Why we draw finite electric field lines passing through a surface when we can draw infinite ? also why electric flux is proportional to the number of lines passing through a surface ? i am confused because it doesnt make sense to calculate lines ...
When we're dealing with problems in electrostatics (especially when we use Gauss' law) we often refer to the density of electric , which is inversely proportional to the radius in the case of a single point charge (all field lines are directed radially).   My question may sound dumb, despite the fact that this concept is quite intuitive, but if you think about it there is actually an infinite amount of field lines which we can draw everywhere (one through every point), so speaking of an area where field lines are more "dense" or "sparse" doesn't make much sense to me.  With this in mind, why can we still use such a concept? Why does it really work?
Suppose $\sum{a_n}$ converges. How do I prove that $\sum{\frac{\sqrt{a_n}}{n}}$ converges Import Large Excel File Windows seems to have a length limit on file names when trying to delete, though it won't prevent those files from being created.  Our build process creates a number of temporary files (many build off of a WSDL) that run afoul of this limit.  Our ant script is somehow able to delete them when doing a clean, but sometimes I need to delete the workarea directory (where all the temp files go) without actually doing a full clean from ant.  This is the same errors , but the answers there don't really work for me as I'm dealing with a directory, not a file, and I don't always know what specific files or subdirectories are causing the problem.  And I'm trying to avoid any manual process (other than triggering a single command) to actually delete them.  If I try deleting the directory from Explorer I get the error   Cannot delete [file name]: The file name you specified is not valid or too long.   Specify a different file name   Trying Remove-Item in powershell gives the following error:  Remove-Item : The specified path, file name, or both are too long. The fully qualified file name must be less than 260 characters, and the directory name must be less than 248 characters. At line:1 char:12 + Remove-Item  &lt;&lt;&lt;&lt; -force -Recurse &lt;directory&gt;   Does anyone know of any tools or easy ways to get around this delete error without having to manually find the problem files and move/rename them? Mac Mini (Mid-2011), 16GB SSD, 16GB RAM, El Capitan (v10.11.6)  The Mac ran fine until I upgraded to Sierra. The latest Mac OS conflicted with most of the specialized apps I use every day, So I immediately returned to El Capitan.  Activity monitor shows that two "Installer/Installer.app" items are always running and are they major users of all of my available memory. Consequently, all my others apps become unresponsive.  I run Disk Utility, and the Installer.app show up there as .dmg files; but I cannot erase, delete, or unmount them. None of my 3rd party app can remove the installers.  My Mac Mini, which should be running super-fast (as it used to), now runs dreadfully and disgustingly slow. I a truly upset with Apple for this kind of garbage. To get their help: $$$. Performance of Non Clustered Indexes on Heaps vs Clustered Indexes Can you provide a list of objects that needs to be disposed in SharePoint? What exactly did mv /tmp/folder/* /* do to my filesystem? It's hard to search for special characters on google, which is why I'm posting this here.  I recently ran (as root) a mv /tmp/folder/* /* when I meant to run mv /tmp/folder/* ./ Big mistake!  Things broke! A lot of files got mixed up and placed into strange places, none of the normal unix commands worked (ls, dir, cat, etc) and once you logged off, you couldn't ssh back in -- it would give you a prompt, but not accept the old passwords.  Running ls /* shows me that it performs ls on every directory in /. If I tried to draw a parallel, then mv should have simply moved (or copied?) the files to every directory in /. Instead, really weird things happened, and I was just curious what exactly was going on.  More info: The files in /tmp/folder had been transferred from a windows machine, and had been named file (#).txt, where (#) is a number up to two digits, with a space between file and the parenthesis. There were ~40 of these text files. Circular References Cause Memory Leak? I'm trying to run down a memory leak in a windows forms application.  I'm looking now at a form which contains several embedded forms.  What worries me is that the child forms, in their constructor, take a reference to the parent form, and keep it in a private member field.  So it seems to me that come garbage-collection time:  Parent has a reference to the child form, via the controls collection (child form is embedded there).  Child form is not GC'd.  Child form has a reference to the parent form, via the private member field.  Parent form is not GC'd.   Is this an accurate understanding of how the garbage collector will evaluate the situation?  Any way to 'prove' it for testing purposes? Is Design School a Requirement for Graphic Design? Is it required for people to go to design schools to become a Graphic Designer? I've heard many cases where they have started from scratch without previous education in design and are doing fine as freelancers/working in studios.  Would it be better to go to a design school to become a Graphic Designer? How much leverage would it give you if you went to one? How to display a video in a web page using html,php I have a char array buffer that I am using to store characters that the user will input one by one.  My code below works but has a few glitches that I can't figure out:   when I execute a printf to see what's in Buffer, it does fill up but I get garbage characters at the end it won't stop at 8 characters despite being declared as char Buffer[8];   Can somebody please explain to me what is going on and perhaps how I could fix this? Thanks.  char Buffer[8]; //holds the byte stream int i=0;  if (/* user input event has occurred */)  {         Buffer[i] = charInput;         i++;          // Display a response to input         printf("Buffer is %s!\n", Buffer);  }   Output:   tagBuffer is 1┬┬w! tagBuffer is 12┬w! tagBuffer is 123w! tagBuffer is 1234! tagBuffer is 12345! tagBuffer is 123456=! tagBuffer is 1234567! tagBuffer is 12345678!  tagBuffer is 123456789! When can I use a forward declaration? I am looking for the definition of when I am allowed to do forward declaration of a class in another class's header file:  Am I allowed to do it for a base class, for a class held as a member, for a class passed to member function by reference, etc. ? How to recursively download a folder via FTP on Linux I'm trying to ftp a folder using the command line ftp client, but so far I've only been able to use 'get' to get individual files. Convert .bbl file to .bib file How can I convert a .bbl file to a .bib file. I  lost my .bib file but I still have my .bbl file. Now , I need to add more references to my .bbl file according to a specific format which I need to produce using Bibtex, so how can I convert my .bbl file to a .bib file so I can add the new references according to the format.  Thanks for any insight. Special event cards and timing Use of pizza stone in gas oven I have a new gas kitchen stove.  The oven seems to burn so easily. I have a thermometer in there and it is registering the temp that I have the oven set on.  I have seen where people have used a pizza stone to even out the heat.  I want to know if you place a rectangle pizza stone directly on the bottom of the oven or should it be placed on a rack on the lowest setting?  I would appreciate replies from anyone who has used this and if it had helped the problem How many combinations are possible in the game tic-tac-toe (Noughts and crosses)?  So for example a game which looked like: (with positions 1-9)  A1   --   B1  A2   --   B2  A3   --   --   [1][3][4][6][7] would be one combination Install Ubuntu, you can not continue Break a previous commit into multiple commits If I remove the heatsink from my processor temporarily, then later put it back without changing the heatsink or CPU, do I need to reapply thermal paste?