Let's assume I have a conductive rod with mass $m$ and with steady current $I$. I can make the current flow in such a direction and magnitude that the magnetic force will make it move up, thus something is doing work on the rod. But it can't be the magnetic field since it's perpendicular to the direction of motion.  I still don't understand; what is doing work on the rod?
I've seen some conflicted answers to this question in texts and on the web, in the case of a dipole, for example.   Do magnetic fields do work directly, or is it their induced electric fields that do work?
StackExchange drop down hiding chat, blog and log out, concerns bashrc lazy substitution How many possible electromagnetic wavelengths are possible? Disclaimer: Please keep in mind that I am a young highschool student with no background in physics, this research was done in the course of an hour, and my reasoning could very well be wrong.  After a short conversation about color, I did some thinking, and read  The answer claims that there are $\infty^{\infty}$ colors   My first problem is the definition of colors, I'm going to simplify this (although it's not the same thing) as electromagnetic frequencies. This is what I mean when I refer to color in the rest of this question  The problem with $\infty^{\infty}$ colors is that the plank length exists. This causes two problems to arise with $\infty^{\infty}$. If $l_p$ is assumed to exist (as it is), this means the smallest distance in the universe is $l_p$. So, all wavelengths of light can be divided into a set, of the wavelengths produced by objects at $0^{\circ}$ Kelvin to $\infty^{\circ}$ Kelvin. According to this logic, there are simply $\infty$ colors.  Things are complicated further, when you introduce the Plank Temperature ($P_t$). $P_t$ is the theoretical limit temperature of the universe (at least for the purposes of light and color) Because an object hotter than $P_t$ will produce light with wavelengths shorter than $l_p$. This would introduce an upper limit on colors too.  Wouldn't this mean that the total number of possible colors is equal to however many plank lengths difference there is between an electromagnetic wave produced by a 0 degree object and a $l_p$ object? And therefor far less than $\infty$? Does this reasoning make sense at all? Hiding get mobile app button on SP online communication site collection For one of the clients, I have spin up a modern communication site collection and on the landing page of the same, I am seeing 'Get the mobile app' showing up, I was able to hide the 'feedback' button using css but no luck with Get the mobile app button.  Can someone please share css to hide 'get mobile app' button, appreciate the help. Can I legally downgrade from Win 7 64 bits to Win 7 32 bits? Possible Duplicate:          Tired of the unstable Win 7 64bit I got when I purchased my laptop (it was impossible to find a powerful laptop with Win 7 32 bits).  Can I legally downgrade from Win 7 64 bits to Win 7 32 bits? The key/activation will work?    Details: Everybody comments about the stability of Win 64.  Well, I made a mistake. Is not that Win 64 is unstable (it never crashed). It just works very poor. It feels choppy. Compiling a large program (on an old AMD desktop PC) takes 1.5 seconds on Win 32. The same program compiles on Win 64 in 4-5 seconds in this new and "powerful" laptop. All programs are less responsive. Quitting a job in the US on a work visa, going to Canada and re-entering on a tourist visa (ESTA waiver) I have been working in the USA on an E-3 visa and intend to return home to Australia, but I want to travel around the US before I do so. I am under the impression that after leaving my current company, I will have 10 days to leave the country.   Will I be able to go into Mexico or Canada and re-enter with an ESTA waiver as a tourist? How to make GRASS and SAGA tools capable to use in QGIS？ I installed QGIS, GRASS and GDAL by OSGeo4w package, and as I finish the installation, I want to use GRASS tool, I face this problem：    But I already installed GRASS and SAGA, how to make those tools in QGIS to be used？ Why can't I launch eclipse from a terminal ? change $PATH environment variable Why are some faces in my mesh darker? While rendering a mesh with smooth shading on, I get a dark region/shadow on certain faces. The effect is more evident when smooth shading is applied to a mesh containing ngons, with the ngons turning black when rendered.   The blackening effect is visible in the viewport too.  How can I solve this problem? The achievements drop-down menu in the new top bar shows me when a question/answer earns me reputation and how much, and that's great, but I don't know what caused that to happen. I'd like to know why I received reputation: was it an upvote? An accepted answer? An accepted edit? If I have the list of reputation values in my head I can figure it out, but it would help me to see it somewhere in the drop-down, even as title text on hover.    Edit:  It sounds like the items in the menu can roll up multiple events, and that's why it doesn't show the event there. How about adding a link to my reputation tab to the menu so I can quickly get to a breakdown? Plotting complex numbers as an Argand Diagram What does Use an Object cover? How do I remove hidden backup files? I have files ending in ~ in my home directory, and I want to delete them. How do I do that? How do I prevent this backup functionality? Decomposition of semisimple Lie algebra via its roots Exercise 14.33 in Fulton and Harris's Representation Theory claims that  If the roots of a semisimple Lie algebra lie in a collection of mutually orthogonal subsets, one sees that the Lie algebra decomposes into a direct sum accordingly.  Although intuitively I can see why this is true, could anybody direct me to a proof of this assertion, or outline how I should go about doing it? Countable set of truth assignments satisfying set of well formed formulas I am trying to answer the following question posed in my logic class: (throughout we work in propositional logic) is there a set $S$ of well-formed-formulas (wffs) satisfied by countable set $V$ of truth assignments such that any truth assignment satisfying $S$ lies in $V$?    My guess is no.  My first reaction to this was to do a diagonalization.  Present $V$ as an array with $v_{i, j}$ the truth value that assignment $v_i$ gives to the $j$-th propositional letter.  Obviously the hard case is when $S$ is infinite; if $S$ is finite, then only finitely many propositional letters occur in the $S$-formulae.  Then there is some maximal $k$ for which all $A_n$ with $n \geq k$ do not occur in V.  Then the diagonalization is trivial: just diagonalize from the $k$-th letter onward, since changing $A_k$ in this range doesn't affect anything in $S$.  But I have little clue about how to approach the main case when $S$ is infinite. I thought maybe I should try using the fact that $S$ is consistent (since it's satisfiable).  If it's maximally consistent, then I think this is simple too, since for every propositional letter $A_n$, either $A_n$ is in $S$ or $(\neg A_n)$ is in $S$, implying that there is only one truth assignment satisfying $S$--since every truth assignment must agree on each propositional letter.    But if $S$ is not maximally consistent, this isn't available to me.  Somehow I would like to show that infinitely many propositional letters do not occur in $S$.  Then I can apply the trick above and just diagonalize through the superfluous letters.    So, yes, just looking for some hints or corrections if you have any please, though maybe if I don't get anywhere on my own I'll give up and ask for more.  Thanks.  (By the way, by referring to letters that "occur in $S$" I mean letters that occur in some formula in $S$). How to restore a system after accidentally removing all kernels? Prove that for every $n\geq m \geq1$ natural numbers, the following number is an integer:  $${\gcd(n,m)\over n}\cdot{n\choose m}$$  Where $\gcd$ is the greatest common divisor.  I tried to make it simpler by cancelling the $n$ from the left side, and making it $(n-1)!$ on the right: $\gcd(n, m) \cdot \frac{(n-1)!}{m!(n-m)!}$, but can't really go further.   This was problem B-2 on the . Is it normal for a fast prime to exhibit purple fringing in middle of the image? I have just bought a Nikon 50mm f/1.8D prime lens.  I took this picture (leg of my glasses frame on a mouse, and a LED desk lamp is on top of it) : f1.8, 1/80s, ISO 200   The purple fringing is right in the middle of the picture. Does it happen very often to this lens? Does excessive markup affect SEO? How many ways can the average of n dice be a?