An Unconventional Introduction to Electricity and Magnetism

Overview:

This textbook sports an aggressively physical and thoughtful approach to E+M.  No more will students ask “which equation should I use for this problem?”  That is my intent, anyway.  From the start, students are guided to discover equations and rationalize their plausibility rather than having equations and applications simply presented them.  This work quickly distinguishes itself from traditional textbooks by preceding all calculus presentations with discrete mathematical approaches to problem solving.  Such an approach forces the student to be very attuned to the physical arguments as well as prepares them for the adoption, even the welcoming, of the calculus approach presented later in the text.  The text is written in an informal style students will find approachable.  Active reading is encouraged by providing reading activities within the text.  The main body of E+M equations are derived and written into the book by the student via the reading activities.  I think the book is challenging and is recommended for usage in colleges with high level students.

Another advantage of this text is that students will learn to solve a wider body of E+M problems than those offered in a traditional introductory textbook.  This is because they are not limited to contrived physical situations (e.g. infinite planes or infinitely long wires), where integrals can be evaluated via basic calculus.  Knowing how to apply finite summations prepares students to evaluate electric fields or apply the Biot-Savart law in situations normally restricted to upper division or graduate level E+M.  On top of improved mastery of fundamental physics, three other pedagogical benefits present themselves:

– this textbook can be used for both calculus AND algebra-based physics since discrete mathematics can be undertaken by students with a working knowledge of algebra; everyone can add.

– this approach helps prepare majors for computational physics.

– without the constraint of problems with analytical solutions, it is much easier for an instructor to create exams with unique, challenging problems.

My experience teaching with this book has been positive.  When I taught from traditional textbooks, my examinations were plagued with ridiculous answers from students with poorly constructed integrals, or integration skills.  Students learning from this textbook are wise enough to test a few finite iterations before committing to an integration result.  A side benefit for professors is that you no longer have to sift through the mathematics of a cocky student who claims the laws of physics are wrong because of a long string of calculus work undertaken on crumpled sheets of paper.  A quick dose of finite sums quickly sobers these types.

A good grip on the ‘physics’ of physics problems can go very far.  From personal experience as a student, I recall office hours where a professor refused to quote equations beyond the fundamentals and still arrived at sound results via physical arguments, never once looking at my gripping calculations on crumpled paper.  Applying this approach to, for example, electrical potential helps precipitate a series of improvements:  Instead of hammering home the mathematical description as done in traditional textbooks, the book initially eschews the math altogether and gives the student a feel for what potential is.  The extra sections of teaching the physical understanding of potential pay for themselves a chapter later, when students independently arrive at Ohm’s law.  In addition, resistance and capacitance are presented via physical/geometrical arguments.  In turn, the rules for addition of these components, in parallel or in series, become a common sense approach rather than a careful application (really memorization) of Kirchhoff’s Laws; students, via physical arguments, solve basic circuits without routine application of Kirchhoff’s Laws.  In fact, Kirchhoff’s Laws are pushed to the last quarter of the book and, even then, are only included for completeness.

The inspiration for this textbook came from a whining student who, during a final exam, with great conviction, told me I was being unfair to not tell him which equation on his equation sheet to use for a particular problem.  With great conviction he told me he could do the problem if I’d just tell him which equation he needed to use.  It dawned on me that, despite my lecture efforts to inculcate a physical intuition tying together the large body of equations, the textbook was sending them a conflicting message.  Traditional textbooks introduce material by presenting equations followed by examples applying the equations.  The message is, ‘Smarter people arrived at these equations for your convenience.  Here is how you use them.’  The Feynman Lectures and Thomas A. Moore’s Six Ideas that Shaped Physics are the exceptions I have found, and come closest to what I tried to achieve in writing this book.  I hope my textbook is a good middle ground.