OpenLLM-France/wikimedia huggingface dataset:
# Electrodynamics/Lienard-Wiechert Potentials

Suppose there is a point charge q traveling with location at all times given by $\mathbf {\gamma } (t)$. We will use the formulas developed in the previous section to find the potentials and the fields.
The retarded time is given by $t_{ret}=t-{\frac {||\mathbf {r} -\mathbf {\gamma } (t_{ret})||}{c}}$ (since, when we measure go back, the particle wasn't where it is now, it is at $\gamma (t_{ret})$) Note that at most one previous instance of the particle is generating the field at the point, since the particle is moving at subluminal speeds. Thus, $\mathbf {\eta } =\mathbf {r} -\mathbf {\gamma } (t_{ret})$ is a unique vector.
Thus, the scalar potential is
    $\phi (\mathbf {r} ,t)={\frac {1}{4\pi \epsilon _{0}}}\int {\frac {\rho (\mathbf {r} -\mathbf {r'} ,t_{ret})}{||\mathbf {\eta } ||}}dV={\frac {1}{4\pi \epsilon _{0}||\mathbf {\eta } ||}}\int \rho (\mathbf {r} -\mathbf {r'} ,t_{ret})dV$
You might think that equals
    ${\frac {q}{4\pi \epsilon _{0}||\mathbf {\eta } ||}}$
but that is wrong! The reason is very subtle: for the integral to be equal to the total charge, the charge distribution has to be taken at a specific time. However, we are obliged to evaluate the distribution at different times for each point! Thus, the charged particle is "smeared" out! Even though we are considering a point particle, the formula is still wrong, since the correction factor doesn't depend on geometric size!
Suppose the particle is a box of length a and is moving towards us. However, we will observe the particle to have length b, because the light that is simultaneously reaching our eyes from the front and back of the box originated from different times. In the time that light from the back of the box travels the extra distance b, the car traveled distance $b-a$, so
    ${\frac {b}{c}}={\frac {b-a}{v}}$, and $b={\frac {a}{1-v/c}}$; the box is stretched by factor ${\frac {1}{1-v/c}}$ that has nothing to do with the size of the object. This is not an effect of length contraction; this is rather more similar to the Doppler shift.
The correct formula for the scalar potential is
    $\phi =\left({\frac {1}{1-\mathbf {\hat {\eta }} \cdot \mathbf {w} '(t_{ret})/c}}\right){\frac {q}{4\pi \epsilon _{0}||\mathbf {\eta } ||}}$
where $\mathbf {w} '(t_{ret})$ is the particle velocity at time $t_{ret}$
The current density is $\rho \mathbf {v}$, and by similar arguments,
    $\mathbf {A} =\left({\frac {1}{1-\mathbf {\hat {\eta }} \cdot \mathbf {w} '(t_{ret})/c}}\right){\frac {\mu _{0}q\mathbf {v} }{4\pi ||\mathbf {\eta } ||}}={\frac {\mathbf {v} }{c}}\phi$
These are the Lienard-Wiechert Potentials for a moving charge. The correction factors are for the components of velocity pointing to the point we are measuring the potentials at.
# Electrodynamics/Magnetic Fields/Solenoids

A solenoid is a coil of wire with a current flowing through it.

## Vertical Wire Array

Let us first consider an array of infinite vertical wires passing through a plane. This can be viewed as a very tall, narrow solenoid where the passing of the wires over the top and bottom can be neglected due to the distance from the plane.
We will find the magnetic field in this plane. Now, recall that the magnetic field around a single infinite, straight, wire is circular and the magnetic field strength at a point is given by:
       $B={\frac {\mu I}{2\pi r}}$
where:
* B is the magnetic field strength, in Tesla
* μ is the permeability of the medium between the wires, in T m A$^{-1}$
* I is the current flowing in the wire, in Ampères
* r is the perpendicular distance from the wire to the point, in metres
Also recall that the total magnetic field at a point can be found by summing individual magnetic fields from each wire. However, we cannot merely add the magnetic field strength from the wires, because the magnetic field has direction as well as strength, and therefore can reinforce or cancel out the field from another wire, depending on relative current directions. Due to this, we much first work out the vector contributions from each wire and sum these instead.
Now, we know that the magnetic field is circular. The vector field xi-yj is circular in the plane about (0,0), but it does not have constant magnitude. The magnitude of this vector field is given by:
       ${\sqrt {x^{2}+y^{2}}}$
Thus the vector field that is of unit magnitude everywhere and circular direction is:
       ${\frac {x}{\sqrt {x^{2}+y^{2}}}}\mathbf {i} -{\frac {y}{\sqrt {x^{2}+y^{2}}}}\mathbf {j}$
Now, we can displace this vector field from being centred on the origin to being centred on a point (x$_i$,y$_i$):
       ${\frac {x-x_{i}}{\sqrt {(x-x_{i})^{2}+(y-y_{i})^{2}}}}\mathbf {i} -{\frac {y-y_{i}}{\sqrt {(x-x_{i})^{2}+(y-y_{i})^{2}}}}\mathbf {j}$
In order to scale the field to match the magnetic field, we must divide again by the distance from the point to the wire (ignoring the factor of μ/2π). However, we do include a current term to allow for the direction of the current:
       ${\frac {x-x_{i}}{(x-x_{i})^{2}+(y-y_{i})^{2}}}I\mathbf {i} -{\frac {y-y_{i}}{(x-x_{i})^{2}+(y-y_{i})^{2}}}I\mathbf {j}$
Now the vector field from all n wires, each at a point (x$_i$,y$_i$), is, by superposition:
       $I\sum _{i=1}^{n}{\frac {x-x_{i}}{(x-x_{i})^{2}+(y-y_{i})^{2}}}\mathbf {i} -I\sum _{i=1}^{n}{\frac {y-y_{i}}{(x-x_{i})^{2}+(y-y_{i})^{2}}}\mathbf {j}$
Recall that the magnitude of a vector is given by:
       $|a\mathbf {i} +b\mathbf {j} |={\sqrt {a^{2}+b^{2}}}$
Therefore the magnitude of the result vector at a point is:
       ${\sqrt {\left(I\sum _{i=1}^{n}{\frac {x-x_{i}}{(x-x_{i})^{2}+(y-y_{i})^{2}}}\right)^{2}-\left(I\sum _{i=1}^{n}{\frac {y-y_{i}}{(x-x_{i})^{2}+(y-y_{i})^{2}}}\right)^{2}}}$
Below is a plot of 12 wires, carrying unit current, showing the magnitude of the magnetic field. Bear in mind each wire is modelled as infinitely thin:
# Electrodynamics/Magnetic Fields
## Electric Currents

In an electric field, especially in a conductor, charged particles will move according to the electromotive force applied by the electric field. In a practical sense, the charged particles in question are the free electrons in the conductor. Electrons are attracted to the areas of positive charge, and are repelled from the area of negative charge.
The mass-flow of electrons through a conductor is known as electric current.

### Units of Current

The flow of electrons through a conductor is measured in Amperes. The electric potential that causes electrons to flow is measured in Volts.

## Magnets

Since ancient times, people have known about special rocks and materials that display a certain attractive and repulsive force on other such rocks. Termed "magnets", the force between them operates on a similar principle to the electric force that we have studied so far.
All magnets have two sides or poles, dubbed "North" and "South". Like positive and negative charges, like poles repel and opposite poles attract. The magnetic force works over distance, with the effect of the magnet decreasing over distance.

## Induction

Electric currents, or moving electric fields produce a magnetic force.

## Magnetic Fields

Like an electric field, there is a magnetic field that extends everywhere. the strength of the magnetic field is dependent on the location of magnets in the field. It is a vector field, so every point has both a strength and a direction.
We will discuss the mathematical determination of the magnetic field starting in the next chapter when we discuss the Biot-Savart Law.

### Field of a Current

the magnetic lines of forces are wrongly shown in the figure as the current is traveling downwards the magnetic lines of force will pop out of the page from the left of the wire and go into the page on the right side

### Field of a Magnet
## Current model of a Magnet
## Solenoids

Solenoids
# Electrodynamics/Magnetic Potential
## Gauss' Law of Magnetostatics

Gauss's Law for electrostatics states that
    $\nabla \cdot \mathbf {E} ={\frac {\rho }{\epsilon _{0}}}$
This tells us that the source of electric fields are charges. However, experiments show that there are no corresponding "charges"(monopoles) for magnetic field. The magnetic field do not have a source, and so always forms closed loops.
Gauss' law of magnetostatics is an expression of the fact. It can be written as such:
    $\nabla \cdot \mathbf {B} =0$

## Vector Potential

Since B is divergence-free, B must be the curl of some vector A. This vector is called the vector potential, the direct analog of the electric potential, also known as the scalar potential.
The Biot-Savart Law can be difficult to compute directly, but if we know the magnetic potential field, we can find the magnetic field easily:
    $\mathbf {B} =\nabla \times \mathbf {A}$

## Calculation of Vector Potential.

The vector potential is given by
    $\mathbf {A} (\mathbf {r} )=\int {\frac {\mathbf {j} (\mathbf {r'} )}{|\mathbf {r} -\mathbf {r'} |}}dV$
# ETD Guide/Technical Issues/Packaged solutions

Since 1995, there have been plans to share work developed in connection with ETDs so as to help others. The first such effort was funded by the Southeastern Universities Research Association (SURA), to spread the work around the Southeast of the USA. Virginia Tech acted as the agent for this effort, creating software, documentation, training materials, and other resources. In particular, it became clear that software was needed to support student submission, staff checking, library processing, and support for access. The Virginia Tech resources were packaged in connection with these efforts and the follow-on work funded by the USA’s Department of Education. These were made available starting in 1996 through local and NDLTD sites, and updated regularly since.
The following subsections give details of the Virginia Tech solutions, as well as extensions to it, and alternatives. NDLTD offers to assist such sharing by providing a clearinghouse for whatever seems appropriate and useful to share.
Next Section: DiTeD and DIENST
# ETD Guide/Technical Issues/Page Description Languages

Evolution of Networks and the World Wide Web
The evolution of networks and the World Wide Web have profoundly affected the content and quality of communications. The complexity and visual content of documents is no longer limited by the artistic skills of the designer. Itranets and Web sites are being tapped into for creative content that is much more complex than could have been imagined. As creative expression expands to new levels, the quality of the printed output must also rise to the challenge.
The Internet and Printing Workflow Process
The Internet has changed not only the dynamics of the creative process but the entire printing workflow process. The Internet is used to transmit information electronically while CD-ROMs and servers are used for storing and accessing data. One often finds difficulty in predicting what will be printed because documents can come from many sources. And it’s equally difficult to predict where they will be printed, because documents can be distributed around the world electronically and printed locally. The printing workflow has evolved from creating, printing, copying, and distributing hard-copy documents to creating, electronically publishing, and printing documents on demand. It was clearly time to advance the imaging standard.
Adobe Postscript
With the introduction of PostScript in 1985, Adobe Systems Incorporated sparked a revolution in how we communicate on the printed page. Since its introduction, Adobe PostScript has become the printing and imaging technology of choice for corporations, publishers, and government agencies throughout the world. In fact, 75 percent of commercial publications are printed on Adobe PostScript devices, including black-and white printers, color printers, imagesetters, platesetters, and direct digital printing systems. Adobe PostScript is also the display imaging system in some of the most advanced workstations on the market today.
Adobe PostScript 3 takes the PostScript standard beyond a page description language into a fully optimized printing system that addresses the broad range of new requirements in today’s increasingly complex and distributed printing environments.
Adobe Postscript and PDF
By fully integrating Portable Document Format (PDF) - an open file format that preserves the visual fidelity of documents across applications and platforms - into Adobe PostScript 3, documents can be delivered electronically and printed directly. A PDF file delivers the single "digital master" for use in electronic, printed, and mixed workflows, ensuring the highest fidelity across all media.
Adobe Postscript Advanced Features
With Adobe PostScript 3, Adobe delivers advanced features for the new digital document. Today, document creators draw on a variety of sources and increasingly rely on color to convey their messages. And tomorrow, these documents will be delivered and printed on a virtually unlimited range of devices.
Next Section: Markup Languages
# ETD Guide/Technical Issues/Production of ETDs

Electronic publishing technology and infrastructure is needed to support the production and archiving of ETDs. Section 4.2.1 provides an overview of this matter. The next two sections explain key issues related to the two main approaches: PDF and SGML/XML. Remaining sections give further information of specific matters such as metadata and post processing.
Next Section: Overview: hardware, software, multimedia, scripts, encoding, document representations/conversions
# ETD Guide/Technical Issues/Networking

Networking and ETDs
With the spread of the Internet and the WWW, and the emergence of local area networks as well as wide area networks (LANs and WANs), network facilities have enormously expanded in many of the educational institutions of the world. To support the needs for access, and the related processes that deal with making content accessible, many universities have made networked computers available to their graduate students, as well as to faculty, staff, and undergraduate students. The ETD initiative can build on those investments, employing them to support submission and downloading of ETDs. By focusing on networked access, there can be considerable savings that result from elimination of manual handling and physical distribution. It is recommended that, except for ETDs that have enormous amounts (e.g., gigabytes) of multimedia content, authors, as well as university staff, avoid procedures that require transfer of content using diskettes, CDs, or other physical media.
Network Traffic and Hardware
Universities should consider the amount of traffic on their networks, making sure that networking hardware (Internet connection, routers, and cable plants) accommodates well the demand for uploading and downloading ETDs). This accommodation generally will not be a problem if adequate support for email, rapid access to WWW, and other types of usage is provided.
Software
Regarding software for accessing ETDs, there is not much of a special nature that is required. Web browsers, support for Java applets, and multimedia presentation tools are typically sufficient. Special aids may be needed for PDF, that Adobe provides for free at Adobe at www.adobe.com, or SGML/XML (becoming more widely available). The real need for special software is to help manage the ETD submission process, handle local workflow, make ETDs accessible, and facilitate search. NDLTD and its various parts have prepared software to help with all of these.
Next Section: Seamless access: Open Archives Initiative, federated search
# ETD Guide/Technical Issues/Naming Standards

This topic is discussed in Naming standards: file names; unique Ids. The focus there is on naming of files and on unique identifiers. Here we consider those matters briefly, but also discuss URNs and OAI naming.
At Virginia Tech, naming of the parts of an ETD is left to authors. Many have a single document, called etd.pdf, but there are many other selections. The entire ETD is referred to by way of a summary page. This has an ID like:
etd-12598-10640 or (in earlier cases) etd-5941513972900
These two correspond to full URLs, respectively:
* http://scholar.lib.vt.edu/theses/public/etd-12598-10640/etd-title.html
* http://scholar.lib.vt.edu/theses/public/etd-5941513972900/etdtitle.html
Other but similar schemes are in use elsewhere - recall Naming standards: file names; unique Ids.
The key point is to have an ID for each work, and a way to resolve that to the actual document. In some cases, a URN is given, such as a handle or PURL, which in turn is resolved to a URL. (See Identifying: URN, PURL, DOI) That allows users to remember the URN, and be assured that over time, as documents are moved about, there still be automatic linking from the URN to the designated document.
IDs as discussed above also are important with regard to OAI. Assuming that, as is required, each archive has a unique identifier, then as long as each record in the archive, as required, has a unique internal ID, then the combination of the two will uniquely determine a record in an archive.
Next Section: Encryption; Watermarking
# Azerbaijani/Contents (Latin)/Lesson Three - Introductions
## Introductions

| 1. | 1. |
| This is Eric. He is my friend. | Bu Erikdir. O mənim dostumdur. |
| This is my father. His name is Fuad. | Bu mənim atamdır. Onun adı Fuaddır. |
| This is my mother. Her name is Nargiz. | Bu mənim anamdır. Onun adı Nərgizdir. |
| This is my sister. Her name is Fidan. | Bu mənim bacımdır. Onun adı Fidandır. |
| This is my brother. His name is Samir. | Bu mənim qardaşımdır. Onun adı Samirdir. |
| This is my director. His name is Vahid. | Bu mənim direktorumdur. Onun adı Vahiddir. |
| Or Vahid muallim (teacher) is my director. | Or Vahid müəllim mənim direktorumdur. |
| 2. | 2. |
| A: Please get acquainted, this is Vahid muallim (teacher). He is the director of our school. | A: Tanış olun, Vahid müəllim. O bizim məktəb direktorudur. |
| B: Hello, Vahid muallim. You are welcome. | B: Salam, Vahid müəllim, xoş gəlmisiniz. |
| V: Thank you so much. | V: Çox sağ olun. |
# Azerbaijani/Contents (Latin)/Lesson Four - Politely Speaking
### Politely Speaking

| 1. | 1. |
| Thank you very much. | Çox sağ olun. |
| Here you go. | Buyurun. |
| Please | Zəhmət olmasa. |
| Sorry or Excuse me. | Bağışlayın. |
| Excuse me. | Üzr istəyirəm |
| 2. | 2. |
| A: Please give me water. | A: Zəhmət olmasa, mənə su verin. |
| B: Here you go. | B: Buyurun. |
| A: Thank you so much. | A: Çox sağ olun. |
| 3. | 3. |
| Please shut the door. | Zəhmət olmasa, qapını ört. |
| Please turn off the light. | Zəhmət olmasa, işığı söndür. |
| 4. | 4. |
| A: Excuse me, where is the bathroom? | A: Bağışlayın, tualet haradadır? |
| B: Over there | B: Orada. |
| A: Thank you very much. | A: Çox sağ olun. |
| 5. | 5. |
| A: Sorry or Excuse me, how can I go to the post office? | A: Üzr istəyirəm, poçta necə getmək olar? |
| B: Go straight. | B: Düz gedin. |
| A: Thank you so much. | A: Çox sağ olun. |
| B: You are welcome. | B: Buyurun. |
# Azerbaijani/Contents (Latin)/Lesson One - Greetings and responding to a greeting
## Greetings and responding to a greeting

| English | Azerbaijani |
| Dialogue-1 | Dialoq-1 |
| A: – Hello! | A: – Salam! |
| B: – Hello | B: – Salam! |
| A: – How are you? | A: – Necəsiniz? (formal) |
| B: – I am fine, thank you very much. How are you? | B: – Yaxşıyam, çox sağ olun. Siz necəsiniz? |
| A: – I am fine too. Thank you. | A: – Mən də yaxşıyam. Sağ olun. |
| Dialogue- 2 | Dialoq- 2 |
| A: – Hi! How are you? | A: – Salam! Necəsən? |
| B: – I am fine, thank you. How are you? | B: – Yaxşıyam, sağ ol. Sən necəsən? |
| A: – I am fine too. How are things? | A: – Mən də yaxşıyam. İşlərin necədir? |
| B: – Not bad. How is everything with you? | B: – Pis deyil. Sənin işlərin necədir? |
| A: – Fine. | A: – Yaxşıdır. |
| Dialogue – 3 | Dialoq –3 |
| A: – Hello! How are things? | A: – Salam! Nə var, nə yox? |
| B: – Hello! Everything is OK. How are things in your life? | B: – Hər şey yaxşıdır. Sizdə nə var, nə yox? |
| A: – Thanks God, everything is fine. (lit. all are in good health) | A: – Şükür Allaha, salamatçılıqdır. |
| Dialogue – 4 | Dialoq – 4 |
| A: – Hello! Are you OK? | A: – Salam! Yaxşısanmı? |
| B: – Yes, I am fine. And you? | B: – Hə, yaxşıyam. Bəs sən? |
| A: – I am fine too. | A: – Mən də yaxşıyam. |
| Dialogue – 5 | Dialoq – 5 |
| A: – Hello, how are you? | A: – Salam, necəsən? |
| B: – Hi, very bad. | B: – Salam, çox pis. |
| A: – Why, what happened? | A: – Niyə, nə olub? |
| B: – It is very hot. | B: – Çox istidir. |

## Other expressions used for greeting

| Good morning | Sabahınız xeyir. |
| Good day | Gün aydın. |
| Good evening | Axşamınız xeyir. |
| Hello | Salaməleyküm. |
| Welcome | Xoş gəlmisiniz. |
# Azerbaijani/Contents (Latin)/Lesson Two - Getting Acquainted
## Getting Acquainted

| 1. | 1. |
| A: Hello, my name is Ryan. I am an American. | A: Salam, mənim adım Rayndır. Mən Amerikalıyam. |
| B: Hello, my name is Aysel. I am an Azerbaijani. | B: Salam, mənim adım Ayseldir. Mən Azərbaycanlıyam. |
| 2. | 2. |
| What is thy name? | Sənin adın nədir? |
| What is your name? | Sizin adınız nədir? (formal) |
| Where art thou from? | Sən haralısan? |
| Where are you from? | Siz haralısınız? (formal) |
| What art thou? (Profession) | Sən nəçisən? |
| What are you? (Profession) | Siz nəçisiniz? (formal) |
| 3. | 3. |
| A: Hello, what is thy name? | A: Salam, sənin adın nədir? |
| B: Hello, my name is Paul. | B: Salam, mənim adım Poldur. |
| A: How old art thou? | A: Sənin neçə yaşın var? |
| B: I am 22. | B: Mənim iyirmi iki (22) yaşım var. |
| A: Where art thou from? | A: Sən haradansan? |
| B: I am from America. I am an American. | B: Mən Amerikadanam. Mən Amerikalıyam. |
| A: What art thou? | A: Sən nəçisən? |
| B: I am a Peace Corps Volunteer. | B: Mən Sülh Korpusu Könüllüsüyəm. |
| A: What art thou doing? | A: Sən nə edirsən? |
| B: I am teaching English. | B: Mən ingilis dili öyrədirəm. |
| 4. | 4. |
| A: Hello, my name is Sandy. | A: Salam, mənim adım Səndidir. |
| B: Hi, my name is Rauf. | B: Salam, mənim adım Raufdur. |
| A: Nice to meet thee. | A: Çox şadam. |
| B: Nice to meet thee too. | B: Mən də çox şadam. |
# Azerbaijani/Contents (Latin)/Lesson Five - Saying Goodbye
## Saying Good-bye

| 1. | 1. |
| A: Good- bye | A: Sağ olun. |
| B: Good-bye, you are welcome. | B: Sağ olun. Xoş gəldiniz. |
| 2. | 2. |
| A: Good – bye | A: Salamat qalın. |
| B: Good luck. | B: Yaxşı yol. |
| 3. | 3. |
| A: Good- bye. So long. | A: Sağ olun. Hələlik. |
| B: So long. Good –bye. | B: Hələlik. Sağ olun. |
| 4. | 4. |
| A: Good night. | A: Gecəniz xeyrə qalsın. |
| B: Good night. | B: Xeyrə qarşı. |
| 5. | 5. |
| A: Good – bye. See you later. | A: Sağ olun, görüşərik. |
| B: See you later. | B: Görüşərik. |

### External Links

* Saying Goodbye (with video)