Posts Tagged ‘Electric field’

So Just HOW Do You Measure the Shape of the Electron?

May 26, 2011 3 comments

A paper recently published in Nature is generating quite a bit of media buzz. [PhysOrg, BBC, Fox, PhysicsWorld]

The paper is entitled ‘Improved measurement of the shape of the electron’ and describes, well, a new method for measuring the electron’s shape.

I love when physics paper titles are easy to understand :)

Anywho, the main thrust of the paper is that the electron appears to be spherical to a very high degree of accuracy. In fact, the press release from the Imperial College of London states that,

the electron differs from being perfectly round by less than 0.000000000000000000000000001 cm. This means that if the electron was magnified to the size of the solar system, it would still appear spherical to within the width of a human hair.

Wow! Now that is pretty darn spherical.

But now you’re thinking “Hey wait, I thought the electron was a wave? Or a string of energy? Or a cloud of virtual particles? How can it actually be spherical?”

These are excellent questions. Indeed, when we first learn about atomic structure in science class the electron, protons and neutrons are all depicted as perfect spheres. As we learn more, we know that this is only an approximation, an easier way of visualizing the complicated subatomic structure.

The truth is, the electron isn’t (well, probably not) spherical. We don’t really know for sure. Current theories point to the most accurate picture being that the electron is a cloud of particles, blinking in and out of existence, which contribute to its mass and size.

So what this paper and these news outlets are actually saying is that this experiment has shown that the electron behaves as though it is a sphere.

Even more accurately, the electric dipole moment of the electron is approximately zero, which is what we would expect from a perfect sphere with uniform charge distribution.

Ok, I know I just said a mouthful. So let’s go through exactly what I mean about the electric dipole moment, and then we’ll go through what this paper actually measured.

Let’s begin with what an electric dipole moment actually is. Imagine you had two particles, one with a negative charge (-q), and one with a positive charge (+q). If you put these two charges close together, you will create special electric field pattern. This type of arrangement creates what is called an electric dipole moment (EDM). The EDM vector (p) is defined as the of the charge on the two particles (q) times the displacement vector between them (d).

The electric dipole moment vector (blue arrow) points, by definition, from the negative charge to the positive charge.

However, you can also create an EDM if you were to have a particle with an uneven charge distribution.

For example, imagine you had a sphere with a total charge +q. In this case, the charge is evenly distributed and you don’t get an EDM.

A perfect sphere with a uniform charge distribution does not have an electric dipole moment.

But now imagine you had an oddly shaped particle that was “squished” at one end.

In this case, there is more charge at one end of the particle than there is at the other. This uneven charge distribution gives the particle its own EDM.

A not-so-perfect sphere has a non-uniform charge distribution. The higher concentration of positive charge at one end creates an electric dipole moment (red arrow).

So if the electron is not perfectly spherical, it should have an EDM. If it has an EDM, we should be able to measure it to infer the electrons shape. Simple, right?

Now, the Standard Model of Physics predicts that the EDM of the electron is too small for us to currently measure; our equipment is just not sensitive enough. But there are variations on the theory that say the electron’s EDM may actually be larger enough to measure using our current technology.

So finding the electron’s EDM will help narrow down our current theories on the subatomic universe.

The existence of an EDM may also help explain why there is so much matter in the Universe and so little antimatter. If the reason for this apparent imbalance in matter and antimatter is the result of an as-of-yet-undiscovered particle interaction, then the current theories of particle physics predict that there should be a measurable EDM for the electron.

So this explains why this experiment is so important. Now lets explain the experiment.

In a simplified picture, the electron EDM in an applied electric field will either point in the same direction as the field, or in the opposite direction. The energy of an EDM in an electric field depends on the direction of the EDM in relation to the electric field.

This means that the EDMs that align with the electric field will have a different energy than those that align against the field. This difference in energy is proportional to the magnitude of the EDM.

So how does one measure this energy difference? One way is to align the spins perpendicular to the field, which will cause them to precess and you can then measure the precession rate, which is proportional to the energy difference.

This effect can also be described in terms of how the two energy states interfere with one another. This interference between the two states can be measured using an interferometer. If there is an EDM present, then a phase shift should be seen in the interferometer signal. If the applied electric field is reversed, then the phase shift should change sign.

So the authors of the paper went looking for this phase shift. They used molecules of Yttrium Fluoride and fired them at a speed of 590 m/s into an apparatus which has a constant electric and magnetic field.

A radiofrequency pulse is applied which excites the molecules into their respective energy states. They are then allowed to interact for a certain amount of time (a few milliseconds) and it is during this time that the molecules in the different energy states develop a phase difference.

A second radiofrequency pulse is applied and the number of molecules which end up in the lower energy state is measured and is proportional to the phase difference they developed during their interaction time in the electric field.

This phase difference is measured via the applied magnetic field and creates an interference curve.

An example of an interference curve from measuring the phase difference via the magnetic field. (Figure 3 from this paper)

If the electric field is reversed, then a small phase shift in the interference curve is seen. Remember that the phase shift is proportional to the electron EDM.

So by varying certain parameters like the magnetic field and the frequency of the radiofrequency pulses, the authors were able to extract the numerical of the electron EDM from the data.

Over 25 million pulses of YbF were used to collect this data. Not only that, but many experiments had to be done to determine systematic sources of error in the experimental setup.

Things like fluctuations in the applied magnetic field, electric field plate potentials not being completely symmetric, magnetic fields generated in the magnetic shielding during switching of the electric field are all sources of error which had to be considered.

So after all this work they finally arrived at their calculated value of the EDM for the electron. The value turned out to be de = (-2.4 ± 5.7stat ± 1.5syst) × 10-28 e · cm, where the first error term is from statistical uncertainty and the second is from systematic uncertainty.

Notice that the error on this measurement makes it consistent with zero and consistent with previous work.

However, this measurement is 54 times more precise than the previous one the author’s previous measurement and puts an upper limit on the EDM of the electron which must be less than 10.5 × 10-28 e · cm.

The next step in these types of experiments is to reduce the uncertainty of the measurements. The authors believe that they should be able to do this using cold molecule techniques and get their measurement down into the 10-29 e · cm range.

Be sure to check out another blog post about this paper by Chad Orzel, author of the blog “Uncertain Principles” and the book “How to Teach Physics to Your Dog”.

Hudson, J., Kara, D., Smallman, I., Sauer, B., Tarbutt, M., & Hinds, E. (2011). Improved measurement of the shape of the electron Nature, 473 (7348), 493-496 DOI: 10.1038/nature10104

Teaching Electricity and Magnetism: Part II

March 30, 2011 2 comments
This is the second part of my posts about teaching Electricity and Magnetism (EM). Part I can be found here, which dealt with the confusion of students in learning electricity and magnetism together. Part II deals with a paper looking at ways to help improve teaching methods for EM. The paper is entitled “Using multimedia learning modules in a hybrid-online course in electricity and magnetism“.

When I was still TAing (about 2 years ago) the University was starting to implement a new way of performing tutorial sessions. They were going to do it online. This was done by the students logging into a virtual classroom with the other students and were able to type out questions to the TA. The TA was in a computer lab somewhere and outfitted with an electronic on-screen writing tool (don’t ask me what it’s really called) and would work out problems on their screen by hand, which the students were able to see in the virtual classroom.

When asked if I wanted to participate in this type of tutorial, I refused. Call me a dinosaur (I’m only 26, but whatever) but I wanted to be in the room with the students when I taught them.

But do online and multimedia learning tools help? Or are they worse? That was the topic of this study.

A multimedia learning module (MLM) was developed by the Physics Education Research Group at the University of Illinois at Urbana Champaign and implemented as a pre-lecture assignment to students in an introductory physics course. MLMs are interactive online exercises which include flash animations which introduced physics concepts to the students. The MLMs were about 12-15 minutes long.

So the goal of the study was to determine if using MLMs prior to learning the concepts in class resulted in better grades for the students and a better student experience. The study tried them out in an introductory Electricity and Magnetism course in the Fall of 2008 at California State Polytechnic University at Pomona.

They used two different sections of the course as the control group and the experimental group. The control group (N = 48) had only the traditional coursework. The experimental group (N = 34) used traditional coursework in conjunction with the MLMs. To make sure any increase in performance was not simply due to increased time spent on the material in the experimental group (i.e. classtime + time spent on MLMs) the amount of time spent in the class was reduced by one-third for the experimental group.

Students in the experimental group viewed the MLMs prior to learning the material in class. Both groups were approximately equal in academic performance  prior to taking the course, as determined by a survey.

Student performance after the term was measured by a multiple choice test, as well as the results of answering questions in class using a personal response system called a  “clicker“. Students were also asked to fill out a questionnaire to rate the usefulness of different aspects of the course, such as the textbook or the MLM.

Students who used the MLM showed an 8% higher normalized gain than those in the control group (45% compared to 37%) in their multiple choice test. In addition, students who used the MLMs answered a slightly higher percentage of in-class clicker questions correctly (60 +/- 4.0%) compared to the control group (54 +/- 3.0%). This leads to an effect size of 0.25, which is considered a small effect.

Finally, students rated the usefulness of the different course material on a scale of 1 (not useful at all) to 5 (extremely useful). Students in the experimental group rated the MLMs higher (~2.5) than the course textbook (~1.3).

So does multimedia course material improve student performance? Well these results show that it is no worse than traditional coursework. One thing to note is that any increased improvement of the group which did MLMs compared to the control group is very small. With a sample size of about 40 students in each group, it is difficult to draw any firm conclusions.

In addition,

It is worth mentioning that the comparison of final exam scores between students in the control and those in hybrid-MLM group showed no significant differences.

So at the end of the day, students did roughly just as well in both groups.

But this is an interesting study nonetheless. Probably the best thing to do would be to offer the MLMs as an optional and additional resource to the students, without cutting out the in-class learning time. Everybody learns differently, whether it be through visual stimuli, auditory or simply repetitiveness. The important thing is to make resources available so people of all learning styles can benefit.

I felt I could teach my students best face-to-face, so I declined to use the new fangled technology for online tutorials. But I understand they are still being used, and some students actually prefer them. So I guess in the end, this study showed that no single manner of learning is better than any other. Do what works for you and stick with it.

Sadaghiani, H. (2011). Using multimedia learning modules in a hybrid-online course in electricity and magnetism Physical Review Special Topics – Physics Education Research, 7 (1) DOI: 10.1103/PhysRevSTPER.7.010102

Teaching Electricity and Magnetism: Part I

March 29, 2011 2 comments

When I was a physics TA, there were two topics which always got the students easily mixed up. The first was Newton’s Laws; students had a hard time knowing which law to apply in what situation. But with a little practice and teaching, they soon found that you could follow a very specific procedure to solving any problem involving Newton’s Laws, which helped immensely.

Electricity and Magnetism (EM) was different, however. There really is no set procedure for solving an EM problem. There are strategies and guidelines, but no step-by-step ways of solving EM problems like there is for Newton’s Laws.

I’m not the only one who has noticed this either. Two papers were published this month in Physical Review Special Topics – Physics Education Research. The first was entitled “Interference between electric and magnetic concepts in introductory physics“.

This study looked at the difficulty students had in determining which direction the force on a charged particle would be, if it were in either an electric or a magnetic field.

For a positive charge in an electric field, the force is always in the same direction as the field. If the charge is negative, the force is in the opposite direction of the electric field. Students generally don’t have a problem with this rule; that is, until you introduce the concept of a magnetic field to them.

In a magnetic field, the force on a charged particle is always perpendicular to the magnetic field lines. So when you get to the end of the term and you ask an EM question, students often (understandably) get confused which rule they should use.

The main hypothesis of the study, therefore, was that students have trouble because they learn about electric fields first, and then apply those lessons to working with magnetic fields.

You can test this hypothesis by seeing if the opposite is true. Does learning about the magnetic field first negatively affect the way students answered questions about electric fields?

The subjects (I mean, ‘participants’ hehe) of the study were students in an introductory physics course at The Ohio State University. The students were asked to answer EM related physics questions. They were split up between groups which had learned i) nothing about EM, ii) electricity but not magnetism, iii) magnetism but not electricity, and iv) having learned both. The order in which the questions were asked and some other variables were randomized for better results. Below is an example of the type of question the students were asked.

Can you get the answer to this question? For the left hand side the answer is 'e - Into Page' and for the right hand side the answer is 'f - Out of Page'

There are actually several results from this study, so if you are interested in them all I encourage you to read it (it is free to read). But the main hypothesis turned out to be true:

directly after instruction about magnetism, many students answer that the direction of the force on a charged particle moving through an electric field is perpendicular to the electric field, presumably by employing the same right-hand rule that was learned for magnetic forces. Thus, despite the fact that directly before magnetic force instruction students were answering electric force questions correctly, up to two weeks (and possible longer) after they learn about magnetic force, they answer electric force questions as though they were magnetic force questions.

So the authors actually showed that it is not electric fields or magnetic fields alone that confuse students, but after learning both they get them mixed up, which makes sense. It doesn’t seem to matter, either, which they learn first. After learning both electric and magnetic fields they still get confused.

The authors suggest (and I agree) that to combat this the instructor must frequently point out the distinction between electric and magnetic forces. It is a difficult thing to get a feel for, kind of like learning the offside rule in hockey.

A good strategy is always visual demonstrations. Take for example this video of MIT professor Walter Lewin demonstrating the perpendicular magnetic force (jump to around 46:40 for the demonstration):

So what else could we do about students having trouble with EM? What about online and multimedia tools?

That will be the topic of Part II of this series.

Scaife, T., & Heckler, A. (2011). Interference between electric and magnetic concepts in introductory physics Physical Review Special Topics – Physics Education Research, 7 (1) DOI: 10.1103/PhysRevSTPER.7.010104