Teaching Electrical Concepts via Gravitational Analogies Page 1 Using Gravitational Analogies To Introduce Elementary Electrical Field Theory Concepts Printed 6 32 AM 1 14 19 Sue Saeli Dept of Physics SUNY Buffalo State College 1300 Elmwood Ave Buffalo NY 14222 Dan MacIsaac Dept of Physics SUNY Buffalo State College 1300 Elmwood Ave Buffalo NY 14222 macisadl buffalostate edu Please direct correspondence regarding this manuscript to MacIsaac Keywords analogies electric gravity field potential force PACS 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 19 Table 1 Introductory Analogies Between Gravitational And Electrical Forces Gravitational Forces Newton s Universal Law of Gravitation and the Coulomb Law for electric forces Electrical Matter has a fundamental property called mass measured in kg which has just one sign positive Students may ask and need to be told that so called anti matter has positive mass and reversed electric charge Matter has another fundamental property called charge measured in Coulombs which can have two signs positive or negative describes the gravitational force Hence Electric forces can be and direction where r repulsive or attractive describes the direction and negative means attractive v Gravitational force is therefore F k q1q2 r e always attractive r2 or in magnitude only v The magnitude of this force is q1q2 F r e k written 2 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 v mm Fg G 1 2 2 r r v mm Fg G 1 2 2 r where in SI units Comments r where in SI units k 9x10 9 Nm 2 C 2 G 6 67x10 11 Nm 2 kg 2 INSERT FIG1E JPG HERE INSERT FIG1G JPG HERE Some have even coined the phrase inertial charge for mass to exploit this analogy Since G is much smaller than k the gravitational v force F is usually much smaller than the v electrical force Fe have students work both forces for 2 protons and 2 electrons and compare via discourse g Students may not be familiar with 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 r as a unit vector pointing to the other point mass or charge rhat 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 19 Table 2 Introductory Analogies Between Gravitational And Electrical Fields Gravitational Vector Fields Electrical 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 m m m Fg G earth 2 2 mG earth2 rearth rearth and further define v v Fg m g v where g Similarly 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 qq Q Fe k 1 22 qo k 2 r r and is readily v calculable producing the v v famous g 9 8 N kg pointing towards F qE defining e the center of the Earth on the surface of v Q the Earth E k 2 r and where Now we can talk about the local field therefore is readily calculable strength of the Earth s gravitation field for uniform electric fields v at the Earth s surface g being the say those very near a charged smooth spherical shell with ratio of the gravitational force a test mass a mass much smaller than that charge Q or between two parallel plates with opposite of the Earth very near the Earth s charges as surface v v F g m Gmearth 2 rearth Comments Although the universal law of gravitation formula will work with any two point or spherically symmetric masses we most commonly experience the downwards force of gravity at the Earth s surface v g In that case one of the masses becomes the mass of the earth and the distance is the radius of the earth Students should perform this calculation of the gravitational field strength g to practice using exponentials in their calculator under teacher v supervision The idea is to make g slightly less mysterious as a local value for gravitational field strength and to permanently move to N kg units which
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