How do I explain electric fields?

Factual Questions
1

I complained in another thread that I was having a hard time getting students to understand the concept of electric fields, and Arwin was kind enought to offer to help. Everyone else is welcome to chuck in their two cents, too. (Any physics people looking in . . . I’m just sticking to the slightly stupid formulations used by our Physics 101 book, which does not use vector equations when they can be avoided.)

Okay, here’s my explanation.

First of all, if there is a pair of electrically charged particles, they exert forces on one another. A positively charged particle is attracted to a negatively charged particle, or repelled from another positively charged particle. A negatively charged particle is attracted to a positively charged particle, or repelled by another negatively charged particle.

All forces are vectors: they have a magntitude and a direction. Consider a particle that is being held in place, and a second particle that is brought near to it. The magnitude of the force on the second particle is proportional to the product of the magnitudes of the charges of the particles (don’t worry about positives and negatives), and inversely proportional to the square of the distance between them: F=kq[sub]1[/sub]q[sub]2[/sub]/r[sup]2[/sup] (where k is just a constant). The direction is either directly toward the stationary particle (if the particles have opposite charges) or directly away from the stationary particle (if the particles have the same charge.)

Now if you have two particles that you hold stationary, and you introduce a third particle, the new particle feels a force from each of the other particles. The total force on the third particle is just the sum of the two vector forces from the other particles.

My students are with me so far. Here’s where the train leaves the tracks:

Imagine that you have just a particle by itself. This particle creates an electric field. The electric field at any point is a vector. You can find the magnitude of the field at any point in space using this formulat: E=kq/r[sup]2[/sup], where q is the magnitude of the charge of your particle. The direction of the eletric field is determined by looking at the charge. If it’s positive, the electric field points away from the charge. If it’s negative, the electric field points toward the charge.

If you have multiple particles, then you find the total electic field at any point by calculating the electric field created by each particle (as though the other particles don’t exist) and adding the vectors.

Now, if you introduce a new charge (q[sub]0[/sub]) to the situation, the magnitude of the force it feels is F=q[sub]0[/sub]E. If q[sub]0[/sub] is positive, the direction of the eletric force is the same as the direction of the electric field. If q[sub]0[/sub] is negative, then the direction of the force is opposite to the direction of the field.

A large number of students do not get this. They do not get this at all. And damned if I can figure out where they lose the thread. Forces, they can handle. They can add vectors okay, too, which is probably the most challenging part of dealing with forces. But suddenly when we get to electric fields, I guess it just all gets too abstract for them. The following symptoms are observed:

  1. They cannot remember that electric fields are vectors and must be added as vectors. I’ve said “electric fields are vectors,” a million times, they had many homework problems about electric fields, and they had a practice exam with an electric field problem on it, yet on the last exam, almost half tried to add two electric field magnitudes as though they were scalars. (A much smaller number have the same problem with forces.)

  2. When given a simple situation, such as two identical particles on a line, so:
    ------------- (+) -------|------- (+) ----------------
    they cannot reliably tell which way the electrical field points at different points on the line. Here’s the answer:


                                            
E:  <--              -->      <--             -->
------------- (+) -------|------- (+) ----------------  
                       E=0 at the bar.

(Sorry, couldn’t figure out how to spoilerize code.)

If you can help me put my finger on exactly where I lose them, it would be most appreciated.

2

Have you tried using a parallel to gravity?

3

Yes. As soon as you mention the words “gravitational field” their heads explode. They’ve seen gravity in other context, but by far the most exposure is just stuff rolling downhill, blocks on inclined planes, etc. And that was all last semester when a different professor was in charge. For most of them, particularly those who have trouble with electric fields, “gravity” means g=9.8 m/s[sup]2[/sup], period (and we are delighted that they grasp that, and remember that it always points straight down). On the final exam last semester, a good chunk of the class answered “True” to “There is no gravity on the Moon.” (And I died a little inside.)

I’ve tried to use gravitational potential as an analogy for electical potential, too, and it was okay . . . until I mentioned negative charges. It’d be nice if I could get find a hunk of negative mass to use for classroom demonstrations. :slight_smile:

4

So let me get this straight, there IS gravity on the moon? No, just teasing. I hope this is for highschool. How about using magnets (maybe with + and - written on the ends)?

5

College level. Algebra-based physics.

Sorry, I don’t see how this would help them grasp the concept of electric fields. They understand that like charges repel and opposite charges attract. This is not a problem. And I’m pretty sure that involving magnets of any sort will just lead to rampant confusion when we actually get to magnetism.

6

This is just off the top of my head, but maybe rubber bands? They are visible, physical things that also exert a force directly toward a point. Maybe with a little fiddling around you can come up with an illustrative model using them.

7

I have no idea if this would help, but here’s my first thought: what might be confusing them is trying to understand the concept of a field (especially if it’s being presented as some seperate thing, different from the forces) while juggling the ‘positive attracts, negative repels, but if the other charge is positive, then positive repels…’ problem at the same time.

I might go over the attraction repulsion thing for a while, until they get the concept with two particles. Then focus on only a + and - pair, and describe the field as just describing what the force is at any point – a map of the force (on that particular particle), if you will. After they get that, only then complicate things with the idea of ++ pairs making the force point the other way, etc.

I’d say, OK let’s just talk for a while about a fixed positive charge, and let’s move this negative charge around (draw a positive charge on the board, and use a little ball for the negative charge). Ask them what the force is like at a bunch of points as you move the ball around. When they respond correctly, draw a little arrow on the board showing the force.

After a bit, you have a little map of the forces at different points drawn on the board (I think ‘map’ might be a good word to use, too). The ‘map’ shows which direction and how strong the force is anywhere. Physicists call that map the electrical field. …
No idea how this would work in practice, but it’s what I would try first, myself.

8

To illustrtate a field hold a lighted flashlight under a sheet of paper-----note the circle of light surrounding the solid core-------move the light closer to,or farther away from, the paper—Note the change in the size of the field-----relate it to the field around a conductor and the exciting force--------Done!

EZ

9

First, let me say that I can wholeheartedly sympathise. I’ve TA’d for a similar class many times, and in three consecutive labs, we have the question “Why can’t electric field lines cross?”. And I’ve seen students give the same wrong answer all three times (even after having gotten the first two labs back and graded).

That said, here’s how I would approach the question: First, give them a simple Coulomb force problem. For instance, have a 1 coulomb charge A “nailed down” at the origin, and a 1 coulomb charge B at 1 meter away. Ask them to calculate the force on charge B. From what you’re saying, they can do this. Now, change charge B to 2 coulombs, and ask them to calculate the force again. Change B to 2.5 coulombs, and ask them to calculate it again. After a few repetitions of this, you can point out that there’s part of that calculation they’re doing again and again: You have F = q[sub]B[/sub](kq[sub]A[/sub]/r[sup]2[/sup]) , and the part in parentheses is the same for every one of those problems. Now, since we’re using that part in parentheses a lot, let’s give it a name, and just calculate it once. So we could call the stuff in parentheses “E”, and just say “F = q[sub]B[/sub]*E”.

Then, of course, you have the concept that the electric field is still there, even if there’s no charge B at all, and I suspect that it’s this level of abstraction that’s losing a lot of your students. But unfortunately, I have no suggestions for dealing with that (and if you do, please let me know).

10

You might find this helpful:

Venus Flytrap Describes the Atom

11

Unless I’m very much mistaken, I’ve seen one of the best explanations of electrical fields in a science museum I see from my train dayly and was recently taken to by a lovely lady.

The setup of this experiment consisted of a field of magnetic arrows on swivels that you could influence by holding a magnet over them. Before I’m going to think this through further, am I correct that this setup was intended to illustrate magnetic fields and are you familiar with this setup? If not I’ll try to google it

12

Could this be helpful?
http://www.colorado.edu/physics/2000/applets/nforcefield.html

13

I think I turned a conceptual corner when someone pointed out that the field represents the force a positive charge would feel at any point in the field.

I think people intuitively understand vectors, they just get bogged down in the notation. If you put a point on a whiteboard (or blackboard) and said “this is a positive charge” and then pointed anywhere else and asked “if this second point is a positive charge, where will it go?” they’ll all get at least that much. Trial with more points might help them intuit vectors. It did for me.

14

Displays like the ones Arwin describes, and like the one provided in the link by drewbert are very good ways of showing the shape of magnetic fields. I remember the same can be done, though less fancy, by holding a magnet under a sheet of paper strewn with iron filings.

However, that only shows the shape of a standard magnetic field. IIRC, from those displays I remembered only the concept of “works at a distance” and the shape itself, a shape I’d remember in the same admiring but uncomprehending way I do remember the shape of a honeycomb, the leaves in a red cabbage cut in half, fractals like a sunflower, or the shape of ripples in water.

But what a magnetic field IS?
I’ve tried to read you explanation, Podkayne, but you lost me at the second paragraph. Too many abstract relations in one sentence. Could you please try again, this time like I’m a five year old?

15

This is very, very good. It’s exactly how teaching works best - connect the new knowledge to existing knowledge in the brain as much as possible. This example is a magnificent example that demonstrates this to the extreme. The new information is rendered to such insignificant proportions that the student almost fails to see he actually learnt something he didn’t already know.

Now the trick is to achieve something similar for the force field example. We can go about this very methodically, but I would like you to help me out. That way we both learn something. :wink: The first step is to make clear definitions of every aspect of the problem - every term, every property - we’re dealing with. Start, like Maastricht, with assuming zero prior knowledge. Your speaking a foreign language to us, in which there are a lot of new words:

I use bold for the first use of a ‘foreign’ term, and italics for all repetitions of it. In this paragraph, a student will have to understand the following terms in order to understand what’s going on:

particle
electric field
vector
magnitude
at any point in space
E=kq/r2
charge
direction
positive
points
negative

I have a pretty good idea of a number of every day situations that act not unlike many of the things going on here (for instance involving crowds watching sports or other entertainment, people blocking each others view, etc.), but we’ll easily get there if you try to explain to me each term I mentioned above. As soon as I understand the term in the context of this problem, I will give you a few analogies that will show whether or not I understood the problem, and I think we’ll be able to build something you can use for the students from there.

16

Okay, here are the definitions. I’ve also noted how familar each term is to my students at this point in the semester so you can see that I’m not just throwing a bunch of jargon at them and being perplexed when they don’t get it. :slight_smile: The OP was, of course, just an attempt at a quick summary to show Arwin what I’m talking about. I present that material over three days of class.

particle: A small piece of matter, usually free to move. They seem to cope particles okay when working with forces.

electric field: A set of vectors, one for each point in space, that tells you what the electric force will be if you put another particle at that point. This is totally new territory for them.

vector: A quantity that has a magnitude and direction. For example, a speed would be: a car goes 50 mph, a rocket goes 2 km/s, etc. The velocity is a speed, with a direction: The car travels 50 mph north. The rocket travels at 2 km/s at an angle of 20 degress from the horizontal, etc.

They are familiar with many examples of vectors, having worked with them all through the last semester: displacement, velocity, acceleration, forces, etc. The majority of them cope quite readily with electric force vectors, but then balk when we get to electric field vectors.

magnitude: The size of a vector, or the size of a scalar when it has been stripped of its sign. For example: The stronger the force, the bigger the magnitude of the force vector. An object may have a charge of -3 Coulombs. The magnitude of the charge is then just 3 Coulombs, without the negative sign.

Before you ask:
scalar: A quantity without a direction. It could be the magnitude of a vector, or it could be some other quantity that never has a direction associated with it: charge, temperature, the balance in your bank account, etc.

They do definitely have a tendency to get confused about what the word “magnitude” means when it’s applied to a scalar, so I’ve made a point of writing it explicitly in several cases and put it on a quiz, and they handled it okay so I think they have it at this point. They’re definitely solid on magnitudes of vectors they’ve been doing since first semester.

at any point in space: This could be a stumbling block which I hadn’t noticed before. We haven’t talked about space, per se, since first semester. And I recall that in previous semesters they’ve had trouble grasping that the magnetic field, in particular, doesn’t just stop when it reaches, say, another magnet.

In general the way I try to explain this concept is by drawing a charged particle, and picking some random points, some close to the particle, and some far away, and sketching the electric field vector at those points, and emphasize that we could pick “any point in the whole Universe” and calculate the electric field there.

And suddenly I realize that they don’t necessarily know what the definition of “Universe” is. Some of my Astro 101 students have a tendency to confuse solar system, galaxy and universe . . . Hmmm!

E=kq/r[sup]2[/sup]: The magnitude of the electric field. k= a constant. q= charge of the particle creating the field, r= the distance from that particle to a point of interest. Can’t think of any other way to “define” this “term”. It’s just an equation, and one that’s very similar to the equation for the force. They can usually calculate this quantity without difficulty.

charge: A property of a particle that lets it create, and be affected by, electric fields and forces. The larger the charge, the stronger the force or field created by the particle. Two like charges (both positive or both negative) repel each other, and two opposite charges (one positive and one negative) attract each other. The students don’t seem to have any trouble with this concept when they work with electric forces.

direction: The orientation of a vector. Again, a familiar vector concept.

positive: Positive numbers are greater than zero.

points: A point is a location in space. They should be a very familiar term. We use it in many contexts.

negative: Negative numbers are less than zero.

17

Yeah, I think that’s a magnetic field demo. We get to play with magnets in lab, and use iron filings, and compasses, and whatnot. Unfortunately, there’s no easy hands-on visualization you can do.

Chronos, yeah, I’ve tried to sell them on electric fields as a time-saving device. :slight_smile:

Yep. That seems to be the rub.

18

Argh . . . "No easy hands-on visualization you can do for electric fields.

19

I’m going to run through this, to give you my own first reaction to learning the terms here.

Particle. Check.

I think I know what you mean, but it sounds unnecessarily sophysicsticated. Surely the correct definition for electric field involves ‘a set of vectors’ but it sounds completely unnatural. Let me tell you why I feel this.

From how I’ve understood it so far, the electric field is the combined set of electric forces of charged particles. That makes a lot more sense to me. A vector sounds more like a way to express the forces, which you need to calculate the electric force that influences any given point in space, or any new particle added to the existing set. So that, in a way, you’re confusing them by mixing levels of abstraction, as it were.

Of course, that’s just me. I haven’t followed your course at all, I had the least amount of physics you can receive in high-school in my country (2 years, no longer possible these days at my level), and the few technical terms that were taught me were in Dutch.

[qoute]vector: A quantity that has a magnitude and direction. For example, a speed would be: a car goes 50 mph, a rocket goes 2 km/s, etc. The velocity is a speed, with a direction: The car travels 50 mph north. The rocket travels at 2 km/s at an angle of 20 degress from the horizontal, etc.
[/quote]

So, in the link given above to a conceptual computer simulation, it’s the pointed arrow exuding from a particle.

I could see where the problem is. A vector is like a mathematical line. It’s not actually something, but it’s a way of looking at a small instance of something. In the case of a charged particle, there are an infinite number of vectors emanating from it, correct? Like light from a lightbulb. It’s very weird to consider just one ray of light, and only possible in theory. Am I seeing this right or is my brain taking another weird excursion?

Check.

Before you ask:

I would definitely have asked, good call. :wink: I think I follow this.

I can imagine their confusion. It would help me too, if you could tell me what the use of scalars are. They sound like absolute values, in a sense. What makes them scalars rather than absolute values? Or are they simply that, and scalar being a nicer, shorter term the locals use?

This may have to do with the vectors. If you talk about vectors, you may lose the concept of the whole, the field. I think this may be a key problem. In a way, it could be more useful to start with the field as the given, and then fill in the details on its dynamics.

That makes sense.

You’re starting to sound eerily sarcastic. :wink:

Ok, clear enough.

That’s one part I’ve been missing in the picture above. How exactly are the particles charged - how do they receive their charge?

Yep, understood. Actually I remember vectors from math now, it’s all coming back.

Yes, but what is a positive charge, and what is a negative charge?

Check.

negative: Negative numbers are less than zero.
[/QUOTE]

As above.

If you can answer my questions above, I think I’m ready to start a first translation attempt.

20

The first part is explained in little words. But vectors is something that I doubt they understand (about half of my classmates didn’t by the time we were studying magnetic resonance), even if they think they do. So using vectors as the “link” between the individual force and the field may be what breaks the explanation.
Try something like:

now imagine that you have, not just two particles, but one particle here (close your fist to signify this central particle) and another particle here and another here and another and another… (mark points in the air with the other hand). Each of these other particles is subject to a force created by this first particle. All those forces together are an “electrical field” and any particle that’s got electrical charge has a field of its own.

I know it’s not a megaexact explanation, but it worked for my 10th grade Chemistry and Physics teacher, and some of my classmates were about as bright as LEDs. Burnt-out ones.