Why is the field inside a hollow sphere zero?
Gravitational field intensity inside a hollow sphere
Wrong place for hyperref link in scaled tikz picture I have a TikZ picture with a node containing a minipage with an itemize environment; each item is a hyperref to other sections of the document.   When scaling the image (for example with \begin{tikzpicture}[scale=.7, transform shape] I've a strange behavior: links in itemize are not in the right place: they present a somewhat vertical offset, as if they don't scale as the rest of image.   Here the MWE:  \documentclass[a4paper]{article} \usepackage{tikz} \usepackage[pdftex]{hyperref} \begin{document}  Here something interesting\label{text:interesting-one} \newpage  Here something interesting, too\label{text:interesting-two} \newpage  and here there are very very interesting stuff\label{text:interesting-three} \newpage  \newpage Now the problem: links rectangles have some offset, making links unusable in case of long itemize  \begin{figure}[htb] \begin{tikzpicture}[scale=.7, transform shape] \node at (0,0) (mynode) { \begin{minipage}{4cm} \begin{itemize} \item \hyperref[text:interesting-one]{First link} \item \hyperref[text:interesting-two]{Second link} \item \hyperref[text:interesting-three]{Third link} \item \hyperref[text:interesting-one]{First link again} \item \hyperref[text:interesting-two]{Second link again} \item \hyperref[text:interesting-three]{Third link again} \end{itemize} \end{minipage} }; \end{tikzpicture} \end{figure} \end{document}   And here a snapshot of the problem    Note: This is evident using the default settings of hyperref package, which draws the red rectangle around links, but it took me some time to found it when only the text is coloured, i.e. when using \usepackage[linkcolor=blue,colorlinks=true]{hyperref} Should I put myself last? "me and my friends" vs. "my friends and me" or "my friends and I" What is the limit of $\lim\limits_{x→∞}\frac{\sin x}{x}$ How to change default window background color in Windows 10? As it is common with people from my country, I have an immense difficulty with prepositions in English, especially with the use of in and on.   When the preposition indicates the position of the object it is a bit easier to decide which one to use, but as it requires thinking from me, I still say things like "I put the bill in the fridge", "my pencil is on my bag", etc, even though if I think about it, I would know how to say it correctly.  Of course, even in those cases where the preposition indicates position the decision is not always clear, as is the case for example with "on the bus" (you are not on top of the bus, you are inside the bus) or "he is in bed" (you are not inside the bed, you are on top of your bed).  Other cases are even less clear, and I believe there is no real rule to decide what should be said; the person should just know it. Two examples are "in a bad mood", "you are on my mind".  So my first question is whether there is really no rule to help me. The second question refers to two of the cases where I still don't know whether to use in or on:   good luck on/in your exam in/on the list   The last one is especially important to me, as I have asked a number of native speakers, and each time I get a different answer. The only consensus seems to be the case where you say "on top of the list". Apart from that, some people will say that I should say "his name is in the list" whereas others think I should say "his name is on the list". And yeah, a couple of people did tell me that I can use either.  Can someone help me? How closely can a game legally resemble another? Bibliography with page numbers In GKP's Concrete Mathematics, there is a useful and interesting feature I would like to see in more books. The bibliography entries include:   a - the page numbers where the book or article is cited in the document. b - a few lines of review of the cited work.   It is a kind of mix between bibliography, index and review.  Are there stable LaTeX packages/BibTeX styles to do (a) and (b) ?  EDIT: I wrote (b) initially as "comments about the work cited". It could be understood as "gathering comments made in the book about the work and reproducing them in the bibliography".  This is not what I meant but this could be something useful for others. Get string after character fleqn document class option, long text lines, and hyperref package When the fleqn option is used, the vertical spacing before an equation placed right after a "long" text line (exactly \linewidth I would say) is improperly set up. See below:    From the mathmode user guide, this could probably be fixed through the \topsep length. Is it the right way to proceed? The problem is reproduced by the code below:  \documentclass[12pt,fleqn]{book} \usepackage{amsmath} \usepackage{hyperref} \begin{document} \chapter{plo} \section{plo} eoiu oieu oeiuoe ueoi ueoi ueoiu eoiu oeu oe iupaêio umùaeoiuaem oeiu eoiu eoiu oeee. eoiu oieu oeiuoe ueoi ueoi ueoiu eoiu oeu oe iupaêio umùaeoiuaemm \begin{equation} \cos\pi=-1 \end{equation} eoiu oieu oeiuoe ueoi ueoi ueoiu eoiu oeu oe iupaêio umùaeoiuaem oeiu eoiu eoiu oeee. eoiu oieu oeiuoe ueoi ueoi ueoiu eoiu oeu oe iupaêio umùae \begin{equation} \cos\pi=-1 \end{equation} \end{document}   There is something wrong involving hyperref, amsmath, and fleqn. Removing one of those removes the problem. Apache2 restart failed in Ubuntu 16.04 this is my first question on PhysicsSE (I'm already an user of MathSE).   I'm a mathematics students trying to understand Faraday's law, that is   $$\varepsilon= -\frac{d \Phi_B}{dt}$$  where $\varepsilon$ means electromotive force and   $$\Phi_B=\iint \mathbf{B}\cdot d\mathbf{S}$$   means flux of magnetic field. As my textbook points out, there is an interpretation problem here: if the change in magnetic flux is due to movement of the conductor, then free charges in it are subject to Lorentz force, which then causes a current. On the contrary, if the conductor holds steady in a changing magnetic field, the induced current must be explained in terms of an electric field $\mathbf{E}$, described by the equations   $$\begin{cases} \nabla \cdot \mathbf{E}=\frac{\rho}{\varepsilon_0} \\ \nabla \times \mathbf{E} = - \frac{\partial \mathbf{B}}{\partial t}\end{cases}.$$  Question Do those equations hold if we have a moving conductor in a stationary magnetic field? I guess not: this would mean $\mathbf{E}=\mathbf{0}$. How to solve this? Impact of changing instances' passwords As part of a security policy, the company I work for has given me the task of changing the sa's and SQL Server Agent service accounts' passwords for several instances.  What's the possible impact of doing this? Is there anything in particular I should watch out for? Is there any whitepaper, guide or even blog post about this kind of task? What kind of 'backup' plan should I have in place in case anything goes wrong?  Any guidance is appreciated. Given a $10×10$ grid with $9$ red blocks and $91$ white blocks, in each step we color one red block black and after that one white block red until there are $91$ black blocks and $9$ red blocks. Prove that there exits a step in which a black block shares an edge with a white block. I ran a few trials and couldn't get past the fifth step without adjacency. But I don't know how to build a proof. Let $R$ be a commutative ring and $I_1, \dots, I_n$ pairwise comaximal ideals in $R$, i.e., $I_i + I_j = R$ for $i \neq j$. Why are the ideals $I_1^{n_1}, ... , I_r^{n_r}$ (for any $n_1,...,n_r \in\mathbb N$) also comaximal? What is integration by parts, really? Integration by parts comes up a lot - for instance, it appears in the definition of a weak derivative / distributional derivative, or as a tool that one can use to turn information about higher derivatives of a function into information about an integral of that function. Concrete examples of this latter category include: proving that $f \in C^2(S^1)$ implies that the Fourier series of $f$ converges absolutely and uniformly, and the Taylor series expansion with the integral formula for remainder.  However, I don't feel like I really understand what integration by parts is really doing. To me, it is just an algebraic trick that follows from the fundamental theorem of calculus and the product rule. Is there some more conceptual way to think about it?  How do you think about this useful idea? Using Euler's Totient Function, how do I find all values n such that $\phi(n)=12$? How do I generalize the equation to be able to plug in any result for $\phi(n)=12$ and find any possible integer that works? Linux command line. Move all files and directories in directory, except some files and directories I have a folder A which has files and directories, I want to move all those files and directories to another folder B, except file, file2, directory, and directory2.  How can this be done? Stripped out bottom bracket Proving $\frac{\sin x}{x} =\left(1-\frac{x^2}{\pi^2}\right)\left(1-\frac{x^2}{2^2\pi^2}\right) \left(1-\frac{x^2}{3^2\pi^2}\right)\cdots$ How to prove the following product? $$\frac{\sin(x)}{x}= \left(1+\frac{x}{\pi}\right) \left(1-\frac{x}{\pi}\right) \left(1+\frac{x}{2\pi}\right) \left(1-\frac{x}{2\pi}\right) \left(1+\frac{x}{3\pi}\right) \left(1-\frac{x}{3\pi}\right)\cdots$$ How to test whether a file uses CRLF or LF without modifying it? I need to periodically run a command that ensures that some text files are kept in Linux mode. Unfortunately dos2unix always modifies the file, which would mess file's and folder's timestamps and cause unnecessary writes.   The script I write is in Bash, so  I'd prefer answers based on Bash.