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26 December 2011

Just the basics, not the sources, of electric, magnetic fields

Electric and magnetic fields frustrate me each year.  They're abstract, leading to few simple quantitative demonstrations.  They always seem to take their turn in the dark, cold, depressing months of January and February.*  And students are perennially confused between the source of an electric or magnetic field, and the victim of said field.

* Except that these were the most wonderful months of the year when I taught in Florida.

Ah, but this year I'm going to do something about that last point.

The AP Physics B redesign is said to be emphasizing "big ideas," physics themes which resonate beyond a particular topic.  For example, the idea of a conservation law permeates physics from mechanics, to rotation, to electronics, to nuclear physics... It takes a substantial level of real physics understanding to explain what quantities might be conserved in a specific situation, and why they are conserved, and just what exactly it means that a quantity is conserved.  Once the concept can be clearly and thoroughly articulared, the algebra involved in applying conservation of foo is generally trivial.  And so it goes with the concept of the field:  Once students get comfortable with the idea that a field of any sort is used to calculate the force on an object, using that force in a Newton's second law calculation becomes trivial.

Students become unintentionally familiar with the gravitational field g as the "conversion" between kilograms and newtons -- one kilogram on Earth weighs 10 N, but on Mars weighs only 4 N.  W = mg serves as what I call the "bible equation" for the gravitational field -- it relates the force on a massive particle to the gravitational field.  Once that gravitational force is known, this force can be drawn on free body diagrams and used in a newton's second law calculation just like tension, friction, or any other force.

Now, those of us who are experienced physicists know that the source of this gravitational field is the enormous mass of the Earth applying on all other massive objects, via Newton's law of gravitation  F = GMm / r2.  But I ask you... who in his or her right mind teaches first-year physics students  F = GMm / r2  BEFORE W = mg?  No one.  Don't be silly.

So why, why, why does every textbook in the universe teach F = kQq / r2 before F = qE?!?

For many years, I've begun electrostatics with the definition of an electric field via F = qE, completely ignoring what might cause such a field.  A field simply exists in space.  If a charge is placed in the field, that charge experiences a force qE in the direction of or opposite to the field, depending on the sign of the charge. Only much later have I broached the confusing subject of fields produced by point charges or parallel plates.

Not only has this approach been effective in getting students to succeed on AP Physics B - style electrostatics problems... in their second year calculus-based AP Physics C course, my students have little trouble with electrostatics.  We can calculate an electric field using superposition, Gauss's law, calculus, whatever -- everyone understands that, once we have an electric field from any source, F = qE.

Currently I'm teaching Honors Physics I, which is intended to anticipate the AP Physics I redesign, rather than AP Physics B.  The "big idea" of a field permeates several different physics topics, and so is ripe for conceptual investigation.  In Honors Physics I, I will ignore sources of electric fields completely.  I want the class to be able to explain what a field does to a charged particle, not necessarily how the field came to be.  And I'll do the same thing with magnetic fields:  We'll discuss the bible equation F = qvB, and the right hand rule for the direction of the magnetic force on a charged particle.  That's it.  Magnetic fields due to current-carrying wires can wait for Physics C.

I encourage you to try ignoring the source of the electric or magnetic field.  If you're teaching to an exam (i.e. AP or Regents) that requires discussion of a field's source, throw that in as part of review at the end of the unit, or even at the end of the year.  Electricity and magnetism will never be easy for first-year students, but by simplifying the initial introduction to fields, you'll get better results long term.

1. I like the idea of teaching F=qE a lot. You tell students that if you have a charge, things happen to you. Figuring out the sources is much harder. I like the calc-based intro book we use at my college for how it does exactly that with mag fields. One or even two chapters on the effects of mag fields before getting into how they're formed. Thanks for the great post.

2. I do like your ideas. But my class this year has many students who prefer to read book right after, sometimes even before my explanations. What reading sources would you recommend for at least the first couple of days (or a week) of electrostatics? Thanks for the great ideas.

3. Good question. I'm open to suggestions -- When I taught out of a text, I instructed students NOT to read about electrostatics. When someone read the text anyway, he invariably was the last to understand the topic.

The 5 Steps book (5 Steps to a 5, AP Physics B & C) uses this sequence, and is appropriate reading previous or simultaneous to your class coverage. This is a prep book, not a text, but is nevertheless a good supplement.

If anyone can recommend a textbook that uses the "field first" approach to electrostatics, please post here!

4. How do you handle students who ask you what is the Newton's 3rd law pair for the force on the charge? And if no one ever asks you, do you ask them?

5. Great question... They do ask, because I've been so insistent all year that only objects, not nebulous concepts like "gravity," can be the source of forces.

I explain that for now, we can call this the force of the electric field on the object, because we do not care what produces the electric field. I tell them that eventually in their study of physics, something must produce that electric field; and the force on the charge is applied by whatever produces the electric field. But for now, since the cause of the electric field is irrelevant, saying "force of the electric field on the charge" is acceptable.

GCJ

6. I taught it this way in my AP B class this year and it was received very well. I talked about the gravitational field strength and its units of N/kg and then drew a uniform electric field and asked what units would describe the electric field strength. The "conversation" flowed so easily that I even pulled in a sneak peek at potential energy and work done in moving charge in a uniform field, comparing mgh to qEd. I feel they're on a much sounder footing going into the deeper aspects of electricity.