One step at a time ...
I think the first (and so far only) question that I asked doesn't require calculus at all (hilite added):
What is the force between the point and a point on the ring?
Yes, there's a (deliberate) ambiguity in this question; let's see if either markie or optiongeek can find it!
JeanTate did not mention calculus.
I was the one who mentioned calculus. I'll try to respond to
hecd2 without giving too much away.
JeanTate wants to take this one step at a time, so piggy-backing my own point(s) on top of his may have been a bit out of line. On the other hand,
JeanTate was addressing
markie, while I was responding to
optiongeek.
I might be wrong, but I don’t think this is a first year calculus problem. If I remember right the integrals are not straightforward (or even closed form?).
Although I mentioned calculus, I didn't say anything about integrals or closed form. Not all calculus problems involve integrals or closed form solutions to integrals. Calculus has more to do with limits than integrals; I thought that point (notice the pun) might fit with
JeanTate's question. Definite integrals are just one particular kind of limit.
Whether a definite integral has a solution in closed form is not important here. That is a point I have been trying to make and
optiongeek has been failing to appreciate:
As I suspected, optiongeek does not understand that solutions need not be in closed form. Most of the solutions we obtain from physics (including classical physics, not just quantum mechanics) are not in closed form, so we use numerical methods when we need numbers.
Randell L Mills has fostered the false belief that solutions don't count as solutions unless they are in closed form. optiongeek has bought into that, just as optiongeek has accepted the Millsian rant against numerical methods.
Although Mills and optiongeek both reject numerical methods as "approximate", they are considerably less approximate than the Millsian equations (e.g. (10.48)), as has been pointed out in this thread.
I suspect
JeanTate's point is qualitative rather than quantitative, so I don't think it matters whether some integral that might somehow be related to
JeanTate's point has a solution in closed form. I don't even think it matters whether coming up with such an integral is a problem first-year calculus students should be able to solve.
I do think students in first-year calculus should be able to translate
JeanTate's problem into a limit, but I suppose that depends on where you went to school, which instructor(s) taught the section of calculus you took, and how much attention you paid when you took the course.
Randell L Mills got his chemistry degree from Franklin and Marshall College. Apart from that one data point, which does not bode well, I am not really in any position to judge whether a pre-med/chemistry major at Franklin and Marshall College would have been taught how to set up that limit. Let me revise my claim to say only that people who have taken first-year calculus courses
should know how to set up that limit.