Stationary electric charges generate radial electric fields, and electric fields push positive charges (and pull negative charges). Moving charges also generate circulating magnetic fields, and magnetic fields deflect moving charges perpendicular to both the fields and their motions. All of electromagnetism follows.

In particular, spin a conducting disk in a perpendicular magnetic field, and connect its axle to its circumference using a wire and two sliding contacts, as in the animation. The magnetic field deflects free changes in the disk radially, and they push other charges through the wire. This rotary electric generator converts mechanical motion into electrical current, which can heat the wire and toast bread.

Is the external magnetic field necessary? No! Bend the wire into circles just above and below disk, as in the animation. If the disk spins fast enough, the internal magnetic field of the charges moving in the wire deflects the charges in the disk, which then push the charges through the wire! This dynamo is the closest thing to perpetual motion in classical physics. It generates the magnetic fields of stars and planets, including Earth’s.

Rotary electric generator needs an external magnetic field, but a dynamo generates its own

Rotary electric generator needs an external magnetic field, but a dynamo generates its own

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March Meeting 2018 – Days 2 to 4!

The March Meeting is always so exciting — there is so much information here!

Graphene origami and micron-sized laser controlled robots at Marc Miskin’s talk on Tuesday morning. SO COOL!

On Tuesday morning, I went to an outstanding session on Atomic Origami.  There is some truly amazing work out there with people designing shapes of graphene (mostly) that fold up on their own into boxes or flowers.  Post-doc Marc Miskin gave a really inspiring talk, including showing a little piece of graphene that folds itself up into a triangle only 15 microns on a side — reversibly and repeatedly!  Harvard professor David Nelson (who gave a colloquium at Wooster just a few years ago) also gave a wonderfully dynamic talk on criticality and crumpling of paper.

Food trucks and extremely long, slow lines in the sun. Good food though.

Emma Brinton ’18 gave her poster in the afternoon, and got good interest from the crowd.



Meanwhile Justine Walker ’18 and I went to a session on the life and legacy of Millie Dresselhaus. Millie was an absolutely outstanding person and physicist, and the first woman to do so many things. I knew of Millie, of course, but learned so much more about her. I also got to catch up with my Ph.D. advisor Laurie McNeil, who was chairing this session.


Spot the Wooster physicists in the crowd waiting for the graphene superconductivity talk. Hint: look for Michelle’s backpack.

Day 3, Wednesday, started off with a buzz of excitement around an invited talk about graphene and a new discovery of superconductivity. This was actually really interesting since I learned a good bit about graphene and carbon compounds in general the day before at the Millie Dresselhaus session, since she was a tremendous pioneer with carbon (and is known as the Queen of Carbon). I don’t know if everyone was already excited about the talk, but the APS sent out an email basically saying “this talk is so cool we’re projecting it in the cafe”, so then of course everyone came.  We had seats at a table, but moved to the balcony when too many people stood in front of us.  It was interesting, but I’m not sure if it’s quite the Woodstock of physics event we were hoping for.

Andrew Blaikie ’13 quizzes Chase Fuller ’19 about BZ waves.

Everybody loves the toys.


Our remaining four students presented their posters and did very well, and had fun gathering up free toys from the vendors in the exhibit hall.

Group selfie, take 2.








Time for a group photo, and a couple more sessions before a big group dinner.  This is always a highlight of the trip (as long as the scheduling works) and this time we got to include alumnus Andrew Blaikie ’13 who is finishing grad school at the University of Oregon.

Wooster physics out for dinner, with bonus alumnus Andrew Blaikie ’13!

Whew! So much more that I could say, but frankly I’m exhausted.  On Thursday, Avi Vajpeyi ’18 presented his bead pile simulation, and I presented the latest experimental  bead pile results later in the same session.

Me, taking credit for Gabe’s excellent work


As I said at the start, the March Meeting is exhilarating, but the counterpoint is that it is exhausting. We are starting to hit brain overload here, but fortunately things are winding down.  The weather has been lovely, so here’s a final image from the atrium at the convention center. I notice reflections all around, and I liked the blue sky with the reflections in the floor.

Sunlight and reflection in the atrium

Next year in Boston!






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March Meeting 2018 – Day 1

I’m currently in Los Angeles for the American Physical Society March Meeting — the largest gathering of physicists in the world. This year there are almost 11,000 attendees, and more than 55 simultaneous sessions to choose from!

The moon setting over downtown LA as the sun rises

There are physicists everywhere — hordes descending on the convention center at 8 am Monday to pick up their badges and find the right room for one of those sessions to hear the talks they’ve picked out.

Registration – 8 am Monday

I had time for just a few interesting talks before I met up with Justine Walker ’18, who was giving an oral presentation on her Senior IS project, Dancing Our Way to Mars Through Physics.

Great crowd waiting for Justine’s talk to start

Justine did a really good job with her presentation, and a lot of people were interested. There was a little gap with a missing speaker just before her talk, and she was the last speaker of the session, so everyone there was there specifically to hear her work.  Lots of interest and lots of good questions, which she handled professionally.  Anyone who has given a talk at the March Meeting knows that the questions can be the toughest part!

Mascot Leo is excited about the new APS coloring book for adults, with a packet of colored pencils to get started!

I spent the afternoon in a long series of invited talks focusing mainly on the advanced lab experiences for physics majors. I’ve been a member of ALPhA since it started about 10 years ago, and this was a session with other people who are interested in how our undergraduate physicists learn how to think about experimental work, analysis, uncertainty, etc.

Several of the speakers talked about how physics instruction needs to be a three-legged stool, where the three legs are the theoretical formalism, computation and modeling, and experiment and design.  We tend to be very heavy on theory, with much less emphasis on experimental ways of thinking and learning. All three of these areas need to be valued.  When we think about the undergraduate curriculum, we tend to think about topics (mechanics, E&M, thermal, etc) as opposed to methods (theory, modeling, experiment).  There was a lot here for me to think about, especially some new ideas about what we should be doing in the introductory labs.  Some studies have shown recently that using the labs to re-inforce concepts taught in intro physics does not actually work the way most professors assumed — the labs don’t help and they might even hurt! So, how can we get rid of the canned labs, and use the lab period to teach more about how to do experimental design and how to draw valid conclusions from the data?  There are some exciting possibilities here.

Lakers game in progress inside! But I’m outside.

Cool pattern of colored globe lights at the restaurant

Just outside this talk, I bumped into some people I hadn’t seen for a few years and a group of us went to dinner a block or so from the Convention Center, which it turns out is right next to the Staples Center. The restaurant was pretty packed until the Lakers game started partway through dinner.

Whew! And that’s just day one! Exciting talks tomorrow on Atomic Origami!

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CUWiP 2018

Well, we’re so busy doing things here at Wooster Physics that we haven’t kept up the blogging about all our exciting activities.

Case in point — CUWiP 2018!

For the last several years, the American Physical Society has been hosting Conferences for Undergraduate Women in Physics (CUWiP). These are regional conferences around the US designed to help young women persist in physics by providing networking opportunities and information about graduate school and careers, in addition to talks about physics research.

We’ve been sending a delegation from Wooster to the nearest CUWiP for several years now, and it has been a really positive event.

This year, we had three Wooster students go to the local conference, which was at the University of Toledo. While there, they also got to meet up with Norah, a student from Hiram who did the Wooster REU over the summer.  Norah was presenting the results of her research with Dr. Lindner on Hannay Hoop-and-Bead Anholonomy.

Abigail and Norah!

Abigail Ambrose ’20 reports:

“One of my favorite speakers Dr. Karen Bjorkman, who is the Dean of the College of Natural Sciences and Mathematics at the University of Toledo. She is an astrophysicist and was an incredibly inspirational speaker.

We also got to go to a lot of different breakout sessions for everything from graduate school to REU applications and from writing papers to imposter syndrome. We all really want to go back and are super excited about some of the things we got to hear Michigan State planning for next year.”



Long day but still good!

And, just because I love it, here’s a picture from 2015 — what a great group of students!

Maggie, Laura, Justine, Popi, Catherine, Amanda, and Ziyi at CUWiP 2015

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Falcon Heavy

I was supervising Jr IS, but as I circulated around the lab, I watched the clock. Everyone was working quietly.

Just before launch, I snuck back to my office and closed the door. The SpaceX Falcon Heavy was surrounded by swirling clouds of condensation at Kennedy Space Center‘s historic Pad 39A. Amidst spectactors’ cheers and the sound suppression system’s deluge, the 27 Merlin rocket engines of the world’s largest launch vehicle ignited. I barely breathed for the first 2.5 minutes of flight under the three Falcon 9 boosters. The two side boosters detached, returned to Cape Canaveral, and landed side-by-side in a 1950s science fiction fantasy. While most test launches use mass simulators of concrete or steel, the payload fairing separated revealing Starman in the driver’s seat of a Tesla Roadster with Earth in the background.

Heart thumping, I returned to Jr IS. Everyone was working quietly.

Falcon Heavy side boosters land side-by-side like a 1950s science fiction fantasy, 2018 February 6

Falcon Heavy boosters land side-by-side, like a 1950s science fiction fantasy, 2018 February 6

Tesla Roadster leaving Earth

Tesla Roadster leaving Earth headed for beyond Mars

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The Impossible Problem

In 1969, Hans Freudenthal posed a puzzle that Martin Gardner would later call “The Impossible Problem”. Below is a 2000 version due to Erich Friedman.

I have secretly chosen two nonzero digits and have separately told their sum to Sam and their product to Pam, both of whom are honest and logical.

Pam says, “I don’t know the numbers”.
Sam says, “I don’t know the numbers”.
Pam says, “I don’t know the numbers”.
Sam says, “I don’t know the numbers”.
Pam says, “I don’t know the numbers”.
Sam says, “I don’t know the numbers”.
Pam says, “I don’t know the numbers”.
Sam says, “I don’t know the numbers”.
Pam says, “I know the numbers”.
Sam says, “I know the numbers”.

What are the numbers?

This beautiful problem may at first seem impossible, as you know neither the sum nor the product of the numbers, but the attached animation illustrates my solution.

Animated solution of "The Impossible Problem". Matrix rows & columns are products and sums of nonzero digit pairs; filled squares indicate products & sums shared by pairs and not yet excluded by Pam or Sam

Animated solution of “The Impossible Problem”. Matrix rows & columns are products and sums of nonzero digit pairs; filled squares indicate products & sums shared by pairs and not yet excluded by Pam or Sam

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Electronic Kilogram

The kilogram is the only metric unit still defined by an artifact. The International Prototype Kilogram, IPK or “Le Grand K”, is a golf-ball-sized platinum-iridium cylinder in a vault outside Paris. This year I expect the General Conference on Weights and Measures to replace the IKP by an electronic realization that balances gravitational and electrical power.

The Kelvin or Ampere balance suspends a horizontal wire loop of mass m, length \ell, and current I, by a radial magnetic field B. Integrate the magnetic force \overrightharpoon{F}=q\overrightharpoon{v}\times\overrightharpoon{B} around the loop to find the force balance

m g = F = \left| \oint d \overrightharpoon{F} \right| = \left| \oint dq \,\overrightharpoon{v} \times \overrightharpoon{B}\right| = \left| \oint I d\overrightharpoon{\ell} \times \overrightharpoon{B}\right| =I \ell B

and solve for m. Unfortunately, \ell and B are difficult to measure accurately.

In 1975, Bryan Kibble proposed the calibration step of moving the current-less wire loop vertically at speed v. Integrate the force per charge \overrightharpoon{F}/q=\overrightharpoon{v}\times\overrightharpoon{B}  around the loop to find the induced voltage

V = \oint \overrightharpoon{E} \cdot d\overrightharpoon{\ell} = \oint \frac{\overrightharpoon{F}}{q}\cdot d\overrightharpoon{\ell} = \oint \overrightharpoon{v} \times \overrightharpoon{B} \cdot d\overrightharpoon{\ell} = v B \ell.

Eliminate \ell and B from the force and voltage expressions to find the virtual power

P = V I = v B L I = m g v

in Watts, and again solve for m. Accurately measure voltage V by comparing to the superconducting Josephson-effect voltage

V =\frac{n_J f}{K_J},

where K_J = 2 e / h = 0.48~\text{THz} / \text{mV} is the Josephson constantn_J is the number of Josephson junctions, and f is their microwave frequency. Convert current I = V_R / R to voltage and resistance by Ohm’s law. Accurately measure resistance R by comparing to the quantum Hall-effect resistance

R =\frac{R_K}{n_L},

where R_K = h /e^2 = 26~\text{k}\Omega is the von Klitzing constant, and n_L is the number of filled Landau levels. Accurately measure velocity v and acceleration g using interferometers.

Hence the mass

m=\frac{VI}{gv}=VV_R\frac{1}{R}\frac{1}{gv}=n_J f\left(\frac{h}{2e}\right) n_J f_R\left(\frac{h}{2e}\right) n_L\left(\frac{e^2}{h}\right)\frac{1}{gv}=\frac{n_L n_J^2 f f_R h}{4gv}\propto h,

where h=0.66~\text{zJ} / \text{THz} is the Planck constant. The Kibble or Watt balance thus defines mass in terms of the rate of change of a photon’s energy with its frequency.

The NIST-4 Kibble balance has measured Planck's constant to 13 parts per billion and is thus accurate enough to help redefine the kilogram

The NIST-4 Kibble balance has measured the Planck constant to 13 parts per billion and is thus accurate enough to help redefine the kilogram. Credit: Jennifer Lauren Lee.

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Taylor Bowl

On Wednesday, September 13, 1989, I met with newly elected Physics Club officers Tom Taczak ’91, Dennis Kuhl ’90, Doug Halverson ’91, and Karen McEwen ’90 in Westminister House. I wrote in my diary, “first phys club meeting w. officers goes well”. That year we invented Taylor Bowl, an annual bowling competition between the Physics and Math clubs, both denizens of Taylor Hall, at the bowling lanes in Lowry Student Center. We intentionally chose an activity that either club could do, but that neither club could do well. The annual event was a great success for both clubs for nearly 30 years, but it ends with the demolition of Scot Lanes this month.

Physics at Taylor Bowl Montage

Physics at Taylor Bowl Montage

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Newton’s Can(n)on

One of my favorite illustrations is the cannon thought experiment from volume three of Isaac Newton‘s Principia Mathematica. Johannes Kepler argued that planets orbit elliptically with Sol at one focus. Galileo Galilei argued that terrestrial bodies fall parabolically in space and time. Living in the next generation and standing on their shoulders, Newton realized that Kepler’s ellipses and Galileo’s parabolas were extremes of the same continuum, the Newtonian synthesis, which he dramatized by imagining a cannon on a tall mountain shooting cannon balls at increasing horizontal speeds: a falling apple orbits Earth (but collides with its surface); the orbiting Luna falls toward Earth (but its tangential velocity prevents a collision).

In Newton's famous thought experiment, subsuming both Galileo and Kepler, cannonballs shot at ever increasing horizontal speed eventually fall around Earth

In Newton’s famous thought experiment, subsuming both Galileo and Kepler,
cannonballs shot at ever increasing horizontal speed eventually fall around Earth

Low-resolution photograph of page 6 volume 3 of Newton's Principia, as it appears in the Voyager interstellar record now en route to the stars

Low-resolution photograph of page 6 volume 3 of Newton’s Principia,
as it appears in the Voyager interstellar records now en route to the stars

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ein Stein

I’ve been fascinated by aperiodic tilings of the plane since Martin Gardner first wrote about them in Scientific American. In the 1960s, Robert Berger discovered a set of 20 426 prototiles or tile-types that can tile the plane but only with no translational periodicity — a wonderful mix of the expected and the surprising, a kind of visual music.

Over the years, the number of required prototiles has been greatly reduced. In the 1970s, Roger Penrose discovered a set of just two concave aperiodic prototiles. Robert Ammann then dissected these to discover a set of three convex aperiodic prototiles. Can a single prototile, one tile or stone, literally ein Stein in German, force a nonperiodic tiling? Despite several near misses and potential applications to quasicrystals, the existence of an ein Stein remains a fascinating unsolved problem.

Three convex Ammann tiles force a non periodic tiling of the plane.

Three convex Ammann tiles force a nonperiodic tiling of the plane.

Two concave Penrose tiles force a nonperiodic tiling of the plane.

Two concave Penrose tiles force a nonperiodic tiling of the plane.

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