Newton's third law in Lorentz Force 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?
Apparent Violation of Newton's $3^{\text{rd}}$ Law and the Conservation of Momentum (and Angular Momentum) For a Pair of Charged Particles 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.
Showing that $(m)\cap (n)=(\operatorname{lcm}(m,n))$ and $(m)+(n)=(\gcd(m,n))$ for any $m,n\in\mathbb{Z}$ Is there a standard delay for consumer ratings of apps on the App Store? I have an app that's been out for a couple of weeks. Its not exactly selling like hot cakes yet, but I'm pretty sure I've gotten a rating or a review by now. But nothing shows when viewing either in iTunes or directly on the AppStore on the iPhone.  Is there a standard delay as to when ratings/reviews show up, that Apple imposes, especially for new apps? Or do you think there is some problem with Apple's system? What does a resistor do? OK, very basic question here.  I read lots of books, searched quite a bit, and every description I read seemed to talk about the flow of electrons and right away go too deep in theory for me to grasp the basic principle of their use.  I understand a resistor limits the "flow", so that an LED doesn't blow up for example. But I fail to understand exactly what a resistor does to current and voltage...  Do resistors affect both current and voltage? In what manner? I was watching some videos on YouTube showing how to get the Duke O' Death in GTA 5, however what I have seen is sort of unclear.  Some people say you must be a returning player on GTA 5 to get it (what does this mean too BTW?), some people don't say that. Some people say you have to be Trevor, some people don't. Some say the time of day matters, some don't. And apparently you can buy it from Warstock website (I can't).   Can someone please tell me how to get it?! GTA 5 came with my PS4 (I didn't play it on PS3) if that helps. $3\times3$ linear system organization How do I install ndiswrapper support for an unsupported RTL8723DE wireless module? Amongst North Indian Students, the phrase "give an exam" is very popular. These students use the phrase to describe the act of writing the answers to examination questions.  The reason being, in Hindi, it's known as "exam dhena" which translates literally to "to give an exam".  In South India, however, a majority of people use the phrase "to take up an exam".  Which of these usages is more common/appropriate/grammatical? (As a prof I have developed a strange aversion toward the "give an exam" phrase; I find it wrong and ugly.) Negative solution to $x^2=2^x$ Just out of curiosity I was trying to solve the equation $x^2=2^x$, initially I thought there would be just the two solutions $x=2$ and $x=4$, but wolfram shows that the two equations intersect at not 2 but 3 locations, the third being a negative value of $x$. The third solution isn't obvious like the other two, so I just have a few questions about the negative solution. Is it rational? is it commonly represented with a greek letter? If it is irrational is there a way to approximate it? What are the rules and limits of Accio spell? We know that Accio spell (aka ) has some limits:   It can be blocked (e.g. Harry couldn't Accio the Diadem in RoR in Deathly Hallows). Many more failures are listed on Wikia.   But what are the exact full rules and limitations governing the spell in Harry Potter world?   Distance?  Line-of-sight?  Knowing exact or approximate location?  Specificity of item (e.g. "Accio Broom" seemed to work for Weasleys in OotP to bring their locked-up brooms - why not just a random broom?) Types of Accio-able stuff? Can you Accio water? Lump of earth? Gases/liquids/etc...? Can you Accio based on jQuery selector (or an SQL where clause), for lack of a better description? E.g. "Accio the book that has the word 'Flammel'"? "Accio biggest green ball from this room"? Can you Accio ALL items of a kind? (the reason I thought of this whole question was seeing "Accio all guns" comment in ). Can you Accio vague stuff? ("Accio meal"). Other rules that can be inferred.   NOTE: While Wikia article has some of the info, it is clearly very lacking in details on specific rules based on specific instances in canon. I'm looking for a fully comprehensive, organized ruleset for the charm, not merely 1-2 tidbits in Wikia article. Who were the hooded people in The Rise of Skywalker? Near the end of Star Wars Episode IX: The Rise of Skywalker there are several hooded figures that are shown chanting stuff (in Sith?) and just hanging out with Palpatine. Who were these people? One hour Lufthansa transit time in Frankfurt from Bangalore to Dublin Need help with a work around I need to take the 'Office' display of the 'Created By' column and display the first 5 digits of it so that my flows can run a conditional check on it. The reason is that Microsoft flows has all the 'Created By' dynamic contents besides 'Office'.  I figured simple enough I'll just do a calculated column on the SharePoint list. Then I find out that 'Created By' cannot be used in calculated columns.   So I figured I'll have my PowerApp write the Users 'Office' as a default to a field when submitting a form and calculate it off that column. Unfortunately PowerApps only has User().FullName, Email, and Image.   I have pretty much exhausted the options for a workaround that my knowledge will allow. Hopefully someone might have some ideas. Is there a continuous function such that $\int_0^{\infty} f(x)dx$ converges, yet $\lim_{x\rightarrow \infty}f(x) \ne 0$? Is there a continuous function such that $\int_0^{\infty} f(x)dx$ converges, yet $\lim_{x\rightarrow \infty}f(x) \ne 0$?  I know there are such functions, but I just can't think of any example. Difference between Session and HttpContext.Current.Session General trigger bulkification - best practices A general question asked from time to time on stack exchange is question of trigger bulkification.  Therefore I have 2 questions:   Which best practices are you using? What is the best way to handle updates of more than 200 records? (In case of more than 200 records the trigger is executed more than once.) I'm reading "BASH pocket guide of Oreilly". It said:      The process ID of the current Bash process.   In some cases, this can differ from $$.   Above explanation , explained $BASHPID variable.  Question: which cases? I have the following validation rule:  AND(  $Profile.Name &lt;&gt; 'System Administrator',  OR(  ISPICKVAL(PRIORVALUE(Level__c), "Archived"),  ISPICKVAL(PRIORVALUE(Level__c), "Closed")  )  )   This validation rule is on the opportunity object, and what I want to achieve is, if the picklist Level__c is either set to Archived or Closed, the opportunity record can only be edited by the System Administrator.  For some reason though, the validation rule also triggers, when I want to set the Level__c to Archived or Closed. But this is not what I want.   Any idea what's wrong with the validation rule? Frequently when EM waves are taught, it is said that the change in electric field causes a change in the magnetic field, which then causes a change in the electric field, and so on and so forth.   But from my understanding of basic electromagnetics, it is not necessarily a changing electric field that creates a change in magnetic field, but instead an accelerating charge. and it is this charge that creates both the electric and magnetic field. Again, from my understanding, a changing magnetic field is not generated by a changing electric field, but instead just happens to always be present perpendicular to a changing electric field due to the laws of electromagnetism.   Am I wrong? Or is the "mutual generation" concept between the electric and magnetic components of an EM wave an actual thing? Hot and Week tabs not shown to non-logged in users (except on SO) Every power series is the Taylor series of some $C^{\infty}$ function