I would like to know why particles follow a circular path in a magnetic field, what path they trace and how this path is measured and controlled?
The Lorentz force on a charged particle is perpendicular to the particle's velocity and the magnetic field it's moving through. This is obvious from the equation:  $$ \mathbf{F} = q\mathbf{v} \times \mathbf{B} $$  Is there an intuitive explanation for this behavior? Every explanation I've seen simply points at the equation and leaves it at that.  I can accept mathematically why $\mathbf{F}$ will be perpendicular to $\mathbf{v}$ and $\mathbf{B}$ (assuming the equation is correct, which it is of course). But that doesn't help me picture what's fundamentally going on.  Trying to create an analogy with common experiences seems useless; if I were running north through a west-flowing "field" of some sort, I wouldn't expect to suddenly go flying into the sky.  I'm hoping there's a way to visualize the reason for this behavior without a deep understanding of advanced theory. Unfortunately, my searching for an explanation makes it seem like something one just has to accept as bizarre until several more years of study.
Say you have a stick which breaks randomly into three pieces (we can choose the points randomly). What is the probability that the area is greater than or equal to $0.4$?   I can see it has something to do with Heron's formula but I just can't put t together. URL to load resources from the classpath in Java How do you know when to wean? What signs can a baby show to indicate he/she is ready for weaning?  What does a parent look for to determine the right timing for this for baby, mom and family? Why are there so many close votes to review and so few of the others? In the SO Review page , I see the following stats for questions awaiting review:   Close votes:  51.8k (and rising) Suggested edits: 10 (fluctuates, but rarely goes above 20) Everything else: 0 (occasionally see some if you're really lucky)   My question is: Why?  Why are there so many close votes waiting for review? Close votes should expire after four days. And even if there's a good reason for them hanging on longer (ie they're not being viewed), there surely has to be a cut-off eventually after which they can be safely dropped?  And yes, I saw , which is asking basically the same thing. But that was several months ago, and it seems that the queue has hardly moved since then. It seems to me that there's a massive backlog that will never be cleared, and apparently will never expire either. That's not good.  And on the flip side, why are there hardly ever any new user posts or low quality posts to review -- there are always new users posting things, and I recall before this new review system was launched that the list of low quality posts to review was always pretty big. I was trying to solve internet problems, and seem to have made things worse: Now when I start the computer it gets stuck on "Booting system without full network configuration".   Does anyone know how to make it unstuck?   Alternatively: It got messed up when I changed the contents of /etc/network/interfaces, so presumably would work again if I changed it back. How can I edit this file during boot?   I'm using Ubuntu 12.10. Is it possible to build a single mysql query (without variables) to remove all records from the table, except latest N (sorted by id desc)?  Something like this, only it doesn't work :)  delete from table order by id ASC limit ((select count(*) from table ) - N)   Thanks. Windows 8 Pro clean install - everything slow; hard drive at constantly at 100% Yesterday, I have downloaded and installed Windows 8 Professional, after downloading it (legally) and burning it to a DVD, on my 3-year-old  (Intel Core Duo 2x2.4&nbsp;GHz, 4&nbsp;GB RAM,  hard disk drive).   The installation failed two or three times, each time differently (error codes, for example 0xc000021a, with an infinite boot loop), but finally I completely formatted the hard drive and installed. Seemingly, everything was OK.  However, after booting successfully, the OS is extremely slow. When I open the task manager, it shows that the HDD is at 100% - however, no application or background process or Windows process can be made responsible. I searched the Internet and found that Windows might try to "index" the hard drive, but I did't find a process that isn't also on my second computer, which still uses the Release Preview (restarting every two hours). Also, the startup is empty, and HD Tune and HDD Health show that the drive health is OK, even though I don't know how reliable these two programs are.  I looked for diagnose software from Toshiba, but they only offer tools for "Fujitsu branded Toshiba devices"; I tried it out, and it did not work on my hard drive.  Does this sound like a hard drive failure? The laptop is 3.5-years-old, has been carried around sometimes roughly and was used (and on) most of the time. However, it would have failed exactly the night before installing Windows&nbsp;8 Profesional, which seems - unlikely.  If this is a software error - then what did I do wrong if this occurs from the moment of installation (even the personalization at the end of installation took half an hour)? How can I fix this? Counting the number of surjections. Is there a simple way to add exFAT support? When I insert a USB stick or camera flash card I get the following error:  unknown filesystem type 'exfat'   Is there a simple way to add exFAT support to Ubuntu without kernel patching? When is "seems to be" used instead of "seems"? The baby seems happy/comfortable. The baby seems to be happy/comfortable.   Are these both correct? If both are correct, what are the differences between them? I am wondering why matrix factorization techniques in the machine learning domain almost always expect the provided matrix to be non-negative. What is the advantage of this constraint?  Background: I want to use matrix factorization algorithms for a sparse user-item matrix containing positive and negative implicit feedback. Is there any another possibility to set interactions with negative indications apart from fields that denote that no interaction happened between the user and the item? How to set system-wide environment variables on OS X Mavericks When is the present perfect tense used instead of the past tense?    I know that the present perfect tense is used when some adverbs (e.g., never, ever) are present in the sentence; the same is true for sentences like the following one.     When you returned, I have been at home since 3:00 PM.   In which other cases should I use the present perfect? Do the following sentences require it?     I have walked downtown everyday for a year.        I have been at home since 3:00 PM. I have a vps using Ubuntu 12.04 LTS and I my host corrupted my vps so now it won't boot up. When it boots up it says:  Booting from Hard Disk... error: file not found. grub rescue&gt;   How can I fix/repair this? Evalute $ \lim_{n\rightarrow \infty}\sum^{n}_{k=0}\frac{\binom{n}{k}}{n^k(k+3)} $ Evaluate $\displaystyle \lim_{n\rightarrow \infty}\sum^{n}_{k=0}\frac{\binom{n}{k}}{n^k(k+3)}$.   $\bf{My\; Try::}$ Although we can solve it by converting into definite Integration.  But I want to solve it without Using Integration.  So $\displaystyle \lim_{n\rightarrow \infty}\sum^{n}_{k=0}\frac{\binom{n}{k}}{n^k(k+3)} = \lim_{n\rightarrow \infty}\sum^{n}_{k=0}\frac{(n-1)(n-2).......(n-k+1)}{k!\cdot n^{k}\cdot (k+3)}$  Now How can i solve after that, Help required, Thanks What is the EV scale? I have seen an "EV" (exposure value) scale that's sometimes used to express a camera's exposure settings, or scene brightness. How exactly does this scale work? How do you validate that two math expressions are equal? Let's say you have a few expressions like the following:  $$\begin{array}((x+17)^2 \\ x^2 + 34x + 289 \end{array} \\ 288 + \frac{x^2}{2} + \frac{x^2}{2} + 34x + 1 \\ [...] $$  You get the idea: there's an infinite number of ways of representing the same expression. The challenge is that my application is validating answers to math problems, input by math students practicing a certain concept. I'd like to make sure that whenever they submit an answer, the checker is completely insensitive to the issues of ordering, simplification, formatting etc. which would be plain frustrating. I'd also ideally like to support more than one variable such as x, y, z in the same expression.  What's a reliable way to check that two expressions are the same? The most brute force way I can think of would be to just plug a number into each variable of each expression and see what the result is.  I have a hunch however that there might be ways of getting false positives this way. That, and I might be either missing something really obvious about this, or there might be a better way of doing the comparison.  Would love to hear what you think. How do I migrate my Keychain's "Local Items" to a new Mac? After preforming a Mavericks-Mavericks migration using Migration Assistant, I have a "Local Items" Keychain on my new machine in which many (perhaps most) items are out of date (using old passwords), and some are missing altogether. While I have access to a copy of the entire contents of the ~/Library/Keychains/ directory from my old machine, which presumably contains all the information I'm missing, I see no way of importing that information into my new machine.  How can I import the "Local Items" from my old Keychain into the Keychain on my new machine? nmake fatal error U1034: syntax error : separator missing How did the transdimensional Edo god (Edo lord) come to be the overseer of the Edo?