Is there a way to derive the field of arbitrarily moving charge from Maxwell's equations?
Deriving Heaviside-Feynman formula for the electric field of an arbitrarily moving charge from Lienard-Wiechert potential
Doubt related to a theorem in congruences of Chapter 5 of Apostol Introduction to analytic number theory I am self studying number theory from Introduction to Analytic number theory by Apostol.   I have a doubt in one argument of proof of Theorem 5.14 and I am posting its image.      My doubt is in 2nd line of 2 nd paragraph how Apostol writes - If y is a solution of (5) then ay $\equiv $ at ( mod m) . How does y being a solution of (5) implies that?       Can someone please help Adding holes simultaneously within mesh I am trying to make folder that everyone can view and can't copy,modify.    For all answers.I thinking about specially ms office files. I tried following methods  Software  - copy protect    - anti copy    This method can't protect save as and upload  MS office macro    Users can enable,disable macros.  MS office restriction    This is best choice but can't protect from file uploading.   Almost I found the solution. Way is combination of MS office restriction and restrict access from browsers using firewall or antivirus. But I don't exact how to do this. Prove that $\lfloor\lfloor x/2 \rfloor / 2 \rfloor = \lfloor x/4 \rfloor$ In the sentence-     You must wear a suit to an interview   shouldn't the to be replaced by for? Or what's the difference between these two here? This is what my GRUB 2 menu looks like so far:  I want to do a few things here:  I want to rename &quot;Windows Boot Manager (on /dev/sda1)&quot; to just &quot;Windows 8.1&quot;. I'd like to rename &quot;Ubuntu&quot; to &quot;Lubuntu 14.04.1&quot;. I'd also like to switch the order of the options to this:  Windows 8.1 Lubuntu 14.04.1 Advanced options for Lubuntu    (Windows will be the default OS) If it helps in any way, I'll explain the steps I took prior to this, since I am very new to Linux and don't know what information is required.  I bought a laptop on Amazon (ASUS X551MAV-EB01-B) pre-installed with Windows 8.1 64-bit I downloaded the proper Lubuntu .iso file for my system (Lubuntu 14.04.1 amd64) and put it on my flash drive (via UNetBootin) I went to Disk Management, and shrunk the C:/ drive down 32Gb so that 32Gb will be free for Lubuntu I used my flash drive (32Gb Sandisk Cruzer) as a LiveUSB for Lubuntu 14.04.1 I went through the install process. It didn't recognize Windows 8.1 so I had to do the &quot;Something Else&quot; option. I highlighted the free space, and pressed the + button I created a 10,000mb ext4 partition and mount point is / (is now dev/sda7) I created a 4,000mb swap area partition (is now dev/sda8) I created an ext4 partition using the rest of the free space and the mount point is /home (is now dev/sda9) I selected dev/sda7 to install Lubuntu and selected dev/sda7 for the bootloader installation It installed just fine, booted up just fine, and I'm happy to know the GRUB menu works. Plotting Complex Quantity Functions PHP PDOException: "SQLSTATE[HY093]: Invalid parameter number" Why are there humans in the Star Wars Universe? Kind of brought to my attention by .  The poster mentions non-humans, which implies that there are humans in the Star Wars universe.  However, since it happened "A long time ago, in a galaxy far far away", how could there be any humans in the Star Wars universe?  Are there "humans" in Star Wars there just because it was easier to make the movies that way?  Other shows such as Star Trek are about the future of humans, so it's easy to understand the existence of humans in those storylines.  However for Star Wars it just doesn't make sense.  It also seems odd that they'd go around creating all these different species and then just leave the main characters as humans. I guess another possibility is that the humans in star Wars eventually populated Earth, but then what happened to all the technology? Can I embed a custom font in an iPhone application? I would like to have an app include a custom font for rendering text, load it, and then use it with standard UIKit elements like UILabel. Is this possible? How do I get the deformed coordinate of a vertex with Python? How might someone find the deformed coordinate via Python or otherwise when using a subdivision modifier with the 'show on cage' option?  For example, a subdivided cube with cage enabled and a vertex selected shows the location of the vertex at 1,1,1 but when manually placing the cursor near on the surface it is closer to .5,.5,.5  I know the vertex location needs to be at its non-deformed location for subdivision to even work but would like to get more accurate point locations at the surface without having to apply to mesh. setting up subdomain on ubuntu server So, in my physics textbook it's written that the kinetic energy possessed by a body is equal to the amount of work done by an opposing force to stop the body, now that got me thinking that when a ball hits a wall, the wall which is the opposing force does no work  because there is no displacement, so to say isn't the kinetic energy possessed by the ball zero? Prove $A\cup (A\cap B) = A$ Intuition behind the Definition of Conditional Probability (for 2 Events) What is the proof that the universal constants ($G$, $\hbar$, $\ldots$) are really constant in time and space? How to change the hostname of a RHEL-based distro? If Z is a square integrable random variable such that $E[Z]&gt;0$, then prove that  $$P(Z\geq k) \geq \frac{(E(Z)-k)^2}{E(Z^2)} \forall k \in [0,E(Z)]. $$  This is a homework question and I don't even understand why the inequality is reversed comparing to Markov/Chebychev inequality. Should Cauchy-Schwartz inequality be used? If yes, then how to begin? Thanks a ton! cron Vs. sleep - which is the better one in terms of efficient cpu/memory utilization? Is the op-amp inverting or non-inverting? I am studying the function and characteristic of an op-amp to build a line-following robot with the schematics below. However, in many tutorials, the way to differentiate an inverting and non-inverting op-amp is by looking at the connection to ground via the inverting or non-inverting terminal.  However, in the schematics, the op-amp is considered to have connections to ground, thus in this case, how do I differentiate it then?  I may have understood the whole concept wrongly. Pls help!    EDIT: Please ignore the switch as it may have been drawn wrongly by the supplier.