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| Electric Field Pic from thefullwiki.org |
I introduce electric fields in an unusual way, one that's not consistent with any textbook.
Most textbooks start with Coulomb's law for the force between two point charges. Then, eventually, they define the electric field as the force per unit charge on a "test charge" in the field. This is of course correct, and consistent with the way many seasoned PhD physicists think of the electric field. Try explaining this to a 17 year old in his first physics class, though -- you might as well try to explain the infield fly rule to someone who's never seen baseball.*
* The infield fly rule is a closed book to many actual baseball players and coaches, too -- trust me, I'm an umpire.
I've found much more success presenting the concept of the electric FIELD as primary. We begin with a full day's class on nothing but F=qE and the definition of the electric field. And F=qE essentially *is* that definition. F=qE gives the magnitude of the force on a charged particle in an electric field. This force is in the same direction of the electric field for a positive charge; the force is opposite the electric field for negative charges.
Those ideas seem so, so basic... but it takes nearly a week of practicing before my students figure this out. What do they do wrong? Everything.
* Label a point in space "point P," and say explicitly "There is nothing at point P but empty space, but the electric field at point P is 200 N/C to the right." Then ask a student point blank: "Is there a charge at point P?" "Is point P positive or negative?" "What is the force on point P?" Merely getting folks to agree that a position in space does not have mass or charge, and cannot experience a force, is a MAJOR challenge.
* Now, put an electron at point P. Verify with the class that an electron has a negative charge. Ask about the direction of the electrical force on the electron. Half the class will get this wrong... even though you just told them the rule about charges and electric fields! Try it. This is more complicated than you might think.
* No matter what you do, students will be confused about negative signs. I tell them again and again: IGNORE NEGATIVE SIGNS when dealing with electric fields. Neither a field or a force can be intrinsically negative. Use F=qE to determine the amount of a force or field; then use the rule about negative charges to determine a relevant direction.
* The electric field does not determine the direction of a charge's MOVEMENT. This is a holdover misconception from mechanics -- force and velocity are independent of one another.
So on the first night of electric field study, I break my rule about assigning only two AP-level problems per night. Instead, I assign six plug-and-chug F=qE problems. All I'm looking for are the basics -- can students state magnitudes and directions of electric fields and forces. See, that's more than half the battle in electrostatics. If we can bust these misconceptions, then perhaps the ideas of parallel plates and point charges won't be so impossible.
Below is the quiz I gave after this first night of homework. You might think this is "too easy" for an AP class -- but no, it's actually on or above their level after the first night of electrostatics. And, I could give this at the end of the year, and I would not expect anything close to perfection from a class of students who will mostly earn 5s. Electrostatics is HARD and ABSTRACT. Anything we can do to simplify, we should do.
GCJ
1. An electric field points right. What is the direction of the electric force on a +3μC charge in this field?
(A) positive
(B) negative
(C) Left
(D) Right
(E) None of the above, the force is zero.
2. An electric field points north. What is the direction of the electric force on an electron in this field?
(A) North
(B) South
(C) positive
(D) negative
(E) None of the above, the force is zero.
3. A 500 N/C electric field points left. What is the electric force on a -2 μC charge in this field?
(A) 1000 μN
(B) 1000 μN left
(C) 1000 μN right
(D) -1000 μN
(E) Zero
Questions 4-5: An electric field points to the right. An electron enters this field while moving to the right.
4. Which way is this electron moving immediately after entering the electric field?
(A) right
(B) left
(C) positive
(D) negative
(E) nowhere, the electron is not moving
5. Which way is this electron forced when it enters the electric field?
(A) right
(B) left
(C) positive
(D) negative
(E) nowhere, the electron is not forced
Questions 6-8: The charge on an electron is 1.6 x 10-19 C; the mass of a proton is 1.7 x 10-27 kg. A proton is placed in an upward electric field of 200 N/C.
6. What is the direction of the electric force on the proton?
(A) Up
(B) Down
(C) Positive
(D) Negative
(E) None of the above, the force on the proton is zero.
7. Which is bigger, the electric force or the gravitational force on the proton?
(A) The electric force
(B) The gravitational force
(C) The electric and gravitational forces are about the same.
8. How many times bigger is the bigger force?
(A) 109 times
(B) 106 times
(C) 103 times
(D) 100 times
Greg,
ReplyDeleteHave you seen theMatter and Interaction curriculum for calculus based physics? This is exactly how they structure the course, treating fields as primary. This lets them get into some really fascinating stuff about what is happening to surface charge distributions in circuits.
Huh. Great idea. I wish Haverford had used this when I practically flunked advanced E&M all those years ago -- looks like they use it now.
ReplyDeleteNow, I'm talking about an ALGEBRA-based course in this post, but the principles of teaching this topic seem the same.
greg
Yes, I know M&I is calculus based, and could not be used as a text for the AP-B, but I've found the approach, particularly its emphasis on explaining a wide range of phenomena with a small handful of ideas, and even the emphasis on building computational models to be applicable even to my 9th graders studying physics first. And it's description of how sparks form is nothing short of beautiful.
ReplyDelete