Let $L , I , \phi$ are self inductance , current and magnetic flux (created by each loop) of a solenoid with $n$ turns . $r$ is the radius of those loops . We have , $LI=n \phi = nAB $  [$A=\pi r^2$]  Now according to textbook , "As there are n loops ,  $\displaystyle B=\frac{n\mu_oI}{2r}$ .   Substituting $B$ , $\displaystyle LI=nA\times\frac{n\mu_oI}{2r}\Rightarrow L=\frac{n^2\mu_o \pi r}{2}$ "  We considered the fact of n loops when we multiplied $n$ with $\phi$ . Again we multiplied $n$ while calculating $B$ .   In the equation $n\phi=nAB$ , $B$ represents magnetic flux density caused by each loop . On the other hand , in the equation $\displaystyle B=\frac{n\mu_oI}{2r}$ , $B$ represents magnetic flux density caused by all loops . We calculated $\displaystyle L=\frac{n^2\mu_o \pi r}{2}$ considering the winding number fact twice . So shouldn't  be the equation wrong ?  (The question other users are refering as "original" of this question (asked by myself a few weeks ago) isn't totally about self-inductance . This question is regarding to deduction of a equation for self-inductance .)
A current I flows through a solenoid (with n turns). Self inductance is $L$. If the magnetic flux is $\phi$, I am taught that $-n\phi=LI$  I dont understand the part with $n$, why do we have multiply by $n$? $\phi$ itself represents the whole magnetic flux there, if $\phi$ implied the flux only occurred by one coil, then it would be correct.   Moreover, flux change by a coil ($n$ turns) in $dt$ time is $d\phi$, so the induced electromagnetic force is   $$dE=n \cdot \frac{d\phi}{dt}$$   Why do we multiply by $n$ here? If $\phi$ means the whole flux, then why multiply?
Converting string into datetime I've got a huge list of date-times like this as strings:  Jun 1 2005  1:33PM Aug 28 1999 12:00AM   I'm going to be shoving these back into proper datetime fields in a database so I need to magic them into real datetime objects.   This is going through Django's ORM so I can't use SQL to do the conversion on insert. What exactly are censored data? I have read different descriptions of censored data:  A) As explained in  thread, unquantified data below or above a certain threshold is censored. Unquantified means data is above or below a certain threshold but we do not know the exact value. Data is then marked at the low or high threshold value in the regression model. It matches the description in this , which I've found very clear (2nd slide on first page). In other words $Y$ is capped to either a minimum, a maximum value or both because we do not know the true value outside of that range.   B) A friend told me that we can apply a censored data model to partially unknown $Y$ observations, provided we have at least some limit information about the unknown $Y_i$ outcomes. For example, we want to estimate the final price for a mix of silent and open auctions based on some qualitative criteria (type of goods, country, bidders wealth, etc.). While for the open auctions we know all final prices $Y_i$, for the silent auctions we only know the first bid (say, $1,000) but not the final price. I was told that in this case data is censored from above and a censored regression model should be applied.  C) Finally there is the definition given by the  where $Y$ is missing altogether but the predictors are available. I'm not sure how this example is different from truncated data.  So what exactly are censored data? Do file descriptors optimise writing to files? GOTO still considered harmful? Everyone is aware of Dijkstra's  (also  .html transcript and  .pdf) and there has been a formidable push since that time to eschew the goto statement whenever possible. While it's possible to use goto to produce unmaintainable, sprawling code, it nevertheless remains in . Even the advanced  control structure in Scheme can be described as a sophisticated goto.  What circumstances warrant the use of goto? When is it best to avoid?  As a followup question: C provides a pair of functions, setjmp and longjmp, that provide the ability to goto not just within the current stack frame but within any of the calling frames. Should these be considered as dangerous as goto? More dangerous?    Dijkstra himself regretted that title, for which he was not responsible. At the end of  (also  .pdf) he wrote:     Finally a short story for the record.   In 1968, the Communications of the ACM   published a text of mine under the   title "The goto statement considered   harmful", which in later years would   be most frequently referenced,   regrettably, however, often by authors   who had seen no more of it than its   title, which became a cornerstone of   my fame by becoming a template: we   would see all sorts of articles under   the title "X considered harmful" for   almost any X, including one titled   "Dijkstra considered harmful". But   what had happened? I had submitted a   paper under the title "A case against   the goto statement", which, in order   to speed up its publication, the   editor had changed into a "letter to   the Editor", and in the process he had   given it a new title of his own   invention! The editor was Niklaus   Wirth.   A well thought out classic paper about this topic, to be matched to that of Dijkstra, is , by Donald E. Knuth. Reading both helps to reestablish context and a non-dogmatic understanding of the subject. In this paper, Dijkstra's opinion on this case is reported and is even more strong:     Donald E. Knuth: I believe that by presenting such a   view I am not in fact disagreeing   sharply with Dijkstra's ideas, since   he recently wrote the following:   "Please don't fall into the trap of   believing that I am terribly   dogmatical about [the go to   statement]. I have the uncomfortable   feeling that others are making a   religion out of it, as if the   conceptual problems of programming   could be solved by a single trick, by   a simple form of coding discipline!" Getting nauseated from air travel, but it's not motion sickness... what to do? Let $\phi : R \to S$ be a homomorphism. If $N$ is an ideal of $S$, then $\phi ^{-1} (N)$ is an ideal of $R$. Using setminus notation with set elements The "correct" way to write a set without a specific element is as follows: $S \setminus \{s\}$  But in some contexts this is cumbersome to write/type or read, and it detracts from the flow of the writing. Is it acceptable to just use $S \setminus s$?  Edit: By "cumbersome" i mean they look bad when you're trying to inline formulas in LaTeX. I want to use  to display my CPU-Core temperatures (haswell i7). However the setting:  order += "cpu_temperature 1" #... cpu_temperature 1{         format = "T: %degree °C" } #   doesn't display the correct core temperature. The numbers it shows seem to correspond to the value xsensors shows for temp1, if I change the 1 to 2 above it corresponds to xsensors temp2. Trying 3 or 4 doesn't have any effect. However I want to get the true core temperatures of all 4 cores with i3 status. How can I do this? Windows 7 File Explorer search not working What features differ between the Xbox 360 and PC versions of Minecraft? What differences does the Xbox 360 version of Minecraft have compared to playing on the PC? To clarify - I'm concerned more about the differences exclusive to each platform, not just differences of features that will probably be added in future updates (for example, crafting). Otherwise, I feel this question could be compared to &quot;What is the difference between Minecraft version x and version y&quot;, which isn't what I'm asking. What issues should be considered when overriding equals and hashCode in Java? What issues / pitfalls must be considered when overriding equals and hashCode? "Questions like this" or "questions like these" $C^2 $embedded in holder space? I have a question on Holder space.Is the space $C^2(\mathbb{R}^n)$ embedded in $C^{1,\alpha}(\mathbb{R}^n)$? I think in the bounded domain case, this should be true. But what if in the case where the domain is not bounded? Thanks for any hint! Entity Query field condition for Webform submissions How to set the font for a \section title (and chapter etc) How do I specify the fonts, and general font size, for the titles, chapters and sections in my document  Update:  I can see how my question is confusing.  I use \section and \chapter etc. to organise my document, and I would like to change the way the section and chapter titles are displayed. Prove that $∂A$ is closed given $∂A = \text{Cl}(A) − \text{Int}(A)$ Similar questions have been asked, but none with the given information. My textbook doesn't give me the fact that  $∂A = \text{Cl}(A) − \text{Int}(A)$. If that were the case, I could just state that definition and note that it's the intersection of closed sets.   I have very little knowledge of set theory and proofs, so I'm not sure how else to prove this. As always, I appreciate any help.  The question comes from “Introduction to Topology: Pure and Applied” by Colin Adams and Robert Franzosa.   "Let $A$ be a subset of a topological space $X$. Prove that $∂A$ is closed given  $∂A = \text{Cl}(A) − \text{Int}(A)$" Bird flying in a cage Assume that you are holding a cage containing a bird.  Do you have to make less effort if the bird flies from its position in the cage and manages to stay in the middle without touching the walls of the cage? Does it make a difference whether the cage is completely closed or it has rods to let air pass? About $\lim \left(1+\frac {x}{n}\right)^n$ I was wondering if it is possible to get a link to a rigorous proof that  $$\displaystyle \lim_{n\to\infty} \left(1+\frac {x}{n}\right)^n=\exp x$$ See my edit below, this is not totally a duplicate of   My reverse-search function in the CLI is broken and I don't know how to fix it back...  When I hit ctrl+r and search a command I did earlier, find it then press the right arrow key to use it, the output is broken. Here is an example:  # I reverse-searched the word "test" then pressed right arrow yoshiji@x1carbon:~/path/to/git/folder (master) $ch)`test': rake test #                                              ^^^^^^^^^^ weird output #                                                     ^ cursor right there   It also "shifts" my cursor to a different position. If I press enter, the right command is executed (rake test in this case) so it means the text displayed is not the same as what is actually executed.  I know this is most-likely related to my PS1 export in my ~/.bashrc, so here are the last lines of this file:  # Git branch in prompt. git_branch() {   branch=$(__git_ps1 2&gt; /dev/null)   if [ "$branch" = " (master)" ]; then      echo -e "\033[33m${branch}\033[00m" # yellow   elif [ "$branch" = "" ]; then      echo -e "\033[90m (no git)\033[00m" # red   else      echo -e "\033[32m${branch}\033[00m" # green   fi } PS1='\u@\h:\w$(git_branch) \$ '   This is something I wrote to displays the git branch in orange (if master branch) or else in green (or no git in gray).  Do you guys have any idea on what is causing this weird behavior?    Edit: This is a different problem from the  in the way that I am using echo -e "some string" to return a string having color+name of the git branch from the function git_branch(). Using echo -e does not escape the characters \[ and \] (try it yourself in your CLI: echo -e "\[\033[33m\]test").  Ideally, I would like to keep those conditional colors based on the branch's presence &amp; name (gray if no branch, orange if master, else green). Why is you subjective? (Catchy title, eh?)  I am asking the following on the photo.SE site:     How do you change from portrait to landscape in Lightroom   DANGER! DANGER! This appears to be subjective and is likely to be closed.  If I ask the following radically different question:     How do I change from portrait to landscape in Lightroom   ... there is no problem.  So, like the title says: Why is "you" subjective?  (And  where Jeff spills the regex)