I'll try to be clear. I'd like to ask you if you know some books or chapters in textbooks which explaining the "meaning" of some physical phenomena or entities.   I may try to be more specific using an example to explain what i'm looking for. Let's take electrodynamics: we use both fields and potentials to describe the whole spectrum of electromagnetic phenomena. I have this doubt:    which concept is "more real" and fundamental: the field or the potential?  Are the potentials just a useful mathematical escamotage?    It may be banal but i don't know the answer. I read that in modern times the vector potential plays a central role in the theory and it is good to build the theory around it, why? "Just" less mathematical complication or a more physical insight? Maybe I never even thought about some interesting question about the fundamental quantities and therefore I'll never look for those answer.  As other example of what I mean I may say I'd like something in the style of the first chapter $1$ of the Feynman vol. $II$, the chapter 19 on the Principle of Least Action, or the chapter on electromagnetic mass in the same book.  Edit: it's not a duplicate. I didn't ask for an undergraduate electrodynamics course. I asked for a book different in the way it explains stuff and not just about EM, but about physics in general. I made the electrodynamical example to explain what I needed. That question thred that has been put here it's of no help
What books are recommended for an advanced undergraduate course in electrodynamics?
Most vexing parse Given Ohm's law, how can current increase if voltage increases, given fixed resistance? According to Ohm's law, $V=IR$ (voltage equals current times resistance).  So if the voltage increases, then the current increases provided that the resistance remains constant.  I know that Voltage or potential difference means work done per unit positive charge in bringing that charge from one point to another.  So according to Ohm's law, if the work done per unit charge increases then current will increase. How can this be true? Point out my mistakes. ShareLaTeX compilation flags Is it possible and if so how can you pass flags to the ShareLaTeX compiler which one would have passed as parameters to the LaTeX compiler?  I am using the minted package and need to pass the -shell-escape flag. What is the capacity of this circuit? I simply can't figure out what the capacity of this circuit is.  I can do the math myself, I just need a hint how to create an equivalent circuit where it is obvious what is parallel and what is in series... How to install TP-LINK Archer T4U driver? I bought the wireless adapter to use with a computer without internet access but I can't figure out how to install it with just a USB with the driver on it. I've read a few articles on how to install the driver but they all require me to have internet access and I don't have internet. I'm completely new to Ubuntu. If you can help that would be great. Thanks!  Ps: I have the latest version of Ubuntu as of 7-5-16. $\text{Let }y=\sqrt{5+\sqrt{5-\sqrt{5+\sqrt{5-...}}}} $, what is the nearest value of $y^2 - y$? I found this question somewhere and have been unable to solve it. It is a modification of a very common algebra question.          $\text{Let }y=\sqrt{5+\sqrt{5-\sqrt{5+\sqrt{5-...}}}} $,  what is the     nearest value of $y^2 - y$?          $\textbf {(1) } 1 \qquad \textbf {(2) } \sqrt5 \qquad \textbf {(3) } 4 \qquad \textbf {(4) } 2\sqrt5$      I worked the problem and got $$y^2 - y = 5+ \sqrt{5-\sqrt{5+\sqrt{5-...}}} -\sqrt{5+\sqrt{5-\sqrt{5+\sqrt{5-...}}}} \\ = 5+ \sqrt{5-y} - y = 5-y + \sqrt{5-y}$$ What do I do next? How to use AP Style commas after dates I was wondering how you are supposed to use commas after full dates in AP style. I've been told to always put a comma after the year, like in the sentence:  On April 4th, 2012, I found a cat.  However, I thought the following might be an exception:  April 4th, 2012 brought the death of my cat.  Notice how there's no comma after &quot;2012.&quot;  My teacher disagreed and told me that the AP style dictates that we always put commas after dates like that. The way I reasoned through it is by replacing the dates with the word &quot;Monday&quot;  On Monday, I found a cat. Monday brought the death of my cat.  And you wouldn't write  Monday, brought the death of my cat.  TL;DR Which one is correct?  April 4th, 2012 brought the death of my cat.  or  April 4th, 2012, brought the death of my cat. How did Sauron remain in control of the Nazgûl? I flagged a question, , as "low quality" but a moderator declined it. I thought that the post was a low quality one and would like to know why the moderator did not.  Hopefully shedding light on this matter will avail me of the knowledge to be a better flagger in future.  My logic was that mysql-fetch-row is not supposed to return an array of results. If it does than its name would be mysql-fetch-rows.  What's your take on the situation? 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. Use a shell variable in awk Convergence of an alternating series : $ \sum_{n\geq 1} \frac{(-1)^n|\sin n|}{n}$ Study the convergence of $$\displaystyle \sum_{n\geq 1} \frac{(-1)^n|\sin n|}{n}.$$   I am stuck with this series, we need probably some measure of irrationally of $\pi$, unfortunately I am unfamiliar with this. So here is my attempt :  Let $f(x) = \sum \frac{|\sin{n}|}{n} x^n, |x| &lt; 1$  It's not difficult to compute the Fourier series of $|\sin(x)|$ :  $$ \displaystyle|\sin(x)|=\frac{2}{\pi}-\frac{4}{\pi}\sum_{n=1}^{+\infty}\frac{\cos(2nx)}{4n^2-1} $$  Then Fubini's theorem () works very well (because the previous series converges absolutely at $x$ fixed ) and all calculations made, we find that for all $x\in( -1,1)$:  $$ \displaystyle f(x)=\frac{2}{\pi}\sum_{n=1}^{+\infty}\frac{x^n}{n}-\frac{4}{\pi}\sum_{p=1}^{+\infty}\frac{x^2-2x\cos(p)}{(4p^2-1)(x^2-2x\cos(p)+1)} $$  However, the second sum I have not been able to show the convergence. I feel the series diverge because the following series $$ \displaystyle\sum\frac{1}{p^2\sin^2\left(\frac{p}{2}\right)} $$  diverge because  $0$ is an accumulation point of $\displaystyle (n\sin(n))$ sequence.  Any ideas (for the original series) ? Origin of the meaning of joe Sometimes it’s possible to use either a noun adjunct or the possessive case.     the shop door   the shop’s door   However, in certain phrases it’s not OK to do so.     the ship’s crew (the ship crew is wrong)   The questions are:   How can one find out what to use in such cases as “the shop(’s) door” when a noun adjunct option and the possessive case option are available?  How can one know which option is wrong in order to avoid the construction “ship crew”? Is there a difference in meaning between (a) the shop door (b) the shop’s door? I am trying to prove some theorem, and in the proof of it I have to check the fact that if the sequence $\{a_n\}_{n\in \mathbb{N}}$ converges, then $$\lim_{n\to \infty} n(a_n - a_{n-1}) = 0. $$ I think that this is true because I have tried with many different sequences and it holds, but I do not know how to prove it.  If this is not true, what is a counterexample for it? I am wondering what we can say, if anything, about the population mean, $\mu$ when all I have is one measurement, $y_1$ (sample size of 1).  Obviously, we'd love to have more measurements, but we can't get them.  It seems to me that since the sample mean, $\bar{y}$, is trivially equal to $y_1$, then $E[\bar{y}]=E[y_1]=\mu$.  However, with a sample size of 1, the sample variance is undefined, and thus our confidence in using $\bar{y}$ as an estimator of $\mu$ is also undefined, correct?  Would there be any way to constrain our estimate of $\mu$ at all? Avoid large spaces between text and equations I use the options  \renewcommand{\baselinestretch}{1.25} \setlength{\parskip}{0pt} \setlength{\parindent}{0pt}    in the preamble of my document and most of the time the document looks like intended. Once in a while though, especially when I use multiline-equations, I get huge spaces right before and after the equation and the surrounding text, for example:    Is there any way I can avoid that without removing the \parskip option? Prove $\lim_{x \rightarrow 0} \frac {\sin(x)}{x} = 1$ with the epsilon-delta definition of limit. It is well known that   $$\lim_{x \rightarrow 0} \frac {\sin(x)}{x} = 1$$  I know several proofs of this: the geometric proof shows that $\cos(\theta)\leq\frac {\sin(\theta)}{\theta}\leq1$ and using the Squeeze Theorem I conclude that $\lim_{x \rightarrow 0} \frac {\sin(x)}{x} = 1$, other proof uses the Maclaurin series of $\sin(x)$. My question is: is there a demonstration of this limit using the epsilon-delta definition of limit? What's the simplest way to wrap extruded text around a cylinder? What's the simplest way to wrap extruded text around a cylinder that has a specific radius (for example, the label on a can of baked beans)?  I've tried using the Simple Deform modifier, but that (a) doesn't allow you to choose a radius and (b) requires the text to be converted to a curve.  I'm trying to model a cylinder with radius of 30, which has a line of embossed text that runs around the curved side, facing outward.  Thanks! Why are my photos not crisp? I use a Canon EOS Rebel T3i (600D) with the kit lens. I have experimented a lot with different settings and modes, but I feel like I have wasted many good shots that could have looked amazing, if only they were a little bit sharper.  I use auto-focus on most of my pictures and make sure to choose the right focus point, but all of my photos are still a little bit out of focus. When I zoom in, I can see that the pixels are not very crisp or well-aligned.  I am not sure if this issue is caused by my equipment or skills.