Teaching Electrical Concepts via Gravitational Analogies Page 1 Printed 6:32 AM 1/14/19Using Gravitational Analogies To Introduce Elementary Electrical Field Theory ConceptsSue Saeli, Dept of Physics, SUNY-Buffalo State College, 1300 Elmwood Ave, Buffalo, NY 14222Dan MacIsaac, Dept of Physics, SUNY-Buffalo State College, 1300 Elmwood Ave, Buffalo, NY 14222 <[email protected]>.Please direct correspondence regarding this manuscript to MacIsaac.Keywords: analogies, electric, gravity, field, potential, forcePACS codes: 01.40Gb, 01.55, 41.90 Abstract:Familiar gravitational phenomena and conceptual analogies are useful in explaining those introductory electrical concepts associated with field theory since the electrical ideas are unfamiliar, abstract and difficult to visualize. These analogies emphasize the underlying continuity of fields in physics and support the spiral development of student understanding. We find the following four tables to be particularly useful in reviewing and summarizing these comparisons after students have conducted through appropriate touchstone activities and discourse as part of the process of making sense of electric fields.Acknowledgements: This manuscript addressed requirements for PHY690: Masters' Project at SUNY-Buffalo State College. Portions were supported by NSF DUE 0302097. All figures by Mr. Matt Coia. Some terms coined in discussion with Dr. David Cole of Northern Arizona University; Mr. John Burgholzer of Amherst HS also provided significant comment. Other ideas were informed by the comments and curricula of The ASU Modeling Physics (REF1) project and personnel, particularly Mr. Gregg Swackhamer and Mr. Larry Dukerich, and the Workshop Physics (REF2) curriculum by Professor Priscilla Laws of Dickinson College. Errors and omissions are the responsibility of the authors.Introduction:Conceptual analogies from more familiar gravitational phenomena are useful in explaining introductory electrical concepts based upon field theory since the electrical ideas are unfamiliar, abstract and difficult to visualize. These analogies emphasize the underlying continuity of field concepts in physics and they support the spiral development of student understanding. We find the following four tables to be particularly useful in summarizing and reviewing these comparisons after students have worked through appropriate activities analyzed via extended student discourse (REF3).Teaching Electrical Concepts via Gravitational Analogies Page 2 Printed 6:32 AM 1/14/19Table 1: Introductory Analogies Between Gravitational And Electrical ForcesForces: Newton's Universal Law of Gravitation and the Coulomb Law for electric forces.GravitationalMatter has a fundamental property called mass, measured in kg, which has just one sign: positive. € v F g= −Gm1m2r2ˆ r describes the gravitational force and direction, where € ˆ r describes the direction and negative means attractive. Gravitational force is therefore always attractive. The magnitude of this force is written: € v F g= Gm1m2r2where in SI units: € G = 6.67x10−11Nm2/kg2INSERT FIG1G.JPG HEREElectricalMatter has another fundamental property called charge, measured in Coulombs which can have twosigns: positive or negative. Hence Electric forces can be repulsive or attractive. € v F e= kq1q2r2ˆ r or in magnitude only: € v F e= kq1q2r2ˆ r where in SI units:€ k = 9x109Nm2/C2INSERT FIG1E.JPG HERECommentsStudents may ask and need to be told that so-called "anti-matter" has positive mass (and reversed electriccharge).Note we are talking about point masses and charges or perfect spherical distributions of mass and charge.This is a non-calculus treatment (easily extended).Some have even coined the phrase "inertial charge" for mass to exploit this analogy.Since Gis much smaller than k, the gravitational force, gFv, is usually much smaller than the electrical force,eFv (have students work both forces for 2 protons and 2 electrons and compare via discourse).Students may not be familiar with € ˆ r (read aloud as r-hat) notation (REF3), but will need it if they go on in physics. As well, this notation is needed to make conceptual sense of centripetal acceleration, so if it is new, now's the right time to discuss it. Note the tiny stick man in the figures defines € ˆ r as a unit vector pointing to the other point mass or charge. r-hat really contains direction information only. Your students might also not recognize the "absolute value" notation used to strip direction from a vector, or the triple bar definition sign. These notations require explicit explanation and repeated student use.If your state exam requires a particular notation, use that as well from the start of the year.Teaching Electrical Concepts via Gravitational Analogies Page 3 Printed 6:32 AM 1/14/19Table 2: Introductory Analogies Between Gravitational And Electrical FieldsVectorFieldsGravitational For a small mass (compared to that of the Earth) on or very near the surface of the Earth we can group together known terms and solve: € v F g= Gmearthm2rearth2= mGmearthrearth2 and further define € v F g= mv g where € v g ≡Gmearthrearth2 and is readily calculable, producing thefamous € v g = 9.8 N/kg pointing towardsthe center of the Earth on the surface ofthe Earth.Now we can talk about the local field strength of the Earth's gravitation field at the Earth's surface, € v g , being the ratio of the gravitational force a "test mass" (a mass much smaller than that of the Earth very near the Earth's surface). € v g =v F mINSERT FIG2G.JPG HEREThe gravitational field strength gives units of force per unit mass or N/kg, which should be shown (by students) tobe the same as the more commonly used m/s2. Henceforth, the field units are to be pedagogically preferred.ElectricalSimilarly, with the electrical force there is a field around a given point charge Q (or spherically symmetrical distribution of charge Q) and it is useful to talk about the field strength around that charge. € v F e= kq1q2r2= qokQr2defining € v F e= qv E where € v E ≡ kQr2, and therefore, is readily calculable for uniform electric fields - say those very near a charged smooth spherical shell with charge Q or between two parallel plates with opposite charges as: € v E =v F qINSERT FIG2E.JPG HEREThe corresponding units for the electric field strength are, therefore, force per unit chargeor N/C, again with more common units of V/m
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