Coda
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#233
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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.
Games by Coda (updated 4/8/2025 - New game: Marianas Miner)
Art by Coda (updated 8/25/2022 - beatBitten and All-Nighter Simulator)
Mega Man: The Light of Will (Mega Man / Green Lantern crossover: In the lead-up to the events of Mega Man 2, Dr. Wily has discovered emotional light technology. How will his creations change how humankind thinks about artificial intelligence? Sadly abandoned. Sufficient Velocity x-post)
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Posted 02-27-2017, 08:07 PM
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