Charge is a property of some subatomic particles. Electrons have one negative charge, protons have positive charge. Without going into Schrödinger’s atom, which is very complicated and not needed for our purposes, you can think of atoms as having a nucleus, in the center, which is formed by protons and neutrons, and electrons orbiting in circles around the nucleus. Protons and neutrons are both pretty heavy, about the same size; neutrons have no charge. How many protons are in the nucleus tells you what the element is: for example, all carbon atoms have 6 protons. The number of neutrons can change within atoms of the same element: carbon-12 is the most common kind and has 6 neutrons, c-13 has 7, c-14 has 8.
In a neutral atom, you have as many electrons floating around the nucleus as protons in the nucleus. The electrons are a lot lighter than nuclear particles.
Atoms can lose electrons through a variety of means (giving it to another atom, being struck by the right kind of light), they can also gain extras. An atom with a different amount of electrons and protons has a charge - positive or negative depending on whether it lost electrons or gained them.
The labeling of the charges as positive and negative is for historical reasons. When electrical fields and currents were discovered, physicists likened them to gravitational fields and thought that “positively charged particles travel from points with high electrical potential to points with a low potential”, like a body falling due to gravity. But they had no idea which side was which and picked one at random to be high - this in turn determined which particle got to be positive (the one attracted by the pole that had been labeled as low). Later it was found that the particles that moved were actually the negatively-charged electrons but nobody wanted to have to change 100 years worth of articles and textbooks. Can’t blame them.
Chemistry is all electricity, and I got two degrees in it the second one in quantum chemistry.
Not quite. A particle on its own cannot create a force Forces only exist between two particles.
One of the words that should have been defined earlier is force, which is something that will cause a particle to accelerate according to Newton’s Second Law : F=ma. Nothing can exert a force on a point in space; only particles, things with mass, can feel forces.
Maybe instead of force, you mean . . . influence? Influence isn’t a word that has a specific physics definition, but kind of gets at the idea that the charge is kind of doing something out there to something.
Can you restate this, without using the word “force” unless it’s acting upon a particle?
Yes. Those arrows represent the force felt by the particle.
I think you’re kind of on to it. One of the conceptual difficulties with electric fields is that, if we’re just thinking about a single particle, there is no electrical field at the location of the particle. (Don’t ask me why. My brain isn’t big enough to understand this; I simply accept that it is true.) Diagrams often show field lines emerging from the particle, but that’s a bit deceiving. A field vector exists for every other point in space, except where the particle is. To draw the vector, you start at the point you’re interested in, then the vector points in the direction that the force would be for a positive particle, and its length represents the strength of the field at that point. The vector doesn’t emanated from the charged particle. You can draw one starting at any point (except the point where the originating charge is).
A scalar is not an absolute value. Scalars could be positive or negative. For example, charge is a scalar. It could be positive or negative.
The magnitude is a special case of a scalar. This is always an absolute value, whether it’s representing the magnitude of a vector or the magnitude of a charge.
I’m not quite sure what you mean by this. I absolutely cannot imagine how we could discuss an electric field without using vectors.
We do begin with electrical forces, and how particles move under the influence of other particles, before we talk about fields
Oh, no, really, I’m not. It just hadn’t occurred to me before! The background of my Physics 101 students isn’t that much different form the background of my Astro 101 students, so it would make sense that many of my physics students might not know exactly what I mean when I say “universe.”
Fundamental particles, such as protons and electrons, the building blocks of matter, have charge. How do they get them? Heck if I know. Particles have mass, and some particles have charge. To be flip, that’s just how God made the Universe.
As for larger objects, neutral objects have equal numbers of protons and electrons. Because electrons are smaller, and have less mass, they’re easier to move around, so in general objects get a charge by having extra electrons, so they are negative, or by having lost some electrons so they have a positive charges. Example: Wool socks in the dryer lose electrons, so they have a positive charge until (ZAP!) they steal some electrons from somewhere else by attracting them.
Again, my wee brain flounders. Electrons have a negative charge, and protons have positive charge. Using signs is convenient, because the math works out. Since we do not use the full vector form of the electric force and field questions for this class, this isn’t obvious, but consider:
positive times negative = negative ; this leads to an attractive force in the full equations.
negative times negative = positive
positive times positive = positive; this leads to a repelling force.
(We do exploit this property in 101 when we do electic potential enegy and electric potential, but no need to go into that unless you’re curious about it.)
If we reversed them, and made protons negative and electrons positive, all the math would work out okay, then, too, so they aren’t positive or negative in any deep sense; all that is important is that the charges have opposite signs.
Thanks very much for taking the time to understand this, Arwin. I really appreciate the effort you’re putting in to helping me. And thanks also to the others who have offered suggestions.
There are a few parts of the explanation I find a bit troublesome, though.
First off, you don’t make any connection between the physicality of a charge to the numbers the variables represent. You might say “This particle has a positive charge. Its charge is 3. This other particle has a negative charge. Its charge is -7. For our purposes, the positivity or negativity of the charge is represented by this value.” Otherwise, your students might think that a positive charge is something special, rather than just a number.
This makes sense, but it took me a bit of thought. Perhaps you might add this:
“Electric fields are always positive, because we have defined them to be so. You know that opposites attract and like charges repel, so a positive particle in an electric field will be pushed in its direction (like a leaf in a stream) but a negative particle will experience a force going the opposite direction of the direction of the field…like a leaf that zips upstream somehow…y’know, it’s negative, sorta contrary…am I babbling?”
So maybe that doesn’t help. But the statement that electric fields are always positive simply because we don’t know how to draw vectors with negative lengths might help. Maybe. Might just confuse them more.
If I get the time I’ll dig through the garage and see if I can find Thinking Physics, which is a fabulous book with conceptual explanations of all sorts of stuff. It might be of use. Actually, if you don’t already have a copy you should just buy one. Can’t recommend it enough.
Awright…upon preview I see there are more responses. And one thing is driving me batshit:
The formulae are using magnitudes of charges. I didn’t get that magnitudes were always positive, but that’s reasonable enough. But why, why, oh why do the formulae use magnitudes? Everything seems to work out pretty well if you enter the charges’ scalar values, with negative values for negative charges.
Using magnitudes, you’re saying “Okay, take away all the negative signs, calculate this, and then apply these fiddly rules to figure out what you would have known already if you hadn’t stripped off all the negative signs.” It seems so much simpler to just plug in negative charge values for negative charges, and if your result comes out negative then your vector will be pointing the other way.
I was thinking when you said “If it’s positive, the electric field points away from the charge. If it’s negative, the electric field points toward the charge” that you needed to make it clear that that was an observation of how the math comes out, rather than a rule to be applied. But because you’re stripping off negative signs before doing your math, it actually is a rule you apply. No wonder people are confused; they have to remember arbitrary-sounding rules.
So, having ranted…um…if you didn’t use the absolute value of the charge strength, would the math come out okay in all situations? Perhaps it make a difference when you get into 3-dimensional problems? I’m suspecting not, but I don’t have the physics ability to be able to say for sure.
I think I’ve understood your explanation of the terms, so I feel more confident now about going back to the original.
So, this is one of the things that made me think that you could have started explaining all of this right here. It doesn’t really get much simpler than this. There is a particle. It has a charge. Like a match lighting up a dark room, this charge has a magnitude that decreases the further you go away from the particle, and increases the closer you get to the particle. Like getting closer to or farther away form a light, a fire, a heater, etc.
Everything else you mention below comes into play at the moment you make this situation more complex.
So this ‘any point’ is a theoretical position, where, if there had been a particle (say, a chargeless one - probably doesn’t exist in real life but hey), it would have created a force between itself and one or more charged particles in its vicinity.
So what you are doing now, is trying to describe the relationship between two particles, but without the particle. We understand that if you have a particle with a positive charge facing another particle with a positive charge, the second particle will be repelled by the first. Taking that second particle away, we have a field of positive charge, electricity radiation if you will. Saying that it points away from the charge, basically means that you’re describing the ‘radiation’ by how other particles react to them.
So now again we look at a situation where we’re determining the ‘electric radiation’ levels at a certain point, without having a particle present. Only this time, the ‘electric radiation’ is created by multiple particles, each with separate charges.
This is the part where I’m lost, a little bit, like your students, as I was the first time I read it. I understand, I think, that if qo is positive, this will as in math, not change the plus or minus, but negative negates the plus or the minus. But what is the charge here? Are we talking about a charged particle, or are we talking about the charge, without the particle? Iif we’re discussing points in fields, rather than the forces between individual particles, it could mean both and you have to be clear.
Currently, I’m imagining a positively charged particle as a particle with a big circle around it (it’s ‘electric radiation fallout’). This is the electric field created by the particle. If I put another particle in that big circle, I can now draw a line between the two particles, and that is the force between the two particles. The original particle, around which I’ve drawn the electric field circle, in itself has a charge that is either positive or negative. Because basically the electric field is the status quo before the second particle arrived, we give the field a fixed direction, either positive or negative, depending on the charge of the particle that creates the field.
The second particle has a charge too, and that too is positive or negative. Quite obviously, if a particle has a positive charge, the electrical field it creates is positive. Once another charged particle is added and a force develops between the two, this force will become either positive or negative, as you describe in the formula.
I sense a metaphor Democrats and a Republican coming up, and swing votes. Yep, there it comes. If a convinced Democrat is in the neighbourhood, all the swing voters within reach will feel like voting Democrats, and if a convinced Republican is in the neighbourhood, all the swing voters will feel like voting Republicans (swing voters are points, or non charged particles).
The influence one of this convinced Democrat or Republican on the swing voters can be expressed in vectors, a combination of the strength of the political conviction of the supporter, and the physical distance between the supporter and the swing votee. So, if you want to know how much influence a convinced Democrat has on his surroundings, simply ask one of the swing voters what he thinks he’ll be voting at the next election and how sure he is (pick a point in the presence of the charged particle, and calculate the vector).
Now, if you put a number of convinced Democrats together in an area, they will exude a stronger influence on the swing voters - just add up the strength convictions and their distances to the swing voters (following the formula given above). If you put one Republican between ten Democrats, most swing voters (except perhaps one or two neighbours) will very likely still vote Democrat.
You can also look at how two citizens with a strong political conviction get along (force). If two citizens vote for the same party, they will develop either a good vibe or a bad vibe (positive, negative). For instance, a Democrat will have a negative vibe (force) with an Republican, and a positive vibe with an important Democrat.
Well, it’s rough, and we can work it out, change it to religion, or support for different sports clubs as desired, but let’s see if it shows I’m starting to understand this at all, or if I’m still way off.
There are labs you can do to demonstrate equipotential field lines, if that’s what you need. We did one (high school AP Physics class) where we had a battery that had a copper wire coming from each terminal. The copper wires were placed on opposite ends of a transparent storage bin. Under the storage bin, we had a paper grid so we could chart the equipotential lines on an identical chart that wasn’t under the bin. The bin was filled with saline water, and we were given voltmeters.
We connected the the positive input for the voltmeter to the positive copper wire (while still leaving it in the water), and stuck a wire connected to the voltmeter’s negative output into the water at different points. By finding places where the voltmeter gave the same reading, then connecting these points, we got ourselves some equipotential lines. Our class didn’t seem to have the same trouble understanding electric field lines, but this is a hands-on way of doing it. I don’t have a lab report (wish I did, now, though) to show you, but if you’re not quite understanding, here’s an electrical diagram. (v)
| |
| |
_________( water )
–
_____________________________
The drawings made by connecting the dots should give them an understanding of equipotential lines. Just tell them that the vectors acting on charged particles are normal to these lines.
If this doesn’t work, my instructor said something about using chopped hair to map electrical field lines in the same way you can use iron fillings to map magnetic field lines, but I know nothing about this.
Good luck!
Er, as I said, the OP represents material covered over the course of three 50 minute lectures, not the sum total of what I tell students about electrostatic forces. The seem to handled the concept of electrical charge okay, since they can manipulate charges just fine when they’re calculating electrical forces.
They know how to deal with vectors and magnitudes of vectors. As far as I can tell, this is not a source of difficulty.
Well, for one thing, because that’s the way the book does it. The book doesn’t have many vector equations in it, and doesn’t teach unit vectors, dot product, cross products, etc. So the way it works is that you use the magnitudes of the charges to compute the magntide electric forces and electric fields, and then you have to think about the arrangment of charges to figure out which way the point.
I don’t think this is a huge problem because, as I’ve said, the book presents forces this way, and by and large can do force problems just fine. If I say, “You put a charge q at point P. What does it do?” and the vast majority can handle that fine, despite the vector shenannigans. If I say, “What’s the electric field at point P?” more than half of them cannot correctly answer that question.
This method is perfectly mathematically legitimate. And keep in mind that while to someone who knows how to handle vectors, this sounds dumb, these students don’t know very much vector math. They can break a vector into cartesian components, compute a magnitude and direction from components, add vectors, and . . . pretty much that’s it. They’ve had a couple problems where they had to subtract vectors and this very nearly blew their minds. Manipulating vectors presents major conceptual difficulties there for them. Getting them up to speed on that would take a tremendous amount of effort, and for many of them, it would be a stumbling block that would block all progress. So we do this kinda-vector, kinda-not thing, that at least lets them understand electric forces.
Thanks for the suggestion, XWalrus2, but we don’t do equipotential lines. We fear them.
Yes, you’re getting the basics, Arwin.
There cannot be a force until you put a particle into the electric field. Only particles can have charge. A point in space cannot have a charge.
Er, well, the electric field isn’t represented by a circle. It’s usually represented by lines drawn radially from the charge. An equipotential line (like what XWalrus2 was talking about) would be a circle around the charge.
It’s better to think of the vectors, a bunch of arrows pointing away from the charge. Close to the charge, the arrows are long, meaning that the field is strong. Farther away, the field is weaker, and the arrows are shorter. Like the diagrams on this page.
Uh, kind of. The force would be parallel to that line, at least.
You’re having the same trouble that some students have at this point. Directions cannot be positive or negative. The direction could be toward the charge (if it’s negative) or away from the charge (if it’s positive.)
This is actually something of a releif. The students kept coming up with these inappropriate applications of “positive” and “negative” to the electric field vectors, and I thought it was because of a particular, ill-chosen example I gave them, but maybe it goes deeper than that.
No, sorry. In the formula that we are using, you take an absolute value of the charge. It could be written:
E=k|q|/r[sup]2[/sup].
I had just defined the q as the magnitude of the charge here, because I thought that might seem simpler, but now I see it wasn’t. The book gives the formula with the absolute value signs. I’m really sorry about this confusion, but I want to emphasize that we do the same weird thing with electric forces, and they seem to manage it okay. There’s just something else about fields that makes them bonkers.
The important thing is that the electric field is a vector. Vectors are not “positive” or “negative”. Vectors have a magnitude (always represented as a positive number) and a direction (which, as I said before, isn’t positive or negative . . . it points somewhere.)
Well, the problem is, you’re not trying to make the charges vote Democrat or Republican, you’re trying to make them travel toward New York, NY or Branson, MO.
I tell them that the electric field at a point is like street sign. There’s a street sign at every corner, and it tells positive particles which way to go. But negative particles are juvenile delinquents, and they go the opposite way.
Ok. I had already been thinking that non-charged particles are swing voters, and points are people who are not going to vote anyway, but at gunpoint they might be willing to give you an opinion.
Sorry, I’m not being exact enough. I mean a fading disc, more potential (close to the charge) drawn as a darker shade depending on how strong the potential, and less potential, increasingly further away, as an increasingly lighter shade.
I’m starting to become convinced that thinking of them as vectors is what is keeping a conceptual understanding at bay.
Understood, but the direction is influenced by whether the charge is positive or negative. So it’s easy to fuse these concepts in the mind, in the context of what you present, because you’re talking about directions towards, or away, correlating with positive and negative. I understand what you mean though, and this sounds more like something for which your students would mix up the terms for without getting really confused about what is going on. But getting the terms right makes it more precise in their minds.
As above.
no problem.
Yes, understood.
You’re really being a physicist now.
Seriously though, nowhere in this discussion have we been talking about the actual movement. We are considering a static representation of a dynamic process. We are looking, not at the living, breathing world itself, but snapshots of it. Agreed?
But I understand your objections to the example. To expand it to what you’re missing, you could say that looking at particles in a static way is like asking the particles what they would vote, but in real life instead of talking to you they just want to run off and be with as many of their Democrat/Republican buddies as possible. Yes?
(You could discuss this in terms of gangs as well, like the atom example. )
It’s not a bad metaphor, but only goes together with the vector bit. By now you can trust me that this is what’s keeping them from understanding the concept of a field - not easily broken, because you yourself are very fixed on looking at the field as a set of vectors, but it is really a field.
I think what you’re picturing in your mind is actually the potential: V=kq/r. (In this case, you’d use the charge, not the absolute value of the charge.)
The potential is a scalar field, not a vector field. It doesn’t have a directional component, just places where it’s high and places where it’s low. Positive particles want to go from high potential to low potential; negative particles want to go from low potential to high potential.
Both the the electric field and the potential tell you what way the particles want to go, but they do this in different ways.
It’s not a mathematical abstraction to say that the electric field has a direction at every point. It most certainly does, in the same way that every force has to operate in some direction, or it wouldn’t be a force. You absolutely positively have to consider the electric field as a field of vectors.
No, that’s not what I’m picturing in my mind. I think we’re at the point where you’ve lost me, and not the other way around.
You absolutely positively do not have to consider the electric field as a field of vectors, for a conceptual understanding of an electric field. If you think this, then I could even imagine that the students do have a conceptual understanding, but you refuse it and confuse them. I’m not saying this is so, but right now you’re giving this impression.
Please, for clarity sake, tell me where my analogy goes awry, as much as possible in my language this time, so that I can see better whether you don’t understand me, or whether I don’t understand you.
I just re-read your original post and realised you said they couldn’t even reliably point to which way an electric field went on a line between two charges. Do we need to start futher back?
How about (1) Have a couple of big charged particles. “If we put a little one here, it would go this way” and draw a little arrow. Repeat, and draw lots of little arrows. If they can’t grasp this concept, either (a) come back for more advice or (b) drown them and improve the gene pool.
(2) These arrows are called vectors. Now notice how they all sort of join up? Imagine there’s arrows everywhere. Instead of drawing them all separatrely, draw a line. This is called a field.
(BTW, I may have got my notions backward, but don’t drown me, if you explained it, I’d get it :))
I don’t understand your analogy, I’m afraid. Particles voting Republican and Democrat? Particles wanting to be with their buddies? They don’t want to be with other particles that are similar to them. They want to be as far away from other like charges as they can get. A vote is not a directional thing, like an electric field is. A particle doesn’t feel an electric force that is “Republican” or “Democrat.” It doesn’t feel a force that is “positive” or “negative.” You can’t just boil it down to an either/or choice, or even a small number of choices. The electric field could point in any of an infinite number of directions.
I see one concrete problem with your analogy. What you describe here: “The influence one of this convinced Democrat or Republican on the swing voters can be expressed in vectors, a combination of the strength of the political conviction of the supporter, and the physical distance between the supporter and the swing votee.” is not the electric field vector. The vector is not the distance between particles. The vector points off in some direction, either toward the “supporter” or away from the “supporter.” It doesn’t represent any kind of a distance at all.
Its properties of the electric field come, not from the fact that it gets weaker with distance, but from the fact that it has a strength and direction at every point. The electric field isn’t a non-directional field that I’m artifically insisting must be about vectors. It is a field that has direction at every point, and the way that we indicate directions is with vectors. I cannot imagine another way to indicate a direction at a single point, except with an arrow!
If you think about potential, then the positive particle wants to move from a region of high potential to a region of low potential (i.e. it wants to slide downhill) . . . but that requires that, mathematically, you think about at least two points to figure out how steep the hill is and what direction the slope is. An electric field has all that information contained at exactly one point.
Shade, I like your idea for explaining field lines. I was working from field lines backward to get vectors, rather than from vectors forward to field lines. I’ll try that, too. (Luckily, there’s no rule that says I can’t explain the same thing different ways several different times. )
It’s what I always think of fields as actually being.
To some extent, intellegence is not being embarassed to draw little pictures and calling them understanding
Indeed, I often feel when explaining something like I’m playing one of those baby’s games with trying to turn wooden blocks so they fit through a hole; I have to try the idea in as many ways as possible until one fo them clicks. But I end up hammering it and shouting “HOW CAN YOU NOT UNDERSTAND, YOU SUBHUMAN!”
Ok, I see that I’m being both imprecise and faulty in my use of this metaphor. Instead I’ll draw abstract pictures first, and check that. Thanks to shade I’m starting to get an impression also of something I’ve misunderstood, but I’ll get back to that.
It’s my experience that if you attempt to give a student multiple explanations, the student will remember whichever one he or she found most confusing, and forget all other explanations. I would therefore advise you to be very cautious about giving multiple independant explanations.
the second one in quantum chemistry.
