If a conductor - a long rod - moves at constant speed across the "lines" of a uniform magnetic field, is there an EMF within this conductor? Or, if a conducting rod rotates at uniform rate,  pivoted in the middle or at one of its ends in a uniform magnetic field perpendicular to the plane of rotation, is there an EMF generated within the conductor?
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?
Limiting range of value types in C++ Suppose I have a LimitedValue class which holds a value, and is parameterized on int types 'min' and 'max'.  You'd use it as a container for holding values which can only be in a certain range.  You could use it such:  LimitedValue&lt; float, 0, 360 &gt; someAngle( 45.0 ); someTrigFunction( someAngle );   so that 'someTrigFunction' knows that it is guaranteed to be supplied a valid input (The constructor would throw an exception if the parameter is invalid).  Copy-construction and assignment are limited to exactly equal types, though.  I'd like to be able to do:  LimitedValue&lt; float, 0, 90 &gt; smallAngle( 45.0 ); LimitedValue&lt; float, 0, 360 &gt; anyAngle( smallAngle );   and have that operation checked at compile-time, so this next example gives an error:  LimitedValue&lt; float, -90, 0 &gt; negativeAngle( -45.0 ); LimitedValue&lt; float, 0, 360 &gt; postiveAngle( negativeAngle ); // ERROR!   Is this possible?  Is there some practical way of doing this, or any examples out there which approach this? Google App Engine: Is it possible to do a Gql LIKE query? No option to create a new Managed Path inside Office 365 SharePoint online 2013 I am working on an Office 365 SharePoint online 2013. Now when I wanted to create a new private site collection, inside the online SharePoint admin center, I did not find the option to create new managed path, as I use to get when creating a site collection inside SharePoint on-premise. So how do I create a new managed paths inside SharePoint online? How to get the directory of open blend file? (from Python) What's the best way to get the full directory of the current Blender file in Python?  It should be cross-platform. How can I compare time in SQL Server? java.lang.RuntimeException Cannot find FacesContext Is there any web browser with NPAPI plugins support? As per  article, Mozilla has dropped the support of NPAPI plugins from Mozilla Firefox version 52. Is there any web browser with NPAPI plugin support? I have to use a website frequently, which uses Oracle Java plugin. I'm using Ubuntu 16.04 64 bit with Java JDK 8u121. Helps are much appreciated. Thanks. Edit1: After 3 years of asking this question, Java plugin still works fine in Palemoon v28.9.2-1 64 bit on Ubuntu 20.04 LTS. Java version is JRE 8u251 64 bit Edit2: As of 20th October 2020, Oracle completely removed Java Plugin from 8u271 JRE and JDK packages mentioned in  article. But 8u261 or prior versions works just fine. I watched a video on youtube (I lost it) that shows rendering parts of the screen to combine them in a single image. I followed it to the point where I couldn't adjust the dimensions under the "set render border", but in the video he had dimensions and I have nothing.  I need it for 4K and 8K renders (without anti-aliasing), but my laptop can't handle it all at once and I don't have time for a 4 hour waiting so this feature will work perfectly.  I'm using version 2.76 so is it moved to another place or removed. Maybe a bug? The  page says that Box-Jenkins is a method of fitting an ARIMA model to a time series. Now, if I want to fit an ARIMA model to a time series, I will open up SAS, call proc ARIMA, supply the parameters $p,d,q$ and SAS will give me AR and MA coefficients. Now, I can try different combinations of $p,d,q$ and SAS will give me a set of coefficients in each case. I select the set with the lowest Akaike information criterion.  My question is: where in the above procedure did I use Box-Jenkins? Am I supposed to use Box-Jenkins to come up with initial estimates of $p,d,q$? Or did SAS use it internally somehow? What's that icon (Oneplus one)? does anybody know what's the meaning of that icon ?  I have a new oneplus one since several days and today this icon appeared in my status bar. cannot start Tomcat 7 server - java.net.BindException: Address already in use Capture characters from standard input without waiting for enter to be pressed I can never remember how I do this because it comes up so infrequently for me. But in C or C++, what is the best way to read a character from standard input without waiting for a newline (press enter).  Also ideally it wouldn't echo the input character to the screen. I just want to capture keystrokes with out effecting the console screen. At what age is the Force detectable in children? Acer Aspire E15 will not dual boot I installed Ubuntu 14.04 onto my Acer Aspire E15. The PC has a 500 Gigabyte HDD.   During the installation it divided the HDD into separate partitions. However every time I turn on the PC it goes directly into Windows 8.1. It doesn't allow you the opportunity to select which OS you want to use.   Question 1: How do I set the PC so it will allow me to select the OS?  Question 2: And if #1 isn't possible. How to I remove Ubuntu from the PC and recover the partition for Windows What is the difference between ++i and i++? Probability distribution in the coupon collector's problem General system specs for large scenes in blender What are the system requirements for working with complex geometry in Blender? Things like RAM, GPU, CPU etc.? Generate the smallest $\sigma$-algebra containing a given family of sets My teacher gave me an example of performing the subject:     Example      Let $\Omega = \Bbb R$ and $\mathcal R = \{(-\infty,-1),(1,+\infty)\}$.   Then $\sigma(\mathcal R) = \{\emptyset, \Bbb R, (-\infty,-1),  (1,+\infty), [-1, \infty), (-\infty,1],  (-\infty,-1)\cup(1,+\infty),[-1,1]\}$.   There was a different example, where she also generated the smallest  $\sigma$-algebra for the family of sets $\mathcal A = \{A,B\} \subset 2^\Omega$ in the same way: $\sigma(\mathcal R) =  \{\emptyset, \Omega, A, B, A^C,B^C,A\cup B, (A\cup B)^C\}$.   I certainly understand why $\emptyset$, $\Omega $ and a family of sets itself are there, and I certainly know that $\sigma$-algebra is closed under the operations of complement and union. What I don't understand about the other elements of generated $\sigma$-algebras: why we are taking exactly them? Does this work in a general case? How to install mods for the new Minecraft launcher How large would the steam explosion at Chernobyl have been? So the  of the HBO series began to cover the  that led to them sending three divers into the water below the reactor to drain the tanks.  This occurred after the initial explosion that destroyed the reactor, and after the fire in the core had been put out. But at this point the decay heat and remaining fission reaction kept the core at more than 1200°C, causing it to melt through the concrete floors below the reactor.  And below the reactor were water tanks which contained 7,000 cubic meters of water (according to the TV show. If anyone has a real figure, I'd love to hear). When the lava of the melted core hit it, it would cause an enormous .  Finally, my question: About how large would this explosion have been? The character in the show says "2-4 megatons" (of TNT equivalent, I assume). I'm pretty sure this is absurd and impossible. But real estimates are hard to come by. Other sources vary wildly, some repeating the "megatons" idea, and others saying it would've "". This still seems crazy.  tl;dr:  I know a lot of it hinges on unknowns and the dynamics of the structures and materials involved, so I can simplify it to a constrained physics question:  Assuming 7,000 cubic meters of water instantly flashes to steam, how much potential energy is momentarily stored in that volume of steam occupying the same volume as the water did?  I don't know what to assume the temperature of the steam is. There were hundreds of tons of core material at temperatures near 1200°C, so worst case scenario you could assume all the steam becomes that temperature as the materials mix. Best case scenario, I guess we could assume normal atmospheric boiling point (100°C)?