How is this a homework problem?

Question

Homework problem ??

How is the problem in the above link a homework problem? Really? In which part of this world has a high school student ever received this kind of problem in "homework"? This is an un-conventional question which people have no idea how to solve so that does not mean its a mere "homework problem". THIS needs to be corrected.

Answer 1

The post you've linked to is in a curious position, in that both of the following are true:

• It is not a solvable problem, and it would never ever be set as homework by a competent instructor.
• It is an archetypal example of the type of question that should get closed under the site's homework policy.

Let me expand a bit on those two points.

• The problem you're asking about (finding the electrostatic potential of a ring of charge away from the axis of the ring) is not solvable in terms of elementary functions. It is relatively easy (cf. e.g. Eur. J. Phys. 30 623 (2009) for a sketch of how it goes) to calculate the potential as an integral of the contributions of all the charge elements around the ring, and this calculation returns an elliptic integral. This means that this is where the calculation stops, since elliptic integrals cannot be reduced to elementary terms.

  (Alternatively, you can approach this via a multipole series; Jackson briefly details it at the end of §3.3, and it's probably not something that you would find satisfying either.)

  Because of this, you'd never see this being assigned as an exercise by an instructor who knows what they're doing, unless (i) they were confident that you know enough electrostatics to formulate the integrals and manipulate them and (ii) they were confident that you are comfortable enough with special functions that you'd be able to recognize elliptic integrals and recognize that their appearance means you should stop there; or (iii) they were shooting this as a hardball in the expectation that you'd work hard at it for a day or two, essentially fail, and come to them for guidance, in order to show how fast these questions become unsolvably tough (or a class of similar teaching methods).

  It's pretty clear from the way you've set the question (and please correct me if I'm wrong) that you've been assigned as an exercise to calculate the on-axis potential, and you've taken it upon yourself to calculate it for off-axis points. (There's several indications of this, starting with the rather clumsy way that you've used "above" to indicate "off-axis"; you rarely see this type of ambiguous language from experienced physicists. The same is true for the inconsistent labelling of the axes in your diagram.)

  As such, it's pretty clear to anybody who knows electrostatics in detail that this is not a set-piece exercise -- it wasn't assigned by an instructor, and it wasn't given as an exercise in a textbook.

• ... and yet: it is completely within the class of questions that this community has decided are off-topic under the umbrella term of homework-and-exercises.

  Why? well, here's a sketch of the structure of the question as you've written it

  • Here's the problem: "We have to find" object X.
  • I can't solve it.
  • I suspect tool Y "is to be used here" (in passive voice, no less).
  • "Please help me with this".
  • (and, conspicuously missing: any attempts on your part to document what you've tried and what's worked and what hasn't. Though note that straight check-my-work questions are also off-topic.)

  That's precisely the script of low-effort do-my-work-for-me homework-and-exercises questions that the community has decided is off-topic here, regardless of the origin of the question. Those rules hold uniformly, regardless of what topic the question is on, or where it came from. (Also of note: that the question follows the script above can be easily determined without knowing all of the electrostatics I detailed above, or indeed without knowing anything about the answer.)

  What that means is that you need to edit your question to take it away from that script: either remove it from that class entirely (say, by being very upfront about why you "have to" calculate this quantity, explaining what you've tried and why it didn't work, and making a clear-cut conceptual question about it -- and, now that you've been given the context, making it context-aware as well) or by treating it as a homework question (i.e. assuming that you've been assigned as a homework problem to take this calculation as far as it will go) and making an on-topic homework question out of it.

If any of that sounds sour, or unpleasant, then those are the rules as they have been decided by the community. Take them or leave them, or campaign to change them (but then, make sure you're fully informed about the background before you do).

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And, while we're here: there's a lot of very emotional language in your post here. It really doesn't help things here, particularly when some of that language starts to blow things way out of proportion.

Some notes:

In which part of this world has a high school student ever received this kind of problem in "homework" ??

It doesn't have to be high-school level to fall under the homework-and-exercises closure reason. I'd wager that about half of the questions that get closed as that are low-effort help-vampire questions at undergrad level, and questions about graduate-level material are just as likely to get closed if they fall under this script. You're not special here.

This is an un-conventional question

No it isn't. This is a standard problem in electrostatics; it doesn't get included in introductory textbooks because it requires more special-functions knowledge than it is appropriate to assume at that level, but that doesn't mean it's "unconventional". It's rather an obvious question to ask, and it's pretty self-important to act as if you're the first one to ever think of it.

which people have no idea how to solve

That's an inference on your part that's entirely unsupported in any evidence at all. The comment thread does include a series of comments that do not seem to be aware of the solution... none of which were posted by the people who closed the question. It doesn't hurt to state this explicitly: never accuse people of ignorance unless you have explicit, public evidence to point to (and even then...) that supports that accusation.

so that does not mean its a mere "homework problem"

This is an undue inference on your part. It was closed as homework because it very much follows all the negative hallmarks of homework questions. You might have had this explained politely in comments if you'd asked it politely to the people that closed it, but you didn't.