I bring along a “snakey,” which is like a smaller-diameter slinky with the coils very close together. One student holds an end of the slinky on the floor, while I hold the other on the floor about 5 yards away. The setup is similar to what you see in the picture above, but with the slinky aligned parallel to and on top of a line between tiles. And my kiddies are somewhat older.

I place a line of paper cups on each side of the snakey, parallel to the snakey but about 1.5 tiles away from the snakey’s resting location. I send a wave pulse along the string. If this wave pulse has an amplitude equal to one tile, then the cups aren’t knocked over. (A two-tile-amplitude pulse knocks over all of the cups.)

But when I have the student holding the other end of the snakey send a one-tile-amplitude pulse to me AT THE SAME TIME that I send a pulse to him, the wave pulses interfere in the middle – knocking down just a couple of cups. You see, this is a manifestation of constructive interference. In the middle, the amplitudes of the wave pulses add to form, briefly, a pulse of amplitude two tiles, knocking down the cups.

There’s more you can do with the snakey – move the cups closer and demonstrate DESTRUCTIVE interference, show what a longitudinal wave looks like, show harmonics of standing waves on the snakey, and more. Play with the setup, see what else you and your students are interested in.

GCJ

Centripetal vs. Centrifugal Force: Golf Cart

A golf cart is moving in a straight line. I want the cart to move in a circle. Should I push or pull the cart TOWARD the center of the circle, or AWAY FROM the center of the circle?

Of course, this is the central (ha!) question of the circular motion unit. Students have preconceived notions of "centrifugal force," as well as mistaken ideas about force in the direction of motion. It's nice to begin the circular motion unit with this central question, followed by a demonstration that shows unambiguously and memorably that force toward the center of the circle is required.

Since I live on campus, about 0.5 miles from my classroom, I drive a golf cart to work. This morning I blocked off about 10 spaces in the little parking lot next to the science dungeon. I tied a sturdy rope to the corner of my cart. With the class watching, I drove the cart forward. A physically strong student pulled on the rope in a direction perpendicular to the cart's velocity. Sure enough, the cart's path arced slightly.

Next, I had THREE students tug on the rope. This time the cart's path described a "tighter" circle. We will use this qualitative observation on Monday, when we write and use the equation for centripetal acceleration.

And finally, I turned to a student who originally answered that we should pull the cart AWAY from the center of the circle. I asked him to do so, but he smiled and politely declined. Woo-hoo -- he gets it.

GCJ

Magnetic field due to a current carrying wire

Reader Scott Milczewski, who teaches at Brooklyn Technical High School, asked me about the deflection of a compass due to a current carrying wire. The question was, can I easily get enough current to see a visible deflection? Or do I need a special high-voltage setup?

The picture to the right shows my setup. The power supply is a standard Elenco Precision, and I'm using the variable voltage input. I don't use much voltage at all -- just a few volts gives me enough current in the wire to see a deflection.

The pictures below show the experiment itself. On the right you see the wire carrying no current... it's aligned (approximately) with the earth's magnetic field. The white end of the compass needle points north. In the left-hand picture, the wire is carrying a current from right to left. By the second right hand rule, this current produces a magnetic field beneath the wire pointing west. (Toward the bottom of the picture. Yeah, sorry, I should've aligned the compass markings with the earth's cardinal directions, but I didn't think of that.

So, why doesn't the compass needle point straight to the bottom of the picture, in the direction of the wire's magnetic field? Because the earth's field is still stronger. In fact, this setup could be used to calculate the earth's magnetic field. Use an ammeter to measure the current in the wire. Use the equation

to calculate the magnetic field due to the wire at the position of the compass needle -- that means the variable r will be equal to only a few millimeters, the distance from the wire nearly to the table. Then, use vector analysis -- the wire's field is perpendicular to the earth's field, and we know that the vector sum of the two magnetic fields points about 30 degrees down from the earth's field. That should be sufficient to get close to the 10^-5 T that is the typical magnitude of the earth's magnetic field.