WONDER AND CURIOUSITY: THE TIGER IN THE JUNGLE

Here’s an update on my journey/decision to go sooner (and hence, further, this academic year than in previous years) into electromagnetism, the first major objective being to make it all the way through magnetism by the end of the third quarter. 

Magnetism, which typically gets half coverage in most courses, is a true curiosity to most all students but is nevertheless heavy going for most.  As it is born of changing electric fields (moving charge) and in changing itself gives birth to electric fields, its toroidal fields having no beginning or end, and has a right-hand-rule at every turn.  And what is more, magnetism makes possible a bewildering array of devices, the workings of nearly every contraption known to man now become explicable.  Most magnetism sections in text books, especially once into Faraday’s Law of Induction, are crammed with applications of all kinds and are difficult to hack through in a timely fashion, hence keeping a focus on the fundamental laws and developing the beginnings of a holistic intuition is a challenge.

So be it, as again, this route has been taken in order to try and put an emphasis on fields, in hope of giving students a deeper understanding of electromagnetic radiation when we finally arrive there.  And ultimately, to give them a first glimpse of a deeper connection, and hopefully spark the wonder in the reality underlying all of nature, vibrations and waves of energy and the order that is manifest, the tiger in the jungle.

There isn’t the space in a single post to report on all the interesting pedagogical fruits that have presented themselves along the way so far but here’s at least one encounter.   I’ll blog about others in the weeks ahead.

Using Electrostatics to help students gain awareness of and get a grip on the concept of the Gravitational Field Strength ‘g’: 

Pedagogically the gravitational field strength ‘g’, better known (if not exclusively known by most) as the acceleration due to gravity, is almost never introduced as a field-strength in the discussion of Newton’s Laws of Motion (NLM).  NLM along with momentum and energy conservation comprise the first semester of a typical high school physics course.  Indeed, this is so in almost all introductory physics courses at any level.  Newton’s Universal Law of Gravity (NLG) is generally introduced late in the first semester and so instructors are reluctant to rely too heavily, if at all, upon the concept of field-strength, which is at best nascent in the first semester. 

This presents a dilemma (often soon forgotten) for most instructors during the first semester, this being the use of the force of gravity to explain the basic concepts of NLM.   As earth’s freely available gravity field, so conveniently uniform at the surface, is a gift for all sorts of demonstrations of NLM.  And in fact, as a consequence of such demonstrations and usages, and a reluctance to properly characterize ‘g’ as a field-strength, results in students conflating the ‘a’ in f=ma with ‘g’ acceleration due to gravity, and in fact for most ‘g’ becomes virtually an integral part of NLM, when in fact, that is not the case at all. 

NLM would of course be entirely at work in the complete absences of gravity.  In fact, if we and our students were on a good size space station, say like the one in the classic film ‘2001: A Space Odyssey’ with its large rotating platform, which amongst other things accommodated a cocktail lounge, etc., thus reproducing all the trappings of an earth like lifestyle, relying solely on various objects’ inertia to simulate gravity (the centrifugal ‘pseudo’ force).  Indeed, in such an environment we would in principle be utterly unaware of gravity (Einstein’s general relativistic equivalence aside) as it would be almost impossible to detect or use for demonstrations, in so far as it arose from the local masses (~10^—6 earth g).  Chances are gravity wouldn’t be an important part of the conversation until late in the first semester.   Explanation of NLM would likely rely entirely on the turn of the wheel, and inertial mass alone.

Nevertheless, as we are here on earth, in the early going of virtually all introductory courses ‘g’ becomes a factor that is frequently invoked to account for changes in motion, unhesitatingly standing in for the ‘a’ in F=ma in a good many applications of NLM, particularly, when crossing over from kinematics to dynamics and for a good while thereafter.  This practice then has the potential to completely blur the distinction between inertial mass and gravitational mass, the force of gravity, and Newton’s Laws of Motion, generally mixing gravity into the student’s laws of motion concept tool kit in a nearly irreversible brew. 

The introduction of static electric fields, the concept of field-strength lEl, charge q, and the force on a quantity of charge qE then bring the real opportunity to go back and show the parallel relationship to the gravity field, field-strength lgl, a quantity of (gravitational) mass m, and the force on the mass mg, and hence, separate potentially deeply entangled physical concepts many students may harbor after the first semester.  

Additionally, the remarkable similarity of Newton’s Universal Law of Gravity (NLG) to Coulomb’s Law is an opportunity to bring attention to the orderliness of nature via the simplicity and similarity of the forms of these two respective force laws (lF_El=kq₁q₂/r², lF_Gl=Gm₁m₂/r²) and field strength relationships ( lEl=kq₁/r², lgl=Gm₁/r²). 

By contrasting and comparing these now two clear examples of fundamental sources of force, and giving meaning to the concepts of fields and associated field-strengths, acting on different kinds of natural stuff, GRAVITATIONAL-MASS in the case of the gravitational field-strength, and CHARGE in the case of the static electric field-strength.   Both of these then account for a different fundamental source of force acting on the inertial mass of their respective objects, which one can then apply Newton’s Laws of Motion to, and via kinematics, work out the dynamical consequences.

Yes, this important distinction between gravitational mass and inertial mass is elusive, because happily, they just so happen to have the same mass values for any given object (to many decimal places, so far).  But of course, this didn’t necessarily have to be so, it’s just so happens that it is, and is one of the wonders of nature! 

(Of course if they were a little different, say by 10%, that’d have been OK by me.  It’d make it easier to point out the distinction when explaining NLM.   For instance, in the static electricity case we’d have F=qE=m_ia and thus a=qE/m_i (m_i for inertial mass), and in the gravitational case we’d have F=m_gg=m_ia or a=(m_g/m_i)g, helping to deconflate gravity from NLM.)

The Challenge of Getting to Electromagnetic Waves in High School Physics Curricula

Traditional high school physics courses, especially those taught to junior and senior level students, cover Electromagnetism in the last half of the second semester. This is true at Lowell High, and in roundtable discussions with other high school physics teachers it is my assessment that this is indeed broadly practiced. And in fact many high school level text books are organized to reflect this reality. It’s unclear which is the chicken and which is the egg in this regard, nevertheless clearly this situation is in part due to some extent to the pedagogical comfort of continuing to deal with hard physical stuff (mass) immediately after linear and rotational mechanics (Newton’s laws) have been covered. Versus say, introducing force fields and electromagnetism which are a rather newer invisible reality, and then pushing on to the further, largely mechanical, topics such as thermodynamics, fluidics, sound, etc.  Which then, by the way, can be given greater explanatory grounding as it is electromagnetism which mediates virtually all consequential material interactions.

The current state of affairs may seem like a harmless enough juxtaposition of material but the reality is the majority of high school physics courses are taught to classes largely comprised of seniors.  This is due to the level of mathematical maturity required and a number of other historical curriculum prioritization factors. Be that as it may, the reality is that seniors graduate early, and in fact have very disrupted schedules in the final month prior to their early departure. Hence all of these circumstances conspire to find the majority of honors level students leaving high school without having been comprehensively introduced to electromagnetism, and most certainly, electromagnetic waves.  This seems particularly alarming when arguably electromagnetism is the most important explanatory source of force and change in our daily lives, and is pervasively interwoven with the understanding of virtually all areas of science and engineering.  And  hence should, one would think given the technological challenges facing the next generation, be given an early and complete pedagogical exposure. 

In recognition of this situation I will in my physics classes this year be turning the second semester back to front, introducing E&M in the third quarter, looking to break for mechanical vibs and waves at the end of the third quarter, and then returning to E&M to cover electromagnetic waves prior to returning to the traditional third quarter material at the end of the fourth quarter.

Listening for the sounds of picks and shovels, and feeling the excitement!

As part of our GK12 effort, and in way of bringing greater awareness of a current scientific research community into the classroom, during the first quarter Molly Clay and I have initiated a long term teams based nanotechnology project wherein students working in groups of two or three are researching one of four topical areas: applications of gold nano particles to cancer, gecko feet stick phenomena, no-stick-surfaces, and nano-scale assembly. The teams are tasked with performing background web based research identifying people, places (research centers) and articles. After completion of the background effort each team will choose a subtopic of focus and delve deeper into the objectives and status of the research in that area. In addition to a qualitative overview teams will be encouraged and guided towards discovering, understanding and reporting on the key variables at issue, and bringing to light the first-order-of-business quantitative techniques and technologies used by researchers in their respective areas. Currently it is anticipated that the projects will be completed towards the end of the first semester, culminating with each team reporting on their findings to the class in the form of a 5-10 minute power point presentation.

Hats off to the UML-GK12 program, and of coursre to Ms. Clay, who is herself a member of the nano research community, for making this possible.

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