This questions has been asked all over the net (here included) but I can't find a satisfactory answer or discussion. Some say it does not radiate if the acceleration is caused by a uniform gravity field. Some even say that it radiates in linear accelerators because of our imperfect technology. All this comes from university member (at least they claim to be). My head is spinning. I always thought (from CED) that any kind of acceleration causes the charge to radiate and loose energy, not that I say that this is the case, but the equivalence principle of relativity never crossed my mind while thinking about this puzzle. Today it did.   Can someone here give some good, kind of fresh, references (no ArXiV please!) or alternatively, try to explain better than what others have done?
The  gives the recoil force, $\mathbf{F_{rad}}$, back on a charged particle $q$ when it emits electromagnetic radiation. It is given by:  $$\mathbf{F_{rad}} = \frac{q^2}{6\pi \epsilon_0 c^3}\mathbf{\dot{a}},$$  where $\mathbf{\dot{a}}$ is the rate of change of acceleration.  If a particle has a constant acceleration, $\mathbf{\dot{a}}=0$, then there is no reaction force acting on it. Therefore the particle does not lose energy.   Does this mean that a constantly accelerating charged particle does not emit electromagnetic radiation?
MWE for externalize + automatic recompilation after tikz figure modification Lost USB BlueTooth Dongle for Keyboard and Mouse I lost my USB bluetooth dongle (from HP) which I used for a wireless keyboard and mouse. They came together in a set when I bought my last HP computer.  Are the keyboard and mouse useless now? or will any bluetooth dongle allow them to work? If I can just buy a new one - any recommendations on a replacement (good price, and perhaps works with Windows and Ubuntu out-of-the-box?   Forgive me if this is an easy question. I'm just not that familiar with wireless mice/keyboards. Direct formula for area of a triangle formed by three lines, given their equations in the cartesian plane. I read this formula in some book but it didn't provide a proof so I thought someone on this website could figure it out. What it says is: If we consider 3 non-concurrent, non parallel lines represented by the equations : $$a_1x+b_1y+c_1=0$$ $$a_2x+b_2y+c_2=0$$ $$a_3x+b_3y+c_3=0$$ Then the area of the triangle that these lines will enclose is given by the magnitude of : $$\frac{det\begin{bmatrix}a_1 &amp; b_1 &amp; c_1\\a_2 &amp; b_2 &amp; c_2\\a_3 &amp; b_3 &amp; c_3\end{bmatrix}^2}{2C_1C_2C_3}$$ Where $C_1,C_2,C_3$ are the co-factors of $c_1,c_2,c_3$ respectively in the above matrix.  What I'm wondering is, where did this come from? And why isn't it famous? Earlier we had to calculate areas by finding the vertices and all but this does it in a minute or so and thus deserves more familiarity. I'm on ub20LTS and I really dislike how much top space the topmost bars use. Any idea on how to remove or reduce their numbers?  Edit: Thanks to everybody's support, this is how my workspace looks like now. I've :  Installed gnome-extensions for firefox. Turned off menu bar in ff. Installed dash to dock. Installed hide top bar.  This way you can better utilize your screen space. I'm just going to throw this out there, but Google indexes Stack Overflow really quickly For example, I  after using Google to try to find an answer. I then turned back to Google and did a search for  and it was already the first result! Similar searches also put my question on the first page, usually in the top 5!  This is insanity. Did I get lucky and post just before an indexing? Is the popularity of SO leading to Google indexing extremely frequently? Or is Jeff using some kind of crazy SEO? Use laptop trackpad as graphics tablet What tense should I use to describe something in the past but probably is still true? The title may be a bit confusing. See the below example:     The movie (was/is) so good.   The simplest guideline on deciding which tense to use, past tense or present tense, to describe an object comes down to whether the description was only true that that time or is true even to the present point of time.  But now we talking about literary work(movies,books,etc) of which quality tend to stay the same over time, which tense should we use? Setting custom UITableViewCells height Fred and George stumbled upon the Marauder's map in their first year. They passed it on to Harry while in their fifth year. Also note that, while talking to Harry on the train, Ron described Scabbers as being "Percy's old rat".   Hence, we can safely assume that the twins had the Marauder's Map for about five years. How could they not see Peter Pettigrew on the map, with Percy for first two years and with Ron for the next three years?  How come Harry didn't see Peter? How was Lupin the only one able to see Peter on the map? Modelling the number of apples an orchard yields with diminishing returns per tree This is   in the University of Washington's precal book.  Sylvia has an apple orchard. One season, her 100 trees yielded 140 apples per tree. She wants to increase her production by adding more trees to the orchard. However, she knows that for every 10 additional trees she plants, she will lose 4 apples per tree (i.e., the yield per tree will decrease by 4 apples). How many trees should she have in the orchard to maximize her production of apples?  Instructing a precal class, I walked through my approach to answering this in class (without preparing) and ended up doing something strange that may have confused the students. How would you clearly explain a way to get the function for the number of apples that we are trying to maximize? More generally, how would approach answering this question? It'd be nice to collect a some different approaches to demonstrate to my students that there is not a single rigid correct way to solve a problem. I was working on historical data looking for anomalous patterns that we would not expect to occur at random. I'd like to create a scheme to analyze data and markets to test for statistical significance and consistency over time.  Question : Are there some tools we could use to evaluate the nonrandomness of a database? What do we use usually to say that something is random or not (statistically)? Figure we work with change in some value over time. Time Complexity of $T(n)=T(n-2)+\frac{1}{\log(n)}$ How do I enumerate the properties of a JavaScript object? How do I enumerate the properties of a JavaScript object?  I actually want to list all the defined variables and their values, but I've learned that defining a variable actually creates a property of the window object. Is there a built-in method to compare collections? I would like to compare the contents of a couple of collections in my Equals method.  I have a Dictionary and an IList.  Is there a built-in method to do this?  Edited: I want to compare two Dictionaries and two ILists, so I think what equality means is clear - if the two dictionaries contain the same keys mapped to the same values, then they're equal. Two players shooting a target alternately Why does resistivity increase with temperature?  The explanations I have heard so far are that increasing temperature increases vibrations in the lattice structure resulting in the number of collisions increasing.  But the vibrations from thermal energy are random, so around half of the vibrations would result in the atoms moving out of the electrons way and half would result in atoms moving into the way of the electrons.  And since half of the vibrations result in increasing the drift speed and half reduce it, shouldn't the average drift speed remain the same? A sine integral $\int_0^{\infty} \left(\frac{\sin x }{x }\right)^n\,\mathrm{d}x$ The following question comes from   post $$\int_0^{\infty} \left(\frac{\sin x }{x }\right)^n\,\mathrm{d}x$$ but now I'd be curious to know how to deal with it by methods of complex analysis. Some suggestions, hints? Thanks!!!  Sis. Why didn't the Ministry use Veritaserum to question criminals? The truth potion (Veritaserum) is one of the most powerful potions that forces the drinker to speak truth. Then why didn't Ministry used it in any criminal cases instead of long discussions and proceedings? I know there are antidotes to the potion (Dumbledore tells Harry in the 6th book , "Slughorn might have been carrying antidote to veritaserum ever since I asked him about the memory"), but why don't keep criminals in custody until the effect of the antidote wears out and then make them drink veritaserum. Won't that result in perfect judgement? How to get GNOME Shell "Applications overview" to show the full name of applications Safari can load internet but none of the other apps cannot! This is by far the weirdest problem I've come across,  My mac can perfectly access internet through safari web browser, but when I tried to do   ping www.google.com   through the terminal, it's requests is being timed out.  None of the other apps are able to reach internet either. Dropbox, Skype, Spotify all showing offline, except the browser itself  I'm guessing something bad with the DNS, but spend 2 hours trying to fix this with no luck