Transformers - Why more coils in second coil causes more voltage
Why do we multiply the magnetic flux by the winding number?
Man undergoes radical surgery to research aliens I just asked my first question on stackoverflow and I'm really impressed that my question seems to be answered sufficiently already! See:    The issue I have is that the last two answers combined would provide the most complete answer. What's the proper way to go about combining them, marking the question answered, and giving credit where credit is due?  Thanks big time guys for saving us all from experts exchange hell!  Edit: Wow, 5 responses in 5 minutes. I think what makes the most sense is that I create my own answer out of the two. I don't think the second part of my question was answered though.  What is the proper way to give credit to the 2 answers that I'm combining? Is an upvote for each sufficient? What is the difference between a predicate and function? I need to to understand the difference between predicates and functions in the context of Clasual Form Logic in order to define the Herbrand universe.  If I have p(x) :- q(f(x)) would I be right in saying that p and q are predicates while f is a function because it is "nested"?  By this thinking then if I have p(x) :- q(x) both p and q are predicates and I have no functions?  If this is incorrect then how can I tell the difference between a predicate and function? Using simple quotes "" instead of \text{} Is there a way to use newcommand or some other nice technique to transform any occurence of  "bla"   in math mode into  \text{bla}   The reason I ask is because it is easy, and doesn't interrupt the flow of reading the (La)TeX code as much.  I would like to keep Xe(La)TeX's nice quote behavior (ie it can use the regular "" instead of backticks to quote some text outside math mode). Vertical line of white pixels between launcher and maximized application (Firefox) Is this a bug or is it expected?  How can it be solved if it's not expected? (a.k.a. "god rays" and many other names) can be created in Blender Internal by checking the Halo checkbox in the lamp properties box.  How can I create a similar effect using Cycles? Proving $\sum_{k=1}^n k k!=(n+1)!-1$ Prove: $\displaystyle\sum_{k=1}^n k k!=(n+1)!-1$ (preferably combinatorially)   It's pretty easy to think of a story for the RHS: arrange $n+1$ people in a row and remove the the option of everyone arranged to height from shortest to highest, but it doesn't hold up for the LHS.   Alternatively, trying to visualize the LHS, I noticed that it's like a right angle tetrahedra:  1  2!+2!  3!+3!+3!  ...  But it doesn't help to see a connection to the RHS.  Note: no integrals or gamma function nor use of other identities without proving them nor generating functions. Divisibility Proof with Induction - Stuck on Induction Step I'm working on a problem that's given me the run around for about a weekend. The statement:  For all $m$ greater than or equal to $2$ and for all $n$ greater than or equal to $0$, $m - 1$ divides $m^n - 1$.  Using induction over $n$, the base step comes easy since $m^n - 1$ is $0$ when $n = 0$.  My induction hypothesis is letting $k \geq 0$ and assuming that $m - 1$ divides $m^k - 1$. In order to show that $m - 1$ divides $m^{k+1} - 1$, I obviously need to use the induction hypothesis. However, no matter where I try to use the fact that $m^k - 1 = (m-1)a$ for some $a$ in the integers, the expression $m^{k+1} - 1$ always becomes more difficult to get to $m^{k+1} - 1$ being equal to $(m-1)b$ for some $b$ in the integers.   In other words, I can't figure out any actually helpful way to apply the induction hypothesis with the goal of proving the next step.  Any help would be appreciated! Suppose the following dialogue:  ... &quot;I accept only one notion of land property. Namely, 'I am doing my stuff here, therefore I am here&quot;. &quot;But this means,&quot; he responded, &quot;you can break into any place and stay there, using this rule.&quot; &quot;There is another rule, though. Right to act in its most natural sense, 'I am here, therefore I am doing my stuff here.&quot; &quot;But do not these rules put together become circular reasoning?&quot; &quot;Of course, they do,&quot; I put my head closer to him, &quot;and this is exactly that rare case when circular reasoning is not only sufficient, but is necessary.&quot; &quot;But why is that? Circular reasoning never was a correct argument.&quot; &quot;There are many circular things happening in nature. Life forms, for example, exist only in order to produce new life forms or to prolongate their own lifetime. Is there any reason to say this can't be the case for reason itself? Why must reasoning not be circular?&quot; ...  Can circular reasoning ever be justified? For example, we know all the words in our languages can't be defined using other words without the use of circularity. We know logic can't prove itself without circularity. Are these arguments rational? Are there any other arguments where circular reasoning is still rational? I want to write several classes, most of them will use KOMA classes as base class.  However I stumbled upon the problem that some options (mainly concerned with layout) are not processed if given in the wrapper class:    \begin{filecontents}{test.cls}     \ProvidesClass{test}[2015/01/01]     \DeclareOption*{\PassOptionsToClass{\CurrentOption}{scrartcl}}     \ProcessOptions\relax     \LoadClass[paper=a5]{scrartcl}   \end{filecontents}  \documentclass{test}  \usepackage{blindtext}  \begin{document}   \section{Test}   \blindtext \end{document}   This results in   LaTeX Warning: Unused global option(s):     [paper=a5]  If i give the option as \documentclass[paper=a5]{test} it is used correctly, because I pass the options to scrartcl. However I want to change the defaults for the layout.   How can I achieve this? I had a heck of time while editing my  question. But, I guess, I discovered a new weird problem in the editor while formatting hyperlink text next to  tag.  To illustrate this problem better, I would like to give the following examples:  Has problem with one or none white-space in between:  [meta-tag:status-planned] [details page reads:][2] [meta-tag:status-planned][details page reads:][2]     Gives weird output as:   [details page reads:]   [details page reads:]   But, its okay with two white-spaces in between:  [meta-tag:status-planned]  [details page reads:][2]   Gives the correct output as:      Something is strange here. I don't understand why do I have to insert two white-spaces instead of just one? Are the two white-spaces are mandatory when using [meta-tag:some-tag] with hyperlink text adjacent to it? Or, is it one of those  thing?  But wait, it's get even further complicated if I do like:   1. No white-spaces in between:  [meta-tag:status-planned][meta-tag:status-completed][Moderator-only Tags][3]     2. One white-space in between:  [meta-tag:status-planned] [meta-tag:status-completed] [Moderator-only Tags][3]       3. Two white-spaces in between:  [meta-tag:status-planned]  [meta-tag:status-completed]  [Moderator-only Tags][3]         They all seems to work perfectly fine. Now, thats very strange! Why would the two [meta-tag:some-tag] works like a charm with or without requiring to insert any white-spaces? Can anyone explain this in a better way. I don't want to jump on the conclusion by calling this as a bug yet, so I used  tag instead of  tag. Please share your thoughts. Disable automatic activation of Gnome Shell activities on mouse over How to change account profile picture? I can't believe I have to ask this...but, how do I change my account profile picture in Ubuntu 12.04 Desktop? One would think it would be under the "User Accounts" section. How can I find maximum power transfer using Thevenin equivalent Was or is? Confusion So we have something like:  \documentclass{article} \setcounter{secnumdepth}{2} \setcounter{tocdepth}{2} \usepackage{amsmath}  \begin{document}  \tableofcontents  \section{Brushless Motor Fundamentals} \subsection{Brushless Motor Operation} \subsubsection{DC Motor Operation} Torque is generated in DC motors from the magnetic force, also known as the Lorentz force, which is produced when an electric current is passed through a coil in a magnetic field. This force is given by $F=q[E+(v\times B)]$, where $F$ is the force perpendicular to the coil, $E$ is the electric field in the coil, $B$ is the magnetic field, and $v$ is the velocity of the charged particles in the coil. From mechanics, torque is $\tau=F\times r$.  \section{Brushless Motor Fundamentals 2} \subsection{Brushless Motor Operation} \subsubsection{DC Motor Operation 2} If the electrical force is ignored and the remaining magnetic force is used, with the assumption that $v$ is perpendicular to $B$, we find that $\tau=qvBrsin\theta$.  \end{document}   How to show subsubsections and paragraphs in TOC? Why am I seeing a bomb icon on my files and folders in Ubuntu? I'm looking to download and install the latest version of Ubuntu to replace the current version of Windows I had pre-installed on my machine when bought it.   I have some really neat features on the machine that I really am hoping will still work when I move over to Ubuntu.  Can someone please confirm if the below will still work and, if not, how I can get them to work:   The USB ports on my machine The ethernet or Network work port on the machine The HDMI output on the machine and finally, the built in webcam   Thanks Sam Is the wave function of a particle re-created after a measurement stops? windows command prompt change directory is now changing directory