[Potironette]

Good night!
I actually finished the worksheet already and had that as one of my questions I didn't understand ^^

[Coda]

Well, the answer you had written in the picture was wrong, so I hope you fixed it. :P

[Potironette]

Err, a is fine right?
B I changed to:
E = 43,000 N/C
..which is a really big number o_o

Work:
m = 4.0 * 10^-6
q = 0.90 * 10^-9
F_N = F_g = F_e
F_g = ma
F_g = (4.0 * 10^-6)(9.81 m/s²) = 3.9 * 10^-5 N = F_e

F_e / |q| = E
(3.9 * 10^-5 N) / (0.90 * 10^-9 C) = E
E = 43,000 N/C

[Coda]

At a quick glance I don't see any particular issues with your work but I haven't worked it myself.

I don't know how realistic that number is, but a search finds me another class's homework where the answers are on the order of 10⁵ N/C so it looks reasonable.

I do recommend asking about those distances. It doesn't make sense to me the way they presented it, even IF it's a red herring.

[Potironette]

Thanks for looking it up! I'd been worried about doing something wrong because of the sudden jump in numbers.

I'll ask my teacher about the distances when I have school tomorrow.

[Potironette]

Checked it just now--it was a typo!

[Coda]

Oh, good, now my scientific intuition feels better. XD

[Potironette]

That's good xD

--
In physics class we had to field or vector diagrams for different combinations of charges--I don't think I'm comfortable with those so can I ask a couple question about this? :

The black color is a field diagram
The colored is one vector

>For field diagrams, we learned that "the number of lines leaving a positive charge or approaching a negative charge is proportional (but not equal to!) the magnitude of the charge". So that just means that every ball of charge is proportional? And the diagram I drew is fine in that respect because every circle of charge is just one charge and has five lines coming out/going to it?
>The teacher also said something about how in field diagrams, the distance between lines mattered. Does that mean something like this is wrong for being too sparse or incomplete?

>When I draw vectors, should I be thinking: Here's what charge circle no. 1 is doing as a vector...here's what charge circle no. 2 is doing...here's what charge circle no. 3 is doing..now I add them all up for a vector?
>When is a vector diagram complete?

[Coda]

The spacing of the field lines represents the field strength in that area. When the lines are spread farther apart, the field is weaker than in the areas where the lines are close together.

Imagine drawing field lines for an isolated point charge. It would just be straight lines extending out from the charge in all directions. The farther from the charge you get, the farther apart the lines become, which matches what you know must be true.

Now, unfortunately, the field line density is only a qualitative description of the field. It doesn't accurately give you anything you can turn into numbers, because lines spreading out on paper don't follow the inverse square law -- they spread out proportional to 1/x, not 1/x². But you can still get some rough comparisons out of it.

Yes, in the first diagram you drew, you correctly suggest that each charge has the same magnitude. And the purple vector is approximately correct (which is all that matters in such a rough diagram).

Your spoilered diagram is bad for a couple reasons and, yes, that's because it's too sparse. The first problem is that having two field lines per charge simply doesn't give enough information about the shape of the field. There are huge regions of the page where you simply don't have information. The second is that the diagram as drawn suggests some real oddball field strengths. As drawn, the field on the bottom side of the positive charge is 3x stronger than the field on the top side of the charge (90 degrees vs. 270 degrees between field lines) when in reality the field strength is hardly any different. And as drawn, the field below the two negative charges is REALLY REALLY strong (stronger than right beside one of the charges!) while it essentially vanishes farther out. (I should really write a program to generate these field diagrams. It wouldn't be that HARD, and I don't know why I can't get WolframAlpha, Google, or the macOS Grapher to do what I want.)

Your strategy for drawing vectors is sound.

A field drawing is complete when there's enough information in the picture to convey the relevant information accurately without anything obviously missing.

[Potironette]

Ohh, so the distance between field lines coming out of a charge does indicate the strength of the field around the charge also!

Anything obviously missing would mean that for a vector diagram, I can tell what all the charges roughly are..?

In drawing a line diagram for more than one charge, can I say I first look at charges, then draw how they interact with each other--and if there's another charge, how they interact with each in an area furthest away from that charge being currently ignored--then move onto the interactions between another pair if there's more charges, and finally draw field lines for each charge depending on the strength of each charge?
...drawing field diagrams seems almost odd to me :/. The teacher said something about getting familiar and developing an intuition for them, so maybe there isn't an easy to follow process for it?

[Coda]

If it helps you feel any better, this kind of field diagram is are ALL ABOUT intuition. They're useless for specific analysis of field phenomena; they exist purely to give you a qualitative idea of what you're looking at. The process of drawing one is a way to translate your mental processes into something easier to visualize.

You use a vector field plot -- that is, the grid of arrows we were looking at a couple pages ago -- or a contour plot (curves of equal field strength instead of curves describing the path of a particle) if you need something more rigorous.

That strategy sounds pretty reasonable. Personally I would start off marking evenly-spaced points around each charge so that I have an idea of what the line density is going to look like before I start drawing and what direction they're going to start off in, and then I'd connect the dots where there's an obvious interaction between the charges, and finally I'd fill in the paths that diverge away from the charges since then I'd have an idea of where the lines need to be spaced for those.

(In reality, me being Coda, I'd hack up a quick rendering program that would throw out some test points and trace their paths on the screen.)

EDIT: Actually that sounds fun. Maybe I WILL do that.

[Potironette]

That can be done quickly :o?

Oh! drawing out the points first instead of hoping to fill them out later is a lot more convenient.

If something's about intuition...Am I expected to be able to visualize the diagram before I draw it :/ ?

[Coda]

It can be done relatively quickly if you're me. ;) More seriously, it's one of those things where a competent programmer using familiar tools can get something close to correct pretty quickly and then spend who-knows-how-many hours fiddling with it to get the results you want.

No, you're not, that's the point of drawing it. If you COULD visualize the whole thing easily there wouldn't be a need for it. Making the drawing gives you a way to translate things you know must be true about the system into something you can actually look at.

[Potironette]

Are the energy of fields completely different from that of moving objects? And that's why the force of a charge is not mass times acceleration? Also, since F_e = |q|E, what kind of force is F = ma? Oh. That's kinetic energy. Do all energies have forces specific to them then? Or maybe they don't, but all I need to know is that the energies are separate in that they each have their own kinds of PE and KE and force equations because they are different kinds of energies?

Whenever a field force is mentioned, am I supposed to assume it is based on the proton? That is, if in a uniform field, E = 20 N/C west, I can assume there are positive charges at the east and/or there are negative charges at the west? And that is why to increase the PE for positive charge, the positive charge must be moved against the field, whereas to increase the PE for a negative charge, the charge must be moved with the field?
Is there no such thing as a negative field force (E)? Also, for point charges to calculate what the field force (E) would be at some point, I suppose it is also based on moving in the direction of the repulsion of a proton because all field forces are defined that way, for whatever reason?

[Coda]

All fields of force have corresponding potential energy. This means it takes energy to move an object against the field lines, and that energy is released by the object moving along with the field lines. This is true regardless of what kind of field it is. The different potential energy formulas are descriptions of how that particular field works. (As far as I know, kinetic energy is just kinetic energy, and there aren't different forms of it.)

F = ma is not a field. It doesn't cause anything to happen. It's a description of a relationship, and it's true of ALL forces, masses, and accelerations. So it doesn't matter "what kind" of energy it is.

By convention, electric fields are described as moving from positive to negative. This is often considered to be a historical mistake -- Benjamin Franklin arbitrarily chose one of the charges he was able to create in his static electricity experiments to be positive, and the other to be negative, and all of the math from then on holds to that convention. It IS just a convention, and as such it doesn't actually MATTER because the whole point is that everyone knows the convention and therefore agrees on what things mean, but it means that the fields describe the motion of a positively-charged particle when in practice the particles in motion are negatively-charged. But to answer your question: Yes.

As for negative fields... No, those aren't possible. Vectors are a magnitude and a direction. While the math works out to consider a vector with negative magnitude, it's 100% congruent to a vector with a positive magnitude in the opposite direction. Negative lengths are considered undefined, because measures are positive by definition. And so, in the interests of keeping everything consistent and unambiguous and mutually understandable, it isn't done.

[Potironette]

Then, can F=ma be F_e=ma?
Does it matter if I use F_e=ma then use v_f²=v_i²+2ad to find a velocity or I use Δ(PE)=qEd then KE=.5mv² to find the velocity?

(I'm given the field E, q, initial velocity, the distance moved, and the mass, and asked to find the final velocity.)
(For some reason solving using the two different methods gave me two different answers. I don't know if I made a calculation mistake or a problem solving mistake)