Like charges repel.     What keeps an electron's charge from repelling itself?  This problem would come up if an electron was divisible and its parts had fractional charge.   A related question is, what keeps an electron from being divisible?
How can it be that, if like charges repel, they don't repel themselves? In other words, why don't charges break apart?  About the possible duplicate: I want to know about charges in general, not just that of an electron. My response to :  Thank you very much for the extensive explanation. Unfortunately it's a bit above my level (I'm a first year electrical engineering bachelor student). This is how I understand it: If the charge is the sum of multiple separate charges, there has to be an external force that keeps this charges together. However we most often think of electrons and protons as point charges. In other words, we don't think of them as if they are made up from different (smaller) parts. But the idea of electrons and protons as point charges has its own problems. I didn't know that the electric field has a mass. From the formula, I understand that $m\propto \frac{1}{r}$. This would mean that $m\rightarrow \infty$ as $r \rightarrow 0$ (or $r = 0$), which of course is physically not possible. But there is a way to calculate the radius of an electron based on the mass, the speed of light and the constant of Planck. (Unfortunately I don't know why.) You can get around this by a technique called called renormalization, which causes the integral to converge. Unfortunately, I don't understand the rest of the answer due to my level in physics. Nevertheless I am grateful for you answer. It would be awesome if you could confirm or correct my understanding.
Package Cache File corrupted From advice on  , I've opened a new question about the same issue, as it turned out my problem was not the one described in the question, information I did not know at the time. I'm running Ubuntu 16.04.  $ sudo apt-get update  Hit:1 http://archive.ubuntu.com/ubuntu xenial InRelease Get:2 http://archive.ubuntu.com/ubuntu xenial-updates InRelease [102 kB] Get:3 http://archive.ubuntu.com/ubuntu xenial-backports InRelease [102 kB] Get:4 http://archive.ubuntu.com/ubuntu xenial-security InRelease [102 kB] Get:5 http://archive.ubuntu.com/ubuntu xenial-updates/main amd64 DEP-11 Metadata [307 kB] Get:6 http://archive.ubuntu.com/ubuntu xenial-updates/main DEP-11 64x64 Icons [226 kB] Get:7 http://archive.ubuntu.com/ubuntu xenial-updates/universe amd64 DEP-11 Metadata [185 kB] Get:8 http://archive.ubuntu.com/ubuntu xenial-updates/universe DEP-11 64x64 Icons [268 kB] Get:9 http://archive.ubuntu.com/ubuntu xenial-updates/multiverse amd64 DEP-11 Metadata [5,888 B] Get:10 http://archive.ubuntu.com/ubuntu xenial-backports/main amd64 DEP-11 Metadata [3,324 B] Get:11 http://archive.ubuntu.com/ubuntu xenial-backports/universe amd64 DEP-11 Metadata [4,712 B] Get:12 http://archive.ubuntu.com/ubuntu xenial-security/main amd64 DEP-11 Metadata [62.7 kB] Get:13 http://archive.ubuntu.com/ubuntu xenial-security/main DEP-11 64x64 Icons [71.2 kB] Get:14 http://archive.ubuntu.com/ubuntu xenial-security/universe amd64 DEP-11 Metadata [51.3 kB] Get:15 http://archive.ubuntu.com/ubuntu xenial-security/universe DEP-11 64x64 Icons [85.1 kB] Fetched 1,578 kB in 1s (1,529 kB/s)                                     Reading package lists... Error! E: Read error - read (5: Input/output error) W: You may want to run apt-get update to correct these problems E: The package cache file is corrupted   If there's any more information you need, don't hesitate to ask in the comments.  Edit 1:  $ sudo df -h Filesystem      Size  Used Avail Use% Mounted on udev            5.9G     0  5.9G   0% /dev tmpfs           1.2G  9.4M  1.2G   1% /run /dev/sda1       135G  7.2G  121G   6% / tmpfs           5.9G   14M  5.9G   1% /dev/shm tmpfs           5.0M  4.0K  5.0M   1% /run/lock tmpfs           5.9G     0  5.9G   0% /sys/fs/cgroup tmpfs           1.2G   88K  1.2G   1% /run/user/1000 /dev/sdb1       932G  300G  633G  33% /media/adoria298/MDrive1   Edit 2 SMART Test results: How to add \part only to TOC? I find in many places mentions of pre-amplifiers being used to boost audio signals prior to feeding to a power amplifier.  Wikipedia's article on  gives some hints at their usage, but it doesn't really explain why it would be necessary to have two amplifiers in series rather than a single one with greater gain.  If a pre-amp is just a power amp with a smaller gain, what's the point, and why the distinction between the two kinds? Is the distinction in function, or simply purpose? What PDF Editors are available on Ubuntu? I was wondering if there is a pdf reader-writer-publisher-editor that can add text, highlight, shapes and general edit an existing pdf document.  Something like Nitro in windows. I don't understand at all why:  \begin{equation} \sum\limits_{n=0}^\infty p_n x^n = \prod\limits_{k=1}^\infty (1-x^k)^{-1} \end{equation}  Where $p_n$ is the number of partitions of $n$. Specifically how can the sum of positive numbers ever be factored into a fraction or factors to the $-1$ power? Is this something purely notational or am I missing something big?  Thanks for all the help! How can I work around this TikZ bug: (\x)^2 and \x^2 produce different results in TikZ plot? Difference between negative and positive temperatures written as absolute value or the negative integer? **In a chemistry class, students were learning about boiling point of various elements.Reuben has compiled a table that gives boiling points of each of various elements.  The lowest boiling point is of Element X: – 200 degrees Fahrenheit. The highest boiling point is of Element Y: 550 degrees Fahrenheit  Find the difference between the lowest and highest boiling point**    I know how to calculate the difference. -200 – 550 = -750.  I am not sure if the answer is written as a negative or positive. Isn’t difference in temperature always written as its absolute value? Will the answer be – 750 F or 750 F ?  Would greatly appreciate if you could explain what the correct answer is. Format a date in XML via XSLT How can I mass rename files? I've got a bunch of files named with a the pattern 99 - DescriptiveName.txt and I'd like to remove the number from the front so I just have DescriptiveName.txt.  How can I do this? Can I do it from the command line or is there a utility that can do this? In how many ways $5$ different rings can be worn on $4$ fingers ?   Although these is similar question here   But I want to answer it in different way which is like take $4$ fingers like $a,b,c,d$. Now $a$ can be filled in $5$ ways and so are others. So total ways are $5^4$ but answer is $4^5$. What is wrong in my reasoning? Which cases have I left out? Problem: James has a pile of n stones for some positive integer n ≥ 2. At each step, he   chooses one pile of stones and splits it into two smaller piles and writes the product   of the new pile sizes on the board. He repeats this process until every pile is exactly   one stone.      For example, if James has n = 12 stones, he could split that pile into a pile of size   4 and another pile of size 8. James would then write the number 4 · 8 = 32 on the   board. He then decides to split the pile of 4 stones into a pile with 1 stone and a   pile with 3 stones and writes 1 · 3 = 3 on the board. He continues this way until he   has 12 piles with one stone each.      Prove that no matter how James splits the piles (starting with a single pile of n   stones), the sum of the numbers on the blackboard at the end of the procedure is   always the same.   Hint: First figure out what the formula for the final sum will be. Then prove it using strong induction.  The formula I came up with is $n(n-1) / $2. It could be totally wrong...  My (Partial) Solution:  1) Base Case: (n=2) James has one pile of 2 stones. Suppose he takes the top-most stone and puts in one pile A, which now has size 1. He takes the remaining stone and places it into another pile B, which now has size 1. Then the product of the sizes is 1. The sum of all the products on his board is 1. Now, if he were to start again, and take the bottom stone first and put it in pile A, he has a pile of size 1, and then takes the top stone and puts it in pile B, he has a pile of size 1, and the product is 1, with sum of all products on the board is 1.   2) Inductive Hypothesis (Strong Induction): Suppose for some $k \geq 2$, $n$ stones can be split in $ 2 \leq n \leq k $ stones and $k-n$ stones.  3) Inductive Step:  Consider $n=k+1$. What do I do now? I would like to know how to find a set of coordinates on a small circle some distance from another point.   For example, lets say A = (39.73, -104.98) #Denver  B = (39.83, -106.06) #point approximately 50 nautical miles away from A along the great circle track to C  C = (40.75, -111.88) #Salt Lake City, approximately 323 nautical miles away from A  How do I get the set of orange coordinates when I don't know the angle but I do know the cross track distance?  For concreteness, lets say the outer points near B have a cross track distance of +- 30 nautical miles and the inner points have a cross track of +- 15nm.  And the points near C have a cross track of +- 25 nm.  Also I have an initial bearing from A to C of -1.34 #radians Notation problem in integration: write $dx$ or ${\mathrm{d}}x$? Show that $\mathbb{E}(T) = \sum\limits^\infty_{k=1}\mathbb{P}(T \geq k)$ for $T$ nonnegative integer valued and $E[T] < \infty$ Let T be a non-negative integer-valued random variable with $\mathbb{E}(T) &lt; \infty $. Prove that $\mathbb{E}(T) = \sum^\infty_{k=1}\mathbb{P}(T \geq k)$.  Had a few attempts, haven't really got anywhere. I'm wondering as I'm typing this if proof by induction is a good way to go.  Edit: One major thing I forgot to add, am I correct in thinking that also, $\mathbb{E}(T) = \sum^\infty_{k=1}k\mathbb{P}(T = k)$? What can I expect from a Skype interview for PhD admissions? If $G$ is a group, show that $x^2ax=a^{-1}$ has a solution if and only if $a$ is a cube in $G$ How to disable captive portal detection? How to remove exclamation mark on Wi-Fi or signal icon in Lollipop? How long can I store a food in the pantry, refrigerator, or freezer? How do I know if a given food or ingredient I have is still good, or if I should discard it?  How can I best preserve a food or ingredient?     This broad question is intended as a "general reference" question to quickly answer many how long will food keep for? questions. Please feel free to edit this question to expand and clarify as needed. I thought this would be really simple, but it's presenting some difficulties. If I have std::string name = &quot;John&quot;; int age = 21;  How do I combine them to get a single string &quot;John21&quot;? inverted breve accent in math mode