Noyou still see the plane going off to infinity, no matter how far you are from it. To understand why this happens, imagine being placed above an infinite plane of constant charge. Note carefully the meaning of r in these equations: It is the distance from the charge element (qi,dl,dA,dV)(qi,dl,dA,dV) to the location of interest, P(x,y,z)P(x,y,z) (the point in space where you want to determine the field). (Please take note of the two different rs here; r is the distance from the differential ring of charge to the point P where we wish to determine the field, whereas rr is the distance from the center of the disk to the differential ring of charge.) Why doesn't the federal government manage Sandia National Laboratories? The first time you do this, youll have to tap Add Bank Account and enter your banks routing number and your account number. Find out about other ways to pay with Apple including Apple Cash and Apple Card. Similar Charges. Scroll down past the message and tap on the Apple Pay button. \label{5.14}\], Again, it can be shown (via a Taylor expansion) that when \(z \gg R\), this reduces to, \[\vec{E}(z) \approx \dfrac{1}{4 \pi \epsilon_0} \dfrac{\sigma \pi R^2}{z^2} \hat{k},\nonumber\]. \label{5.12}\]. An infinite loop is a loop that repeats indefinitely and does not terminate. First seen on February 13, 2015, Last updated on April 8, 2019 \end{align*}\], \[\vec{E}(z) = \dfrac{1}{4 \pi \epsilon_0} \dfrac{\lambda L}{z\sqrt{z^2 + \dfrac{L^2}{4}}} \, \hat{k}. Our mission is to improve educational access and learning for everyone. This is a very common strategy for calculating electric fields. When you purchase through links in our articles, we may earn a small commission. 53 0 obj
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1-800-MY-APPLE, or, Sales and iTunes media purchases: These include music, movies, TV shows, or eBooks. iOS 11.2or later. Want to cite, share, or modify this book? Shop online with a Specialist Reserve an in-store shopping session Not the answer you're looking for? Hardware purchases: Made on Apple.com or at an Apple Store. and you must attribute OpenStax. Turn the digital grown to adjust the dollar amount. which is the expression for a point charge Q=R2.Q=R2. - About Us 1. Also, we already performed the polar angle integral in writing down \(dA\). vegan) just to try it, does this inconvenience the caterers and staff? If you recall that \(\lambda L = q\) the total charge on the wire, we have retrieved the expression for the field of a point charge, as expected. We can do that the same way we did for the two point charges: by noticing that, \[\cos \, \theta = \dfrac{z}{r} = \dfrac{z}{(z^2 + x^2)^{1/2}}. This book uses the Have you checked your accounts purchase history to see what it was for : See your purchase history in the iTunes Store Apple Support? This represents almost 40% of the 8,800,000 square feet (820,000m2) of office space and facilities for research and development available in the city. Our first step is to define a charge density for a charge distribution along a line, across a surface, or within a volume, as shown in Figure \(\PageIndex{1}\). 1999-2023, Rice University. Instead, we will need to calculate each of the two components of the electric field with their own integral. Our first step is to define a charge density for a charge distribution along a line, across a surface, or within a volume, as shown in Figure 5.22. This leaves, \[ \begin{align*} \vec{E}(P) &= E_{1z}\hat{k} + E_{2z}\hat{k} \\[4pt] &= E_1 \, \cos \, \theta \hat{k} + E_2 \, \cos \, \theta \hat{k}. After the first transaction, most users will have Apple Cash set to automatically accept payments (thats the default), so you probably wont have much opportunity to cancel. \label{5.15} \end{align}\]. Finally, we integrate this differential field expression over the length of the wire (half of it, actually, as we explain below) to obtain the complete electric field expression. How to avoid running into infinite loops? Similar to Some banks or card issuers provide only initial authorization amounts to Wallet, which might be different from the final transaction amount. Why must a product of symmetric random variables be symmetric? Since the \(\sigma\) are equal and opposite, this means that in the region outside of the two planes, the electric fields cancel each other out to zero. Since this is a continuous charge distribution, we conceptually break the wire segment into differential pieces of length \(dl\), each of which carries a differential amount of charge. Creative Commons Attribution License Steve Jobs left additional marks on the campus, for example, banning employees' pets[2] and dramatically improving the cafeteria menu. There used to be a 3% fee when adding money to it via credit card, but Apple stopped allowing credit cards to be used for this purpose back in 2019. 3. Then, for a line charge, a surface charge, and a volume charge, the summation in Equation 5.4 becomes an integral and qiqi is replaced by dq=dldq=dl, dAdA, or dVdV, respectively: The integrals are generalizations of the expression for the field of a point charge. This is in contrast with a continuous charge distribution, which has at least one nonzero dimension. The Apple Campus is the former corporate headquarters of Apple Inc. from 1993 until 2017, when it was largely replaced by Apple Park, though it is still used by Apple as office and lab space. I recently wrote a simple console game in C++ and implemented a while loop that continued to ask the player if they wanted to play again until they had entered valid input. are not subject to the Creative Commons license and may not be reproduced without the prior and express written First seen on August 20, 2016, Last updated on January 24, 2022. Was Galileo expecting to see so many stars? \nonumber\]. CHKCARD APL* ITUNE 1 INFINITE LOOP; Similar Charges. \[ \begin{align*} \vec{E}(P) &= \vec{E}(z) \\[4pt] &= \dfrac{1}{4 \pi \epsilon_0} \int_0^R \dfrac{\sigma (2\pi r' dr')z}{(r'^2 + z^2)^{3/2}} \hat{k} \\[4pt] &= \dfrac{1}{4 \pi \epsilon_0} (2\pi \sigma z)\left(\dfrac{1}{z} - \dfrac{1}{\sqrt{R^2 + z^2}}\right) \hat{k} \end{align*}\], \[\vec{E}(z) = \dfrac{1}{4 \pi \epsilon_0} \left( 2 \pi \sigma - \dfrac{2 \pi \sigma z}{\sqrt{R^2 + z^2}}\right)\hat{k}. How much does a good two person tent cost? This will become even more intriguing in the case of an infinite plane. This site contains user submitted content, comments and opinions and is for informational purposes Just open Messages, go to a conversation, and tap the Apple Pay iMessage app like you would when sending money. All Rights Reserved. They implicitly include and assume the principle of superposition. chloe johnson peter buck wedding; le mal en elle fin du film In the Watch app, just tap Wallet & Apple Pay, tap your card, and tap the Transactions tab. In this case, both \(r\) and \(\theta\) change as we integrate outward to the end of the line charge, so those are the variables to get rid of. Subscribe to the Macworld Digital Magazine. Its essentially a special prepaid card with some financial services provided to Apple byGreen Dot Bank. So we'll have 2250 joules per coulomb plus 9000 joules per coulomb plus negative 6000 joules per coulomb. Employees refer to these buildings as IL1 to IL6 for Infinite Loop 16. Taking moneyoff your Apple Cash card is just a little more complicated. Legal. 721 Smith Rd. An interesting artifact of this infinite limit is that we have lost the usual \(1/r^2\) dependence that we are used to. From my point of view, anyone reading the code would have a faster grasp on the program logic. APL* ITUNES.COM/BILL,1 INFINITE LOOP 866-712-7753 CAUS Learn about the "Apl* Itunes.Com/Bill,1 Infinite Loop 866 712 7753 Caus" charge and why it appears on your credit card statement. Launching the CI/CD and R Collectives and community editing features for What are the differences between a pointer variable and a reference variable? You can also use Siri with a phrase like, Ask Jason for $15 for tacos.. © 2023 What's That Charge 4. \nonumber\]. citation tool such as, Authors: Samuel J. Ling, William Moebs, Jeff Sanny. If a charge distribution is continuous rather than discrete, we can generalize the definition of the electric field. First, you may need to head into the Settings menu and make sure Apple Cash is enabled. APL* ITUNES.COM/BILL 1 INFINITE LO 866-712-7753 US, APL*ITUNES.COM/BILL 1 INFINITE LOOP 866-7, APL* ITUNES.COM/BILL 1 INFINITE LOOP 866-712-7753 CA, APL* ITUNES.COM/BILL 1 INFINITE LOOP 866-712-7753 CAU, APL* ITUNES.COM/BILL,1 INFINITE LOOP 866-712-7753 CAUS, CHKCARDapl* itunes.com/bill 1 infinite loop, CHECKCARD apl* itunes.com/bill 1 infinite loop, POS Debit apl* itunes.com/bill 1 infinite loop, POS PUR apl* itunes.com/bill 1 infinite loop, POS PURCH apl* itunes.com/bill 1 infinite loop, POS PURCHASE apl* itunes.com/bill 1 infinite loop, POS REFUND apl* itunes.com/bill 1 infinite loop, PRE-AUTH apl* itunes.com/bill 1 infinite loop, PENDING apl* itunes.com/bill 1 infinite loop, Visa Check Card apl* itunes.com/bill 1 infinite loop MC, Misc. Note that because charge is quantized, there is no such thing as a truly continuous charge distribution. Youll be prompted to double-click the side button to confirm. As in the line charge example, the field above the center of this disk can be calculated by taking advantage of the symmetry of the charge distribution. provided; every potential issue may involve several factors not detailed in the conversations If you dont see an Apple Pay Cash card in Wallet, make sure its enabled in Settings. where our differential line element dl is dx, in this example, since we are integrating along a line of charge that lies on the x-axis. I had membership with them, but they continue billing even after the service was canceled. We also acknowledge previous National Science Foundation support under grant numbers 1246120, 1525057, and 1413739. How would the strategy used above change to calculate the electric field at a point a distance \(z\) above one end of the finite line segment? Enter an amount, tapTransfer, then confirm with Touch ID or Face ID. Rumors about the iPhone 15 Ultra, iPhone SE, and more. As before, we need to rewrite the unknown factors in the integrand in terms of the given quantities. %%EOF
How do I break out of nested loops in Java? CHKCARD APL*APPLE 1 INFINITE LOOP 866-712-7753 CA Similar Charges. The symmetry of the situation (our choice of the two identical differential pieces of charge) implies the horizontal (x)-components of the field cancel, so that the net field points in the \(z\)-direction. Launch Messages and then start a new message, or open an existing one. Learn about the "Apl*Apple 1 Infinite Loop 866 712 7753 Ca " charge and why it appears on your credit card statement. We can do that the same way we did for the two point charges: by noticing that. We can do that the same way we did for the two point charges: by noticing that, \[\cos \, \theta = \dfrac{z}{r} = \dfrac{z}{(z^2 + x^2)^{1/2}}. Never leave the terminating condition to be dependent on the user. Note carefully the meaning of \(r\) in these equations: It is the distance from the charge element (\(q_i, \, \lambda \, dl, \, \sigma \, dA, \, \rho \, dV\)) to the location of interest, \(P(x, y, z)\) (the point in space where you want to determine the field). They implicitly include and assume the principle of superposition. Declaring variables inside loops, good practice or bad practice? The LibreTexts libraries arePowered by NICE CXone Expertand are supported by the Department of Education Open Textbook Pilot Project, the UC Davis Office of the Provost, the UC Davis Library, the California State University Affordable Learning Solutions Program, and Merlot. Try saying Send Jane $14 for tacos or Apple Pay Greg $12 for tacos. Or to request money, maybe, Ask Glenda for $18 for tacos.. Unknown charges-Apple Cash Pmnt Sent 1 Infinite Loop I have several charges in my bank account that I don't recognize. Relying on someone (or the operating system during shutdown) to kill the process is not good form. Find the electric field a distance \(z\) above the midpoint of an infinite line of charge that carries a uniform line charge density \(\lambda\). By clicking Accept all cookies, you agree Stack Exchange can store cookies on your device and disclose information in accordance with our Cookie Policy. We simply divide the charge into infinitesimal pieces and treat each piece as a point charge. ), In principle, this is complete. Instead, we will need to calculate each of the two components of the electric field with their own integral. Does the plane look any different if you vary your altitude? a 201x1 . The charge 1 infinite Loop CA 95014 was first reported Feb 6, 2016. Find the electric field a distance \(z\) above the midpoint of a straight line segment of length \(L\) that carries a uniform line charge density \(\lambda\). Again, \[ \begin{align*} \cos \, \theta &= \dfrac{z}{r} \\[4pt] &= \dfrac{z}{(z^2 + x^2)^{1/2}}. . (The limits of integration are 0 to \(\frac{L}{2}\), not \(-\frac{L}{2}\) to \(+\frac{L}{2}\), because we have constructed the net field from two differential pieces of charge \(dq\). Heres what you need to know about setting up and using it. omissions and conduct of any third parties in connection with or related to your use of the site. If you are redistributing all or part of this book in a print format, 1. Our first step is to define a charge density for a charge distribution along a line, across a surface, or within a volume, as shown in Figure \(\PageIndex{1}\). Tap Cancel Subscription. it is not an infinite loop because you break out of it. In other words, the total electric potential at point P will just be the values of all of the potentials created by each charge added up. I found others that are being charged $700.00 at a time! Find the electric field everywhere resulting from two infinite planes with equal but opposite charge densities (Figure \(\PageIndex{5}\)). If you recall that \(\lambda L = q\) the total charge on the wire, we have retrieved the expression for the field of a point charge, as expected. %PDF-1.6
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Tap Pay. I have written about technology for my entire professional life - over 25 years. On Apple Watch, tap the Pay button at the bottom of a conversation, set the amount, and then swipe the big Pay button to the left to turn it into a Request button. - Personal Finance Club - Nyckel, machine learning API An interesting artifact of this infinite limit is that we have lost the usual \(1/r^2\) dependence that we are used to. Can you help? What are the basic rules and idioms for operator overloading? It is important to note that Equation 5.15 is because we are above the plane. for the electric field. We will no longer be able to take advantage of symmetry. Also, we already performed the polar angle integral in writing down \(dA\). 1 INFINITE LOOP, CA 95014 866-712-7753 1 INFINITE LOOP, CA 95014 866-712-7753 Learn about the "1 Infinite Loop, Ca 95014 866 712 7753" charge and why it appears on your credit card statement. The element is at a distance of r=z2+R2r=z2+R2 from P, the angle is cos=zz2+R2cos=zz2+R2, and therefore the electric field is, To solve surface charge problems, we break the surface into symmetrical differential strips that match the shape of the surface; here, well use rings, as shown in the figure. All Rights Reserved. Is anyone else experiencing unauthorized bank charges at random dates & amounts from "APL * APPLE 1 INFINITE LOOP 866-712-7753"?? This is exactly like the preceding example, except the limits of integration will be \(-\infty\) to \(+\infty\). The street address we recognize so well today didn't even exist until 1992, when Apple began building its Infinite Loop complex as a R&D facility. An infinite loop is a sequence of instructions in a computer program which loops endlessly, either due to the loop having no terminating condition, [4] having one that can never be met, or one that causes the loop to start over. 1 INFINITY LOOP CA 95014 Learn about the "1 Infinity Loop Ca 95014 " charge and why it appears on your credit card statement. Youll need to add a bank account. The \(\hat{i}\) is because in the figure, the field is pointing in the +x-direction. ), In principle, this is complete. The Max1873 can work with all of these batteries by setting the maximum cell voltage using resistors R5 and R6 (see schematic below). It is important to note that Equation \ref{5.15} is because we are above the plane. 2. In the limit LL, on the other hand, we get the field of an infinite straight wire, which is a straight wire whose length is much, much greater than either of its other dimensions, and also much, much greater than the distance at which the field is to be calculated: An interesting artifact of this infinite limit is that we have lost the usual 1/r21/r2 dependence that we are used to. How did StorageTek STC 4305 use backing HDDs? Does Apple still use 1 Infinite Loop? [3], The Apple Campus is located on the southeast corner of Interstate 280 and De Anza Boulevard, and occupies 32 acres (130,000m2)[4] in six buildings spread over four floors. Sep 1, 2015 12:59 PM in response to King_Penguin. However, dont confuse this with the meaning of r^r^; we are using it and the vector notation EE to write three integrals at once. We use the same procedure as for the charged wire. In the limit \(L \rightarrow \infty\) on the other hand, we get the field of an infinite straight wire, which is a straight wire whose length is much, much greater than either of its other dimensions, and also much, much greater than the distance at which the field is to be calculated: \[\vec{E}(z) = \dfrac{1}{4 \pi \epsilon_0} \dfrac{2\lambda}{z}\hat{k}. These charges are just showing up on my acct since Feb 15. We will check the expression we get to see if it meets this expectation. Also note that (d) some of the components of the total electric field cancel out, with the remainder resulting in a net electric field. Open Messages on your Apple Watch and either start a new message or open an existing one. The firefighters worked for hours until the following morning to extinguish the fire. Note that because charge is quantized, there is no such thing as a truly continuous charge distribution. where our differential line element dl is dx, in this example, since we are integrating along a line of charge that lies on the x-axis. As before, we need to rewrite the unknown factors in the integrand in terms of the given quantities. How would the strategy used above change to calculate the electric field at a point a distance \(z\) above one end of the finite line segment? \end{align*}\], As usual, symmetry simplified this problem, in this particular case resulting in a trivial integral. Go to Messages and tap on the payment, or find the payment in the Transaction History of your Apple Cash card in the Wallet app or Settings. We already know the electric field resulting from a single infinite plane, so we may use the principle of superposition to find the field from two. \label{infinite straight wire}\]. Select Apple Cash from the list of sharable features. No injuries were reported, but the forty-year-old building suffered $2 million of fire damage. Answer: A: 1 Infinite Loop is the address for Apples HQ. Last updated on January 12, 2017. 1 Infinite Loop, CA 95014 Learn about the "1 Infinite Loop, Ca 95014 " charge and why it appears on your credit card statement. Why is "using namespace std;" considered bad practice? This is exactly like the preceding example, except the limits of integration will be \(-\infty\) to \(+\infty\). Tap the Apps button and then the Apple Pay button. The street, in conjunction with Mariani Avenue, actually does form a circuit (or cycle) that can circulate indefinitely. This is just as easy as it is on your iPhone. If we integrated along the entire length, we would pick up an erroneous factor of 2. Accessibility StatementFor more information contact us atinfo@libretexts.orgor check out our status page at https://status.libretexts.org. The total field \(\vec{E}(P)\) is the vector sum of the fields from each of the two charge elements (call them \(\vec{E}_1\) and \(\vec{E}_2\), for now): \[ \begin{align*} \vec{E}(P) &= \vec{E}_1 + \vec{E}_2 \\[4pt] &= E_{1x}\hat{i} + E_{1z}\hat{k} + E_{2x} (-\hat{i}) + E_{2z}\hat{k}. any proposed solutions on the community forums. In the limit \(L \rightarrow \infty\) on the other hand, we get the field of an infinite straight wire, which is a straight wire whose length is much, much greater than either of its other dimensions, and also much, much greater than the distance at which the field is to be calculated: \[\vec{E}(z) = \dfrac{1}{4 \pi \epsilon_0} \dfrac{2\lambda}{z}\hat{k}. Learn about the "Apl* Itune 1 Infinite Loop" charge and why it appears on your credit card statement. \label{5.14}\], Again, it can be shown (via a Taylor expansion) that when \(z \gg R\), this reduces to, \[\vec{E}(z) \approx \dfrac{1}{4 \pi \epsilon_0} \dfrac{\sigma \pi R^2}{z^2} \hat{k},\nonumber\]. The point charge would be \(Q = \sigma ab\) where \(a\) and \(b\) are the sides of the rectangle but otherwise identical. An internet search is showing that number as a scam company, it's not Apple. Macworld is your best source for all things Apple. The point charge would be \(Q = \sigma ab\) where \(a\) and \(b\) are the sides of the rectangle but otherwise identical. Lets check this formally. Debit APL* ITUNES.COM/BILL,1 INFINITE LOOP 866-712-7753 CAUS, CHKCARD APL* ITUNES.COM/BILL,1 INFINITE LOOP 866-712-7753 CAUS. Browse other questions tagged, Where developers & technologists share private knowledge with coworkers, Reach developers & technologists worldwide. The vertical component of the electric field is extracted by multiplying by coscos, so. If we integrated along the entire length, we would pick up an erroneous factor of 2.
The fields of nonsymmetrical charge distributions have to be handled with multiple integrals and may need to be calculated numerically by a computer. Again, by symmetry, the horizontal components cancel and the field is entirely in the vertical (k^)(k^) direction. How would the above limit change with a uniformly charged rectangle instead of a disk? Once its all set up, youll be able to send money to friends right within Messages on your iPhone, iPad, or Apple Watch. However, in the region between the planes, the electric fields add, and we get. \end{align*}\], These components are also equal, so we have, \[ \begin{align*} \vec{E}(P) &= \dfrac{1}{4 \pi \epsilon_0}\int \dfrac{\lambda dl}{r^2} \, \cos \, \theta \hat{k} + \dfrac{1}{4 \pi \epsilon_0}\int \dfrac{\lambda dl}{r^2} \, \cos \, \theta \hat{k} \\[4pt] &= \dfrac{1}{4 \pi \epsilon_0}\int_0^{L/2} \dfrac{2\lambda dx}{r^2} \, \cos \, \theta \hat{k} \end{align*}\], where our differential line element dl is dx, in this example, since we are integrating along a line of charge that lies on the x-axis. The trick to using them is almost always in coming up with correct expressions for dl, dA, or dV, as the case may be, expressed in terms of r, and also expressing the charge density function appropriately. However, to actually calculate this integral, we need to eliminate all the variables that are not given. Noyou still see the plane going off to infinity, no matter how far you are from it. Press the + or buttons to adjust the amount, or tapShow Keypad to enter an exact amount. You should contact your card company and file a dispute with them and get your card cancelled and replaced. Then, we calculate the differential field created by two symmetrically placed pieces of the wire, using the symmetry of the setup to simplify the calculation (Figure \(\PageIndex{2}\)). Apple may provide or recommend responses as a possible solution based on the information \nonumber\]. However, in most practical cases, the total charge creating the field involves such a huge number of discrete charges that we can safely ignore the discrete nature of the charge and consider it to be continuous. Does the plane look any different if you vary your altitude? Again, \[ \begin{align*} \cos \, \theta &= \dfrac{z}{r} \\[4pt] &= \dfrac{z}{(z^2 + x^2)^{1/2}}. This is exactly the kind of approximation we make when we deal with a bucket of water as a continuous fluid, rather than a collection of \(\ce{H2O}\) molecules. Any info would be appreciated! You have to transfer at least $1 (though you can transfer your entire balance if you have less), you cant transfer more than $3,000 at a time, and you cant transfer more than $20,000 in a 7-day period. I looked at my purchases with iTunes etc and in my wallet for Apple Cash - no similar charges. The electric field would be zero in between, and have magnitude \(\dfrac{\sigma}{\epsilon_0}\) everywhere else. similar charges. Is a hot staple gun good enough for interior switch repair? University Physics II - Thermodynamics, Electricity, and Magnetism (OpenStax), { "5.01:_Prelude_to_Electric_Charges_and_Fields" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.
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MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()" }, 5.6: Calculating Electric Fields of Charge Distributions, [ "article:topic", "authorname:openstax", "Continuous Charge Distribution", "infinite plane", "infinite straight wire", "linear charge density", "surface charge density", "volume charge density", "license:ccby", "showtoc:no", "program:openstax", "licenseversion:40", "source@https://openstax.org/details/books/university-physics-volume-2" ], https://phys.libretexts.org/@app/auth/3/login?returnto=https%3A%2F%2Fphys.libretexts.org%2FBookshelves%2FUniversity_Physics%2FBook%253A_University_Physics_(OpenStax)%2FBook%253A_University_Physics_II_-_Thermodynamics_Electricity_and_Magnetism_(OpenStax)%2F05%253A_Electric_Charges_and_Fields%2F5.06%253A_Calculating_Electric_Fields_of_Charge_Distributions, \( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}}}\) \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash{#1}}} \)\(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\) \(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\)\(\newcommand{\AA}{\unicode[.8,0]{x212B}}\), Example \(\PageIndex{1}\): Electric Field of a Line Segment, Example \(\PageIndex{2}\): Electric Field of an Infinite Line of Charge, Example \(\PageIndex{3A}\): Electric Field due to a Ring of Charge, Example \(\PageIndex{3B}\): The Field of a Disk, Example \(\PageIndex{4}\): The Field of Two Infinite Planes, source@https://openstax.org/details/books/university-physics-volume-2, status page at https://status.libretexts.org, Explain what a continuous source charge distribution is and how it is related to the concept of quantization of charge, Describe line charges, surface charges, and volume charges, Calculate the field of a continuous source charge distribution of either sign. 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