May I know if we have a current flowing through a wire, and the wire is between two strong magnets. The wire would experience a force called the Lorentz Force given by F = IxB, or F equals I cross B. Based on Newton's third law of motion, will the magnets also feel a force in the opposite direction of the wire?    In this case the wire is feeling a downward force. But by Newton's third law of motion will the magnetic around it feel an upward force?
Consider a system of the two identical positive point charges situated in free space (isolated from the influence of any other external fields) as shown in the attached diagram. Particle $1$ is at $(a,a,0)$ and particle $2$ is at $(0,a,0)$. Their velocities, at the considered instant of time, are as shown in the diagram ($\mathbf{v}_1$ along the $+x$ axis, $\mathbf{v}_2$ along the $+z$ axis).    Now, by applying the Biot-Savart law, we find that the magnetic field due to particle $2$ at the position of particle $1$ is along $+y$ axis, which means that the force acting on particle $1$ is along $+z$ axis according to Fleming’s left-hand rule. A similar analysis shows that there is no magnetic force on particle $2$ as the magnetic field of particle $1$ should vanish at positions (relative to particle $1$) located along its velocity vector.  Now, if we observe the net torque on the system of two particles about the $y$ axis then it is non-zero and is directed along the $-y$ axis. Here, there are no external forces or torques acting on the isolated two-particle system, and yet the net torque, as well as the net force on the particles, are nonzero. Why? Also, Newton's third law of motion seems to be broken in this scenario. Why?    Edit $1$  I have come to know from the responses that the electromagnetic field itself takes away some momentum and angular momentum about the considered axis. However, I think that if I consider only two charged particles as my system then the Abraham-Lorentz force can be assumed to be acting upon the system, and that is sufficient to make sure that we have considered the momentum being carried away by the electromagnetic field itself.   Even after considering the action of the Abraham-Lorentz force for the two-particle system, the scenario breaks both Newton's third law and the conservation of linear and angular momentum. This is because the Abraham Lorentz forces do not exactly counterbalance the force and the torques, on the two-particle system under consideration, due to the magnetic field.    Edit $2$  The previous edit was a result of confusion and misunderstanding on my part. The force associated with the momentum carried away by the electromagnetic field as a result of the electromagnetic interaction described in the question is the Lorentz force itself which simply doesn't obey the third law of motion. The Abraham-Lorentz force is a different story. It is associated with the momentum carried away by the radiation emitted by the accelerated charged particles. This is an additional force apart from the Lorentz force and corresponds to an additional carriage of momentum by the electromagnetic field. The momentum carried away by the electromagnetic field in correspondence with the Lorentz force doesn't correspond to radiation.
Suppose you have an object with zero for the value of all the derivatives of position. In order to get the object moving you would need to increase the value of the velocity from zero to some finite value. A change is velocity is acceleration, so the value of the acceleration would have to increase from zero to some value. You would also need to increase the jerk from zero to some value to have a change in acceleration.  Is there an infinite series of higher derivatives of position for this to work? Or am I missing something? I would like to port Ubuntu Touch to a device that is currently not supported. What are the requirements for doing this and where do I begin? Let $f \in C [a,b]$ such that $\forall x\exists y$ such that $|f(y)| \leq \frac{1}{2}|f(x)|$. Prove that $\exists c\in [a,b]$ such that $f(c) = 0$. How to get new answers to old/popular questions read/voted on? If a question has more than one page of answers then a new answer is not likely to get much attention.  I think the stackoverflow engine should give some more weight to newer answers to old questions but I'm not sure how.  Maybe a tweaked UI to get access to newer answers.  NB. In the related questions this  popped up, I hadnt realised either that these tools existed. What happens if I beat Ganon in Zelda: Breath of the Wild? I'm close to maxing out my character and I want to beat Ganon solely for the TRUE ending, but I'm too scared of losing some of my personal favorites from the Guardian Spear++ to fighting those damned Guardians (it was so fun).  So, after beating Ganon    Do monsters disappear? - Including the corrupted Guardians, but also the blood moons, I don't want to just face off against the Yiga Clan... Am I gonna run out of resources? - As a survival game Zelda BOTW has some emphasis on the survival genre but to me it is a survival-esque action-adventure game. Are special weapons still available when you max out? - Like the Savage Lynel Spears or Swords) I have lost my passport here in Beograd. Can I travel just with my Czech ID card from Belgrade to Budapest? $dx$ appears in differential equations, such us derivatives and integrals.  For example, a function $f(x)$ its first derivative is $\dfrac{d}{dx}f(x)$ and its integral $\displaystyle\int f(x)dx$. But I don't really understand what $dx$ is. Link to the recommended job is broken in the mobile apps The link to the recommended job in the app brings you to a page with the text: Not Found    Looking at the link it seems like after changing the URL structure in Stack Overflow Jobs they have not been updated in the apps.  For the job in the screenshot this is the used URL in the app:    The correct URL is: I'm looking for a specific scifi book that I read years ago, I only partially remember the story, and I don't remember the author or the title.  What I remember of the story is:   An alien race picks up a signal from humans that includes instructions on how to make their own humans (genetic instructions). The humans grow up knowing they are created and are taught by the alien race. They are eventually given resources to build a ship, and go looking for their origins. They eventually find the solar system, but nobody answers. They find some stations orbiting earth and find that the station is very old, so old in fact that humans have long been extinct and other creatures have reached local space, and have been looking around the station as an archeological dig. I think they refer to two developed races from earth, but one developed from rats.   If anyone know what story this is, and can point me at it, its been driving me crazy for at least 15 years, and I think it's actually been much longer, since I can't remember when I read it. How do I run a sudo command needing password input in the background? I have recently disabled  so that it now prompts me for a password every time.  And though this is good for security, it has caused one slight problem which I haven't been able to figure out a solution for, I am unable to run commands which go along the lines of:   sudo &lt;command&gt; &amp;   In the past I would have run a sudo command before that, it would have cached my password and allowed me to run sudo commands without prompt for the next few minutes, and thus it would allow me to run the command.  But when I run it now as there is no caching before hand and as it starts a new thread immediately and sudo doesn't even prompt me for a password, I am unable to run it in this way.  So unless I run sudo -i before it I am unable to run a command in this format which is becoming rather annoying. So I was wondering if there is any way to get around this and still run programs and commands in this way?  I am running Ubuntu GNOME 15.10 with GNOME 3.18, and specifically the program I want to run in this fashion is etherape if that makes any difference, but I would really like the solution to work for all programs and commands. Does a first generation iPod touch have the ability to download apps and use emojis? I am getting a 1st gen iPod touch for a friend and I was wondering if you can download like apps and games on it and if it has emojis? It would help to get an answer before I buy it! How to use JACK and Pulseaudio/ALSA at the same time on the same audio device? Whenever I launch hydrogen it breaks my audio in all other applications which use Pulse, for example, I can no longer play videos in Chrome after having launched Hydrogen once, until I restart my PC or do sudo alsa force-reload. I have found people with similar issues, but no actual guide to fix this, often there are links to  (which has moved to  ) I am using Ubuntu Studio 14.04 64bit.  ALTERNATIVELY if this is truly impossible to achieve, can someone tell me how to use Jack on one soundcard and Pulse on another? This way I could plug in a USB sound card only when I need JACK.  Please don't make me use windows. Live CD asks for a username and password How does find -name work? If I enter my password correct first time, I login as normal.  If I enter my password wrong, it says invalid password. If I attempt to enter the correct password now then the screen freezes and doesn't go to dock as normal. I must restart using a physical button or shutdown to get out. Login works normally after restart, assuming I get it right first time.  EDIT:  After entering a wrong password, if I click cancel and then go back to my user to login, it works fine. Overflow to left instead of right I have a div with overflow:hidden, inside which I show a phone number as the user types it. The text inside the div is aligned to right and incoming characters are added to right as the text grows to left.  But once the text is big enough not to fit in the div, last characters of the number is automatically cropped and the user cannot see the new characters she types.  What I want to do is crop the left characters, like the div is showing the rightmost of its content and overflowing to the left side. How can I create this effect? When entering the US on an international flight, and then on to a connecting domestic flight, what is the exact order of the process that will take place? In other words, what happens first, second, third, etc.? "ignorance" can also mean a "willful disregard of something"? I try to use the 2nd or 3rd definition of words (to slow down speed readers). However, I am not sure if "ignorance" has a 2nd definition.  (common meaning)  is "a lack of knowledge". With this meaning, no syllable is stressed.   My ignorance of hardware means I cannot build my own pc.   (2nd meaning?) If pronounced differently, I think that "ignorance" can also mean "a willful and careless disregard of something". The "nor" syllable in "ig-NOR-ance" must be stressed.     The French were aware of the strategic weakness of the Maginot Line, and their ignorance of it enabled the German blitz through the Low Countries.   My ignorance of my girlfriend's hourly text messages quickly caused our break-up.   In a dictionary, "ignorance" is only defined as "lack of knowledge". But, I am not talking about that "ignorance". I am talking about the "ignorance" that is derived from "to ignore" and thus pronounced just like "to ignore", and thus has the meaning of "to ignore". There is precedence for this:  "to accept" --- derive ---> "acceptance" "to ignore" --- derive ---> "ignorance" ....  Anyone agree with me? C programming: How to program for Unicode? Manually change filetype icons in Windows 7 I'm trying to find the dialog tab in Windows 7 that allows a user to change the icon used for a particular file type.  In Windows XP it would be under the Folder Options properties dialog.    Where is it on Windows 7?  I only want to change the icon of a specific filetype, to anything I want but this tab is no longer present in Folder Options of Windows 7.