Math 'N IT

Problem Solving - Interactive code!

2020-07-13T09:19:00.001-07:00

So here I got this problem to solve:

Write an INTERACTIVE python program that will print the average value of the elements of a list.

Writing these programs is easy. Just make logic and code it out. Debugging is also a whole lot easier. But interactive programs are really a pain! For that case we will have to:

Take input from the user,
Use a function to run the code
Define when to stop,
Make the program suitable for input mistakes. (it's the toughest thing to do

Let's see what I have to do for solving this problem.

First I have to define a function for calculating the average.

def average(li):
x = sum(li) / len(li)
print(x)

Then I have to make an input system to start and stop counting. My logic is simple. If the input is given as an integer, it'll append that number to the list. And if some string or other values than integer comes, the program will take the list to the function to calculate the average. I used simple try-expect commands.

list1 = []
try:
while True:
list1.append(int(input("Enter the numbers:")))

except:
print(list1)

Lastly, I have to put list1 in the average() function.

But if someone presses enter at the very beginning of the code he will have a ZeroDivisionError.

So, I have to put another try-expect command.

try:
while True:
average(list1)
break
except:
print("you should add some numbers, then other characters in order to get an average of those numbers")

Now it all came together. Let's have a look to the full code.

Image by Johnson Martin from Pixabay

Re-Learning Python - A Journey to Remember!

2020-06-28T14:34:00.003-07:00

I haven't coded in python for a long time, then when I came back, I just realized that I forgot almost everything in python! So I decided to learn things again, from the very beginning (the beginning is the end and end is the beginning!). But this time I used the CLASSIC method. Yes, I learned from the books.

I love to introduce myself as a "self-taught" programmer, which means I have no academic experience in this sector. Learned this whole code thing from websites like SoloLearn and KhanAcademy. But this time I wanted something really different, so I grabbed some coding books, which are not even written in English.

Yes, I used these books to re-learn everything, and had a great journey! These are actually some of the most popular programming books written in Bengali. If you are familiar with the Bangla language, you can use these books to start your programming journey. Click here to buy these books.

While studying the "while" loop, stopped at an example, a simple program to print the multiplication table of a certain number. The given code was very straightforward,

n = input("Please enter a positive integer: ")
n = int(n)

m = 1
while m <= 10:
print(n, "X", m, "=", n*m)
m += 1

Nice code indeed. But I wanted to go to a higher level. When I was young, I used to own a pencil box that had 10 multiplication tables printed on the backside. That info helped me do a lot of cheating on the tests. So, from that gratitude, I wanted to print that whole thing. First I wanted to think about the problem, but then I realized that my brain is so small! So I wrote it down to deal with it.

Problem:

I need some output like:

n X m

1 X 1

1 X 2

1 X 3

1 X 9

1 X 10

2 X 1

2 X 2

2 X 3

10 X 9

10 X 10

Attempt 1:

So It's easy! I need to make a loop and increase the m and n value from time to time. I was obvious as hell, so I coded fast like those fancy hackers in movies,

m = 1
n = 1
while m <= 10:
if n <= 10:
print(n, "X", m, "=", n*m)
m += 1
n += 1

But! Once some coding legend(!) said, "If you are obvious before even running your code, I'm pretty sure your code is wrong." Yes. Thad did print something, but that was like this.

OUTPUT:

1 X 1 = 1

2 X 2 = 4

3 X 3 = 9

10 X 10 = 100

So I have a look at the code and saw the problem. Just change some blocks and done!

IS IT?

Attempt 2:

m = 1
n = 1
while m <= 10:
print(n, "X", m, "=", n*m)
m += 1
if n <= 10:
n += 1

Yes, legit speaking, it was my second attempt! How stupid am I!

Yes, the output was the same. So this time I looked at the code a bit more closely. And felt like, I found the real solution to my problem.

The code was not that simple like my thoughts! Here the value of m is increasing in every iteration. When this value will reach 11, we have to reassign the value of m to 1 and increase the value of n by one each time m reaches 11. A bit complex but it works.

Attempt 3:

n = 1
m = 1
while m <= 11:
print(n, "X" , m , "=", n*m)
m += 1
if m == 11:
m = 1
n += 1

Well, is it the solution? Can this code print the thing? NO!

This code works good, but doesn't stop! We have to stop it.

FINAL CODE:

n = 1
m = 1
while m <= 11:
print(n, "X" , m , "=", n*m)
m += 1
if m == 11:
m = 1
n += 1
if n == 11:
break

So that is the final solution of the simplest problem, my dumb brain took 3 attempts to just solve such an easy problem!

I hope you had fun reading the article. A follow or comment will be much appreciated!

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Introduction and setting things up - Python 3.x Tutorial

2020-06-06T07:57:00.000-07:00

Python is one of the most popular programming languages in the world. And the best thing about it is, it's extremely easy to learn! So for the newbies in programming, it's the most appealing language to learn. This tutorial is designed for absolute newcomers in the programming world.

Python is easy to learn but it is a high-level programming language even with object-oriented supports. So it's nothing different than other languages. Once you learn Python properly, other languages are as easy as hell.

Installing Python in Computer

If you use MacOS or Linux, you can skip this part. Python is pre-installed in these operating systems. But if you use Windows you have to download python and install it.

Once you install Python, it'll also install PIP on your PC. What's PIP? It's like a robot. When you are missing something, you can download that using PIP. We'll talk about pip later.

If you are learning through an Android phone, you can still use Python. Just download this app name Pydroid and you are good to go. (Download: Android)

Unfortunately, in IOS there is no good app for free. If you are ok to pay $9.99 you can download Pythonista 3. We recommend not to pay money for these.

Anyway in this site you can do programming in on-page interpreters. So don't bother downloading things now.

First Step in Programming

We programmers have a tradition of starting a new language. Let's follow that!

The tradition is, our first program should be a set of codes that will print "Hello, World!" on the screen.

Press the play button (that triangle right after the colorful icon) to run the code. You can see that on the right there is something written. Yes, you just wrote a line of code that prints the writing "Hello, World!". (if you use a phone, its recommended to rotate the phone to landscape mode for the best view)

So, what on earth happened here? Ok. first, there is the print() statement which orders the computer to print something. And that something is your first words, "Hello, World!". So have you ever wondered, why we used the quotes("")? That transforms the Hello, World text to a string! The string is a data type in python, which actually lets us enter text to a program. Anyway, congratulations! You mad your first program in python!

Ok. this is not actually a tutorial post, it's more like an introduction post. So let's not talk much about these. Wanna have some fun? Delete all the codes and write import this in the interpreter. Then click run. TADA!

This beautiful(?) poem is the main basics of python programmers. We'll learn to apply them all along with this tutorial.

Need better places to learn?

We know that we are not the best. But there are the best things, the best resources on the internet to learn python. Try them out, you'll love them.

NEXT

How to make Free Space in disk on Windows

2020-05-26T10:08:00.000-07:00

Free Space in the disk is a space which is at the out side of the partition from where it's created. It's used for various reasons such as for making a new partition(New Volume), installing an another operating system(Dual booting) etc. Free space of a hard drive can be accessed out side form the operating system. Free space is created by shrinking a volume or by deleting a whole volume.

So let's learn how to make a free space in the hard drive by shrinking or deleting a volume on Windows.

1st of 2 methods: Make free space by shrinking.

1.Right click on the Windows button and select Disk Managment.

2.Then a window like this will apear.

3.There right click on the volume from where you want to srrink the storage then select Shrink Volume

4.Then a loading window and after that Srink window like this will appear.

5.Then on the Srink window enter the amount of space in MB(Mega Byte) you want to srink. Here it's 4096MB(4GB).

6.Then click Shrink.

7.Then a Free space will created like this. The free space is denoted by green color.

2nd of 2 methods: make free space by deleting.

3.There right click on one of the volume that you want to make free space then select Delete Volume.
Note:Firstly remove all data from the drive and save it to other drive otherwise you will lost then.

4.Then a window with a worning will appear. If you have removed all the data to another drive then select Yes otherwise if you didn't removed your data you'll lost them.

5.Then you'll get a free storage. Here it's 100GB(Giga Byte) as our volume was of 100GB(Giga Byte). The free space is denoted by green color.

Hope that you've gotten a free space in your hard drive. If you've any question you can comment below or can use our Ask Question page.

How to create New Volume from existing volume on Windows

2020-05-24T03:01:00.001-07:00

On the This PC or My Computer of our computer(on Windows) we get a ceatain number of Volume. You might need more Volume for any particular work. You can do so on the Disk Managment utility of Windows operating system by srinking space from an existing volume.

So let's learn how to create a New Volume on Windows.

1.Right click on the Windows button and select Disk Managment.

2.Then a window like this will apear.

3.There right click on the volume from where you want to srrink the storage then select Srink Volume

4.Then a loading window and after that Srink window like this will appear.

5.Then on the Srink window enter the amount of space in MB(Mega Byte) you want to srink. Here it's 102400MB(100GB).

6.Then click Shrink.

7.Then a Free space will created like this. The free space is denoted by green color.

8.Then right click on the free space and select New Simple Volume....

9.Then a wizard Window like this will appear there click Next.

10.Then enter the size of the volume in MB(Mega Byte) and click Next. Here it's 102400MB(100GB).

Note: In the fill of Simple volume size in MB: the given amount is the totle free space detected in the drive if you want to use the whole then just click Next.

11.Then on the next window select the volume letter you want. Here it's M.

12.Then you can change the other settings and click next.

Note:If you select the fill Do not assign a drive lettet or drive path then the volume won't be visible on This PC or My Computer.

13.Then on the next window select the File system:. The given is NTFS it's used on windows.

14.Then on the same window select the Allocation unit size:. Keep it Default if you don't know about it.

15.Then on the same window enter the Volume label then click Next. Here it's New Volume.

16.Then on the next window check all the selected settings in the You selected the following settings: fill and click Finish.

17.Then a New volume like this will created. You can also check it in This PC or in My Computer(on the 2nd picture).

Hope that you've created New Volume and enjoing it. If you've any question you can comment below or can use our Ask Question page.

How to add two existing volume and make a single volume on Windows.

2020-05-22T23:58:00.001-07:00

On the This PC or My Computer of our computer(on Windows) we get a ceatain number of Volume that contains alimited storage. THis limited storage might not be sufficent for any particular work(such as for any big project). In such situation you can add two existing volume and make it a single one that will contain the total storage of the two volume.

So let's learn how to to add two existing volume and male a single volume on Windows.

1.Right click on the Windows button and select Disk Managment.

2.Then a window like this will apear.

3.There right click on one of the either volume that you want to add then select Delete Volume.

Note:Firstly remove all data from one of the either drive and to the other drive. You just need to delete one drive so you can save all yur data into the other one.

4.Then a window with a worning will appear. If you have removed all the data to another drive then select Yes otherwise if you didn't removed your data you'll lost them.

5.Then you'll get a free storage. Here it's 100GB(Giga Byte) as our volume was of 100GB(Giga Byte). The free space is denoted by green color.

6.Then right click on the second volume that you want to add and select Extend Volume....

Note:This one isn't deleted space it's a Healthy partition.

7.Then a wizard window will appear there click Next.

8.On the next window enter the amount of space that you want to add with the partition in the fill Select the amount of space in MB: then click Next.

Note: In the fill of Select the amount of space in MB: the given amount is the totle free space detected in the drive if you want to use the whole then just click Next.

9.Then on the next window check all the selected settings in the You selected the following settings: fill and click Finish.

10.Then you will get the Volume with the total storage of the two volume. Here it's the New Volume(F:) it has benn increased to 208.85GB but before it was of 108GB.

Hope that you've made your volume and enjoing it. If you've any question you can comment below or can use our Ask Question page.

How to make a tree program to refresh all drives

2020-05-19T03:32:00.001-07:00

How to make a tree program to refresh all drives

tree is a command that lists all the directory of the specified path. It produce a depth-indented listings of files. That also do the work of refreshing the system. By using Batch Scripting it's possible to make a file that can tree all the directory of the system. So if we tree all the drives of our system it would refreshes all the drives. This can help you to refresh a your system more efficiently than refreshing it manually by clicking "Refresh option of the right button menu or by pressing the F5 key.

So lets make a tre program.

1.Right Click on desktop and click on New then select Text Document.

2.Then open the file with Notepad or with other text editor that you prefer and write down the Batch script given bellow.

@Echo off

cd\

tree

3. Then at the top left side click on File and select Save As.

4. Then set the file name as tree.bat or whatever you want but keep in mind that the name must be terminated by a .bat extension.

5. Then click on the Save as type and select All Files then click Save.

Note. If you don't set the Save as type as All Files then the file will save as a Text Document that can't run as a Batch file and you won't get your tree program. So in order to get your program set the type as All Files.

6.Then you will get a file named tree(or whatever you've typed in the File Name fill on the Save as window).

7.Then run the file by double click on it or you can run it as Administrator to do so follow the next step.

7.1 Then right click on the file and select Run as Administrator then the program will run like the picture given on the 7. point.

Hope that you've gotten your tree program and it's running without any error. If you've any question you can comment below or can use our Ask Question page.

Is Python Overrated? Why?

2020-05-17T11:41:00.003-07:00

Currently, you can find python programmers everywhere. Python programming language (Python 3.x to be exact) is gaining popularity at a super rapid rate. From Stackify, we can see Python is rising gradually for more than 15 years. Presently, it is the 3rd most popular programming language in the world. But why is it so popular? Is it overrated?

Python is vastly overrated. Because it is effortless to learn and most of the schools recommend it. And also, python typically got a bunch of sponsors from tech giants like Facebook, Google, Microsoft, and even SurveyMonkey.

Now, why these tech-giants sponsor Python? Well, to be honest, Python is the most future protected language. Leading websites like Google, Facebook, Python, YouTube, and Pinterest are written in Python. To work efficiently with these leading companies, you'll have to be an expert in Python.

Let's have a look at the factors that made Python popular.

Python is easy.

Not really. Python is easy to learn. It's dynamically typing system helps a lot to them who are learning. No need for declaring data type, Python is smart enough to detect data types.

Python is smart.

Well, this programming language is the smartest programming language ever. It can detect your tone (data) and process it.

Python is for beginners.

For absolute beginners in programming, Python has no alternatives. If you start with Python, you'll fall in love with programming.

Python is fun.

Ever used the Turtle Draw in Python? A fully functional painting thing that has no use, but fun! Crazy stuff!

But why then people hate python? Because of its speed. Python is slower than other languages and it is a massive memory consuming language. But that is not a problem, anymore. Because day by day our computers are becoming faster. Each of us has at least four gigs of ram in our PC. Smartphones are becoming faster too. So we don't have to think about this speed problem anymore.

Python is overrated for its convenience.

Now we are at a time where we need many programmers. And the main programming skill depends on developing algorithms, not on using a particular fast, yet complex language. So if you are willing to learn to program, Python is your best friend!

The Math 'N IT blog is about to launch a tutorial on Python. Follow the blog to get updates!

How to install Visual Studio Code on Windows from ZIP file

2020-05-17T03:48:00.008-07:00

How to install Visual Studio Code on Windows from ZIP file

If you need a new playground for yourself, the Visual Studio Code is your best choice. Is this a full IDE? No! But you can highly customize it according to your needs. You can literally download your desired language extensions from the ocean of about 2,660 extensions! So you won't have to worry about the "Language support" thing. Need any more support? Download it! You'll get access to a massive library of programming languages, including Nitrogen or Lean (have you ever heard of these? Me neither!). You can also debug your codes from 68 free debuggers from them(including C/C++, Java, PHP, Python, Ruby, C#, Go, Lua, Haxe, Android, and others). Well, if you have less internet access, the VS code should not work as expected, but it'll work better than most other IDEs in the market.

So let's see how you can install it and make it useful to be a professional programmer! Here are the steps to install Visual Studio Code(VS Code) on Windows system:

Download Visual Studio Code from it's official Website here: Visual Studio Code

1. Right click on the downloaded file and select""Extract Al"(if any ZIP file extract utility isn't installed).

2.Then a window like this will appear there click "Browse..." and select the directory where you want it to be extracted.

3.Then click "Extract".

4.Then the progress will start on a window like below.

5.Then a window will appear with the extracted files if you have clicked the radio button "Show extracted files when complete" on the "Extract Compressed(Zipped) Folder" window.

6.Here's the extracted files, click on the "Code" file then the Visual Studio Code will start.

Here the Start Page of Visual Code.

Hope that you have done it and are enjoying the smart IDE. If you have any problem comment bellow or you can ask question on our Ask Question Page.

How to put "This PC" on Desktop.

2019-11-27T05:05:00.000-08:00

How to put "This PC" on Desktop.

After installing Windows 10 you won't get any shortcut of any softwear or any folder on the desktop. Even you won't get any genuiene utility's icon such as "This PC", "User" icon etc. Here the desktop you will get:

You have to put them on the desktop. Here the ways to put them on the desktop:

1.Right click on the desktop and select "Personalize".

There on the left side of Personalize tab click on "Theme".

There on the right side of Theme tab you'll see "Related Settings", under Related Settings click on "Desktop icon settings", then a new window will be opened.

On the new window under "Desktop icon" select the icons you need.

Then click "Apply".

Then click "OK".

After that you will see the icons on the Desktop, that you have added.

Hope that it has fix your problems. If you have any question on it comment us or you can use our Ask A Question page to ask any question.

How to create multiple users in Windows 10

2019-11-13T00:43:00.000-08:00

How to create multiple user on Windows 10

Hello there sometimes our other family members use our PC. In this cases our privacy and security are very important matter. If the user delete any kind of our data we can fall in a crisis. So we need a system to prevent other users to do so. As we are Windows operating system user we don't have to wary cause the operating system we are using is a great operating system. It's maded by many geneus people and they have maded a system to create many other user so that multiple users can use it comfortably. On Windows 10 we can create many users. Here the ways:

1: Firstly go to Settings and select "Accounts."

2:Then in Accounts on your left side select "Family & other users"

3:Then select "Add someone else to this PC

4:Then a window will be open. There if the person you want to add have a Microsoft Account then input the account name and click "Next". or if the person don't have any Microsoft Account then go ahead it's in further next step.

5:Then there will be a massage window there click "Finish" when the user will login to his account they will ask the user to input his password and after that he will be taken to the Windows interface

6:If the person don't have any Microsoft Account then click "I don't have this person's sing-in information".

7:Then they will ask you to create Microsoft Account. If you want to create one then input the information and click "Next" and follow their instruction then create a user

8:If you don't want so then after clicking "I don't have this person's sing-in information" click "Add a user without a Microsoft account"

9:There on input the information and select 3 questions to recover your password and click"Next".

10:Then we will see a Account under the "Add someone else to this PC" button you can change account by restarting the system they will ask you to choose account on the startup and will ask password(if you have given).

11Or you can change account from the start menu like this:

Hope that it has fix your problems. If you have any question on it comment us or you can use our Ask A Question page to ask any question.

A shortcut of Homologous Series

2019-11-05T23:17:00.000-08:00

A shortcut of Homologous Series

Hello there in Organic Chemistry there is a term "Homologous Series" that means those compounds that have the same physical and chemical properties due to their formula . In homologous series all the compounds have a standard formula such as alkoholes are specified by C_n H_2n+1 O H. Here a list iof all homologous standard formula.

Homologous	Standard Formula	Example
Alkane	C_n H_2n+2	Methane (CH₄)
Alkene	C_n H_2n	Ethene (C₂H₄)
Alkyne	C_n H_2n-2	Propyne (C₃H₄)
Alkohol	C_n H_2n+1OH	Butanol (C₄H₉OH
Aldehyde	C_n H_2n	Propanal(C₃H₇)CHO
Carboxylic Acids	C_n H_2n+1COOH	Hexanoic acid (CH₃(CH₂)₄COOH

In some times it seems very hard to remember this tabble. For this we have found an shortcut to memorise it. Here it's
Here if we take all the standard formula of all homologous we cam see a common tern in all homologous here it's.

So here C_n H_2n is common in all homolohous and after that there were added an suffix. Now for our conveniency of understanding we are rearranging the list. Here it's:
So noew firstly after C_n H_2n there were added -2 in Alkynes, secondly there were added 0 n Alkenes, thirdly there added +2 in Alkanes forthly there were added +1 in Alkohol, Aldehyde, Carboxylic Acids with their formila.
So now think about a line of numbers where there are $ points. First of them is -2 then 0 then +1 and then +2.
Now if we put C_n H_2n at the point -2 we will get the homologous standrad formula of Alkynes, if we put C_n H_2n at the point 0 we will get the homologous standrad formula of Alkenes, if we put C_n H_2n at the point +2 we will get the homologous standrad formula of Alkanes and if we put C_n H_2n at the point +1 with the formula of Alkohol, Aldehyde and Carboxylic Acids we will get the homologous standrad formula of them. So finally we get:

Now a short line to remember it is that "Alkyne is at -2, Alkene is at 0, Alkane is at +2 and all the others are at the point +1 with their formula.
Hope that you have understand it and it seems easy to you. Of you have any question aboutit comment us or you vacn use ask us on our Ask A Question page

How to active Windows 10

2019-11-01T11:31:00.000-07:00

How to active Windows 10

Hello there on windows operating system we usually see a massage at the right bottom corner that" Active Windows. Go to settings to active Windows" whisc is like this:

Now here some way to active windows.

Method 1: Active windows using Windows Command Prompt(cmd).

In order to active Windows 10 using Windows Command Prompt or cmd firstly you have to open Administrator Windows Command Prompt or cmd. On the search box at the left bottom corner type cmd.

Then right click on Command Prompt and select Run as administrator.

Note:Dont click the left button cause it will open User Windows Command Prompt but in order to active windows you need to open the Adminiostrator Windows Command Prompt

Then on the command line interface type "slmgr /ipk XXXXX-XXXXX-XXXXX-XXXXX-XXXXX" and hit Enter here "XXXXX-XXXXX-XXXXX-XXXXX-XXXXX" is your product key. It's a key given to you by the service provider or you can find it on internet. Here are some of them:

Home: TX9XD-98N7V-6WMQ6-BX7FG-H8Q99
Home N: 3KHY7-WNT83-DGQKR-F7HPR-844BM
Home Single Language: 7HNRX-D7KGG-3K4RQ-4WPJ4-YTDFH
Home Country Specific: PVMJN-6DFY6-9CCP6-7BKTT-D3WVR
Professional: W269N-WFGWX-YVC9B-4J6C9-T83GX
Professional N: MH37W-N47XK-V7XM9-C7227-GCQG9
Education: NW6C2-QMPVW-D7KKK-3GKT6-VCFB2
Education N: 2WH4N-8QGBV-H22JP-CT43Q-MDWWJ
Enterprise: NPPR9-FWDCX-D2C8J-H872K-2YT43
Enterprise N: DPH2V-TTNVB-4X9Q3-TJR4H-KHJW4

Then you will see a massage window like this, there click "Ok"

Then on the next line type "slmgr /skms kms8.msguides.com” and hit Enter.

Then you will see a massage window again like this, there also click "Ok"

Then on the next line type "slmgr /ato".

Then you will see a massage window like this, there click "Ok" then restatr your system and your windows will be Active

Method : Active windows using a Batch file.

In order to active Windows 10 using a Batch file you need a file contain a Batch script to active Windows 10

On your Desktop or in any derectory create a new Text Document.

Then copy the code given bellow and past it on the file

@echo off
title Activate Windows 10 ALL versions for FREE!&cls&echo ============================================================================&echo #Project: Activating Microsoft software products for FREE without software&echo ============================================================================&echo.&echo #Supported products:&echo - Windows 10 Home&echo - Windows 10 Home N&echo - Windows 10 Home Single Language&echo - Windows 10 Home Country Specific&echo - Windows 10 Professional&echo - Windows 10 Professional N&echo - Windows 10 Education&echo - Windows 10 Education N&echo - Windows 10 Enterprise&echo - Windows 10 Enterprise N&echo - Windows 10 Enterprise LTSB&echo - Windows 10 Enterprise LTSB N&echo.&echo.&echo ============================================================================&echo Activating your Windows...&cscript //nologo slmgr.vbs /ckms >nul&cscript //nologo slmgr.vbs /upk >nul&cscript //nologo slmgr.vbs /cpky >nul&set i=1&wmic os | findstr /I "enterprise" >nul
if %errorlevel% EQU 0 (cscript //nologo slmgr.vbs /ipk NPPR9-FWDCX-D2C8J-H872K-2YT43 >nul&cscript //nologo slmgr.vbs /ipk DPH2V-TTNVB-4X9Q3-TJR4H-KHJW4 >nul&cscript //nologo slmgr.vbs /ipk WNMTR-4C88C-JK8YV-HQ7T2-76DF9 >nul&cscript //nologo slmgr.vbs /ipk 2F77B-TNFGY-69QQF-B8YKP-D69TJ >nul&cscript //nologo slmgr.vbs /ipk DCPHK-NFMTC-H88MJ-PFHPY-QJ4BJ >nul&cscript //nologo slmgr.vbs /ipk QFFDN-GRT3P-VKWWX-X7T3R-8B639 >nul&goto server) else wmic os | findstr /I "home" >nul
if %errorlevel% EQU 0 (cscript //nologo slmgr.vbs /ipk TX9XD-98N7V-6WMQ6-BX7FG-H8Q99 >nul&cscript //nologo slmgr.vbs /ipk 3KHY7-WNT83-DGQKR-F7HPR-844BM >nul&cscript //nologo slmgr.vbs /ipk 7HNRX-D7KGG-3K4RQ-4WPJ4-YTDFH >nul&cscript //nologo slmgr.vbs /ipk PVMJN-6DFY6-9CCP6-7BKTT-D3WVR >nul&goto server) else wmic os | findstr /I "education" >nul
if %errorlevel% EQU 0 (cscript //nologo slmgr.vbs /ipk NW6C2-QMPVW-D7KKK-3GKT6-VCFB2 >nul&cscript //nologo slmgr.vbs /ipk 2WH4N-8QGBV-H22JP-CT43Q-MDWWJ >nul&goto server) else wmic os | findstr /I "10 pro" >nul
if %errorlevel% EQU 0 (cscript //nologo slmgr.vbs /ipk W269N-WFGWX-YVC9B-4J6C9-T83GX >nul&cscript //nologo slmgr.vbs /ipk MH37W-N47XK-V7XM9-C7227-GCQG9 >nul&goto server) else (goto notsupported)
:server
if %i%==1 set KMS=kms7.MSGuides.com
if %i%==2 set KMS=kms8.MSGuides.com
if %i%==3 set KMS=kms9.MSGuides.com
if %i%==4 goto notsupported
cscript //nologo slmgr.vbs /skms %KMS%:1688 >nul&echo ============================================================================&echo.&echo.
cscript //nologo slmgr.vbs /ato | find /i "successfully" && (echo.&echo ============================================================================&echo.&echo #My official blog: MSGuides.com&echo.&echo #How it works: bit.ly/kms-server&echo.&echo #Please feel free to contact me at msguides.com@gmail.com if you have any questions or concerns.&echo.&echo #Please consider supporting this project: donate.msguides.com&echo #Your support is helping me keep my servers running everyday!&echo.&echo ============================================================================&choice /n /c YN /m "Would you like to visit my blog [Y,N]?" & if errorlevel 2 exit) || (echo The connection to my KMS server failed! Trying to connect to another one... & echo Please wait... & echo. & echo. & set /a i+=1 & goto server)
explorer "http://MSGuides.com"&goto halt
:notsupported
echo ============================================================================&echo.&echo Sorry! Your version is not supported.&echo.
:halt
pause >nul

Then at the top right corner click on "File" and select "Save as" and you will see a new window.

Then name the file with a ".bat" extention and on the next tab of "Save as type" select "All Files" type and save it.

Then right click on the file and select Run as administrator

Then after finishing running the code they wiil ask you "Would you like to visit my blog [Y,N]" here if you want to visit their site type "Y" and if you don't want then type "N"

Then restatr your system and your windows will be Active

Hope that it have solved your problem. Have a good day.

Is Gravitational Force 0 N at infinity point?

2019-10-16T01:51:00.001-07:00

Is Gravitational Force 0 N at infinity point?

Hi there we know that Gravitational Force is 0 N at the center of an object, but is it also 0N at infinity point. Let's calculate it and see weather it is 0N or not.

So for this we are considering two object m₁ and m₂ and here both m₁ and m₂ are of 1 kg(For the continence of cauculating we consider it of 1kg, you can consider whatever you want). As we're measuring force it infinity point so the distance between m₁ and m₂ r is ∞ . So finally we got :

m₁ = 1kg
m₂ = 1kg
r = ∞
G = 6.674 × 10^-11 N m² kg^-2

As we know,

F = G
m₁ × m₂ / r²

F = G
1kg × 1kg / ∞²

F =
G × 1kg / ∞²

F =
6.674 × 10^-11 N m² / ∞²

But as we know 1 / ∞ = 0.

So

F =
6.674 × 10^-11 N m² / ∞²
= 0 N

Then is Gravitational Force at infinity point is 0 N? The answer is 'No', gravitational force at infinity is not 0 N.

Now you can say that are I joking, when we're getting 0 N by calculating it then it's 0 N. But on it's not 0 N cause infinity is not a specific number.

Infinity is a symbole which indicates all the number after the last number of a set. So it means that instead of having a specific valu it has different value.

Now let's see some calculation. Here we'll find out the value of 1/∞. As infinity is a set of numbers so we are considering a variab n to indicates each element of the set. Let's see the value of 1/n for various value of n.

when n = 0.2, 1 / n = 5

when n = 0.25, 1 / n = 4

when n = 0.5, 1 / n = 2

when n = 1, 1 / n = 1

when n = 2, 1 / n = 0.5

when n = 4, 1 / n = 0.25

when n = 5, 1 / n = 0.2

Here we can see that when the value of n is less then the value of 1/n is more it means when lim n → ∞ then 1/n → 0 again when the value of n is more then the value of 1/n is less it means that when lim n → 0 then 1/n → ∞ .

In the same way when infinity means a large distance then the Gravitational force become less and when infinity means a less distance the gravitational force become large. It means when lim r → ∞ then F_G → 0 but never = 0 and when lim r → 0 then F_G → ∞ but never = ∞ .

That's why Gravitational Force at infinity point isn't equal to 0 N instead it goes towards 0 N.

The attraction force of M87's Black Hole and our Earth.

2019-09-29T06:43:00.000-07:00

The attraction force of M87's Black Hole and our Earth.

Hi there in 10 April 2019 we came to see the First Ever Image of A Black Hole, which was captured by Event Horizon Teliscope. And we also have knew some properties of the Black Hole such as mass, distance from earth etc. So now let's d some madness with these properties. Let's calculate the Gravitational force of the Black Hole and ou Earth.

So first of all we need some information such aas mass of the Black Hole, it's distance from earth etc. Here we get them from Google:

Here they are:

mass of the Black Hole is m_B = 1.29285×10⁴⁰kg
mass of Earth is m_E = 5.972×10²⁴ kg
distance between the Black Hole and the Earth is r = 5.0141872×10²³ m

Note: Acording to Wikipedia the distance between the Black Hole and the Earth is about 53 million light years which is 5.0141872 × 10²³ m in meter scale.

Newtonian Constant G = 6.67408 ×10⁻¹¹

and now as we know:

F = G

m_B m_E / r²

F = G

1.29285×10⁴⁰kg × 5.972 × 10²⁴ kg / (5.0141872 × 10²³m)²

F =

G × 7.7209002×10⁶⁴kg / 2.51420733×10⁴⁷m²

F =

5.15299056×10⁵⁴ N m² / 2.51420733×10⁴⁷m²

F = 2.049548778 × 10⁷ N

According to scientific notation the F = 2.0495 × 10⁷ N.

Don't scard on this it won't cause any problems on our Earth. Cause all the object around our earth are attracting our earth with a greate force such as the Sun is attracting Earth with 3.52*10^22 N which is about 1.717×10¹⁵ times more then the force of the Black Hole.

What are the difference between Valence and Valence Electron.

2019-09-08T06:00:00.000-07:00

What are the difference between Valence and Valence Electron.

Hi guys in chemistry we see two word "Valence" and "Valence Electron". You might think that these two terms are the same, but no these two terms are totally different. Both are periodic properties of element. First of all let’s see the definition of these terms.

Valence:Valence is the number of combining power of an atom. While forming a chemical bond an atom needs to give or take or share electron. Valence means the number of electron that an atom can give or take or share. For example let's see the electron configuration of Chlorine(Cl) . Cl have 17 electron.

Cl(17)--> 1s² 2s² 2p⁶ 3s²3p⁵.

As we know all the element of periodic table want to have the same electron configuration that the nearby noble gas have. So Cl will receive an electron in order to have the same electron configuration that the nearby noble gas Argon have. Here the electron that Cl will receive is the Valence of Cl which is 1. So Cl’s Valence is -1. We add a negative sign(“-“) because by receiving the electron Cl will become an negative ion.

Valence Electron:Valence Electron is the electron of the outer orbit of an atom. It can participate in forming a chemical bond. For example let's see the electron configuration of Aluminum(Al). Aluminum has 13 electron.

Al(13)--> 1s² 2s² 2p⁶ 3s² 3p¹.

Here the outer orbit of Al is 3 that has 3 electron. These 3 electron are the valence electron of Al. Al can use them to form chemical bond.

So you can see that they are totally different. Valence is the combining power of an atom where Valence Electron is the electron of the outer orbit of an atom. Valence is power but Valence electron is the number of electron. Valence means the number of electron that an atom can receive but Valence Electron is the number of electron that an atom can give and share.

That's why "Valence" and "Valence Electron" are different.

Why Atomic Radius is less for the element having more particles.

2019-08-28T21:11:00.002-07:00

Why Atomic Radius is less for the element having more particles.

Hi guys we know that Atomic Radius is the distance between the center of the nucleus and the outer orbit of an element. Atomic Radius is less for the element those have more particles(Neutron, Proton, Electron), but why? Let’s know the reason.

It’s an Periodic Properties of an element. It decreases from left to right in the period and increase from up to down in a group . And if we look at the periodic table we can see that element of left side have less particles(Neutron, Proton, Electron), then the element of right side. If we thought generally, we can say that the element having more particles(Neutron, Proton, Electron) should have more Atomic Radius. But really it’s opposite to our thought. Element having more particles(Neutron, Proton, Electron) have less Atomic Radius instead of having more. The reason is gravitational force between the nucleus and electrons.|

All we know all the bodies of the universe attrac each other to itself. This cause a displacement to the lighter body. For the same reason the Atomic Radius of element having more particles(Neutron, Proton, Electron) is less than the Atomic Radius of the element having less particles(Neutron, Proton, Electron). When an atom have more Neutron, Proton and Electron then the mass of the nucleus is more. So it can attrack the electron with more force and that cause a displacement of the electron. For this the electron of outer orbit comes closer to the nucleus, so the outer orbit also comes closer the nucleus, and decrease the Atomic Radius.

The another things is Atomic Radius increase feom up to down in the periodic table. The Reason is that every times there added a new orbit from up to down. That cause more distance from the nucleus to the outer orbit.

That’s why Atomic Radius is less for the element having more particles.

Why h is equal to 0m.

2019-07-28T23:25:00.000-07:00

When h is equal to 0m.

Why distance or h is 0m while measuring the distance of a body that is thrown from Earth's surface and then it comes to the same place from where it was thrown.

While doing maths from Galileo's Laws Of Falling Bodies, sometimes we see that when a body thrown from earth surface and after that it fall down on the same place from where it was thrown then we measure the distance or h as 0m. Now the question is why we measure the distance or h as 0m? For example tou throw a body from a point of earth surfece and you named it X and it goes up to a point 12 meter above from X and you named it Y. Now if I asked you the distance you can say that its 24. Cause first of all at the time of going up it arive 12 meter then at the time of fall down it again arive 12 meter, so the distance that it has passed is 12 meter + 12 meter = 24 meter.

Yeah you do 24 for meter if I want the displacement.Now the question is that aren't distance and displacement the same things?

The answer is "No", distance and displacement aren't same things. Let's know why distance and displacement aren't same things

Distance means difference of two point at a specific Direction where displacement means difference of two point at any direction.Let's see a picture to understand it easily.

Here thought that you are at the point A and want to go the point G. So as here shown first you will go 4m forward then after turning 90° left you will go 12m forward then you will turn 90° right and will go 10m forward then you will turn 90° left again and will go 6m forward and again turn 90° right and go 4m forward after that you will turn 90° left and will go 3m forward. Thuse you will go to your destination. So here the the way you have passed is (4m + 12m + 10m + 6m + 4m + 3m) = 49m. It's tour displacement but the distance you have passed is the length of the blue line of the picture which is 18m long. So distance is length of the way that you have passed at a specific angle but displacement is the total way that you have passed. That's why Distance and Displacement are not same.

Let's go back to the thrown body.So when a body is thrown from Earth's surface it goes up to the point. Here its direction is straight up and then it comes back to the same place from where it was thrown.So here it change its direction and we know that distance doesn't deppend on the change of ditrection. Distance is the difference of the point from where it was thrown and the point where it cames. As here the body cames to the same place from where it was thrown so here the difference is of the same point so it is surealy 0m. And as the difference is 0m then the distance is 0m. But if we cosider the displacement it will 24. Cause displacement is the difference of all the way it has passed and here at the time of going above it passed 12m and after changing its derection it again passed 12m at the time of fall down. So the displacement is 12m but distance is 0m.

That's why disatnce or h is 0m while measuring the distance of a body that is thrown from Earth's surface and then it cames to the same place from where it was thrown.

On The Electrodynamics Of Moving Bodies part:11

2019-07-22T23:06:00.000-07:00

On The Electrodynamics Of Moving Bodies part:11

§ 10. Dynamics of the Slowly Accelerated Electron

Let there be in motion in an electromagnetic field an electrically charged particle (in the sequel called an “electron”), for the law of motion of which we assume as follows:—

If the electron is at rest at a given epoch, the motion of the electron ensues in the next instant of time according to the equations

where x, y, z denote the co-ordinates of the electron, and m the mass of the electron, as long as its motion is slow.

Now, secondly, let the velocity of the electron at a given epoch be v. We seek the law of motion of the electron in the immediately ensuing instants of time.

Without affecting the general character of our considerations, we may and will assume that the electron, at the moment when we give it our attention, is at the origin of the co-ordinates, and moves with the velocity v along the axis of X of the system K. It is then clear that at the given moment (t = 0) the electron is at rest relatively to a system of co-ordinates which is in parallel motion with velocity v along the axis of X.

From the above assumption, in combination with the principle of relativity, it is clear that in the immediately ensuing time (for small values of t) the electron, viewed from the system k, moves in accordance with the equations

in which the symbols ξ, η, ζ, X', Y', Z' refer to the system k. If, further, we decide that when t = x = y = z = 0 then τ = ξ = η = ζ = 0, the transformation equations of §§ 3 and 6 hold good, so that we have

With the help of these equations we transform the above equations of motion from system k to system K, and obtain

Taking the ordinary point of view we now inquire as to the “longitudinal” and the “transverse” mass of the moving electron. We write the equations (A) in the form

and remark firstly that εX', εY', εZ' are the components of the ponderomotive force acting upon the electron, and are so indeed as viewed in a system moving at the moment with the electron, with the same velocity as the electron. (This force might be measured, for example, by a spring balance at rest in the last-mentioned system.) Now if we call this force simply “the force acting upon the electron,”⁹ and maintain the equation—mass × acceleration = force—and if we also decide that the accelerations are to be measured in the stationary system K, we derive from the above equations

With a different definition of force and acceleration we should naturally obtain other values for the masses. This shows us that in comparing different theories of the motion of the electron we must proceed very cautiously.

We remark that these results as to the mass are also valid for ponderable material points, because a ponderable material point can be made into an electron (in our sense of the word) by the addition of an electric charge, no matter how small.

We will now determine the kinetic energy of the electron. If an electron moves from rest at the origin of co-ordinates of the system K along the axis of X under the action of an electrostatic force X, it is clear that the energy withdrawn from the electrostatic field has the value ∫ εX dx. As the electron is to be slowly accelerated, and consequently may not give off any energy in the form of radiation, the energy withdrawn from the electrostatic field must be put down as equal to the energy of motion W of the electron. Bearing in mind that during the whole process of motion which we are considering, the first of the equations (A) applies, we therefore obtain

Thus, when v = c, W becomes infinite. Velocities greater than that of light have—as in our previous results—no possibility of existence.

This expression for the kinetic energy must also, by virtue of the argument stated above, apply to ponderable masses as well.

We will now enumerate the properties of the motion of the electron which result from the system of equations (A), and are accessible to experiment.

1. From the second equation of the system (A) it follows that an electric force Y and a magnetic force N have an equally strong deflective action on an electron moving with the velocity v, when Y = Nv/c. Thus we see that it is possible by our theory to determine the velocity of the electron from the ratio of the magnetic power of deflexion A_m to the electric power of deflexion A_e, for any velocity, by applying the law

This relationship may be tested experimentally, since the velocity of the electron can be directly measured, e.g. by means of rapidly oscillating electric and magnetic fields.

2. From the deduction for the kinetic energy of the electron it follows that between the potential difference, P, traversed and the acquired velocity v of the electron there must be the relationship

3. We calculate the radius of curvature of the path of the electron when a magnetic force N is present (as the only deflective force), acting perpendicularly to the velocity of the electron. From the second of the equations (A) we obtain

These three relationships are a complete expression for the laws according to which, by the theory here advanced, the electron must move.

In conclusion I wish to say that in working at the problem here dealt with I have had the loyal assistance of my friend and colleague M. Besso, and that I am indebted to him for several valuable suggestions.

⁹The definition of force here given is not advantageous, as was first shown by M. Planck. It is more to the point to define force in such a way that the laws of momentum and energy assume the simplest form.

On The Electrodynamics Of Moving Bodies Part:10

2019-07-22T10:49:00.001-07:00

On The Electrodynamics Of Moving Bodies Part:10

§ 9. Transformation of the Maxwell-Hertz Equations when Convection-Currents are Taken into Account

We start from the equations

where

denotes 4π times the density of electricity, and (u_x,u_y, u_z) the velocity-vector of the charge. If we imagine the electric charges to be invariably coupled to small rigid bodies (ions, electrons), these equations are the electromagnetic basis of the Lorentzian electrodynamics and optics of moving bodies.

Let these equations be valid in the system K, and transform them, with the assistance of the equations of transformation given in §§ 3 and 6, to the system k. We then obtain the equations

where

and

Since—as follows from the theorem of addition of velocities (§ 5)—the vector (u_ξ, u_η, u_ζ ) is nothing else than the velocity of the electric charge, measured in the system k, we have the proof that, on the basis of our kinematical principles, the electrodynamic foundation of Lorentz’s theory of the electrodynamics of moving bodies is in agreement with the principle of relativity.

In addition I may briefly remark that the following important law may easily be deduced from the developed equations: If an electrically charged body is in motion anywhere in space without altering its charge when regarded from a system of co-ordinates moving with the body, its charge also remains—when regarded from the “stationary” system K—constant.

On The Electrodynamics Of Moving Bodies Part:9

2019-07-21T22:02:00.001-07:00

On The Electrodynamics Of Moving Bodies Part:9

§ 8. Transformation of the Energy of Light Rays. Theory of the Pressure of Radiation Exerted on Perfect Reflectors

Since A²/8π equals the energy of light per unit of volume, we have to regard A'²/8π, by the principle of relativity, as the energy of light in the moving system. Thus A'²/A² would be the ratio of the “measured in motion” to the “measured at rest” energy of a given light complex, if the volume of a light complex were the same, whether measured in K or in k. But this is not the case. If l, m, n are the direction-cosines of the wave-normals of the light in the stationary system, no energy passes through the surface elements of a spherical surface moving with the velocity of light:—

We may therefore say that this surface permanently encloses the same light complex. We inquire as to the quantity of energy enclosed by this surface, viewed in system k, that is, as to the energy of the light complex relatively to the system k

The spherical surface—viewed in the moving system—is an ellipsoidal surface, the equation for which, at the time τ = 0, is

If S is the volume of the sphere, and S' that of this ellipsoid, then by a simple calculation

Thus, if we call the light energy enclosed by this surface E when it is measured in the stationary system, and E' when measured in the moving system, we obtain

and this formula, when φ = 0, simplifies into

It is remarkable that the energy and the frequency of a light complex vary with the state of motion of the observer in accordance with the same law.

Now let the co-ordinate plane ξ = 0 be a perfectly reflecting surface, at which the plane waves considered in § 7 are reflected. We seek for the pressure of light exerted on the reflecting surface, and for the direction, frequency, and intensity of the light after reflexion.

Let the incidental light be defined by the quantities A, cos φ, ν(referred to system K). Viewed from k the corresponding quantities are

For the reflected light, referring the process to system k, we obtain

Finally, by transforming back to the stationary system K, we obtain for the reflected light

The energy (measured in the stationary system) which is incident upon unit area of the mirror in unit time is evidently A²(c cos φ−v)/8π. The energy leaving the unit of surface of the mirror in the unit of time is A'''²(−c cos φ''' +v)/8π.

The difference of these two expressions is, by the principle of energy, the work done by the pressure of light in the unit of time. If we set down this work as equal to the product Pv, where P is the pressure of light, we obtain

In agreement with experiment and with other theories, we obtain to a first approximation

All problems in the optics of moving bodies can be solved by the method here employed. What is essential is, that the electric and magnetic force of the light which is influenced by a moving body, be transformed into a system of co-ordinates at rest relatively to the body. By this means all problems in the optics of moving bodies will be reduced to a series of problems in the optics of stationary bodies.

On The Electrodynamics Of Moving Bodies Part:8

2019-07-20T23:18:00.002-07:00

On The Electrodynamics Of Moving Bodies Part:8

§ 7. Theory of Doppler’s Principle and of Aberration

In the system K, very far from the origin of co-ordinates, let there be a source of electrodynamic waves, which in a part of space containing the origin of co-ordinates may be represented to a sufficient degree of approximation by the equations

where

Here (X', Y', Z') and (L₀, M₀, N₀) are the vectors defining the amplitude of the wave-train, and l, m, n the direction-cosines of the wave-normals. We wish to know the constitution of these waves, when they are examined by an observer at rest in the moving system k.

Applying the equations of transformation found in § 6 for electric and magnetic forces, and those found in § 3 for the co-ordinates and the time, we obtain directly

where

From the equation for ω' it follows that if an observer is moving with velocity v relatively to an infinitely distant source of light of frequency ν, in such a way that the connecting line “source-observer” makes the angle φ with the velocity of the observer referred to a system of co-ordinates which is at rest relatively to the source of light, the frequency v' of the light perceived by the observer is given by the equation

This is Doppler’s principle for any velocities whatever. When φ = 0 the equation assumes the perspicuous form

We see that, in contrast with the customary view, when v = −c, ν' = ∞.

If we call the angle between the wave normal (direction of the ray) in the moving system and the connecting line “source observer” φ', the equation for φ'^† assumes the form

This equation expresses the law of aberration in its most general form. If φ = ¹⁄₂π, the equation becomes simply

We still have to find the amplitude of the waves, as it appears in the moving system. If we call the amplitude of the electric or magnetic force A or A' respectively, accordingly as it is measured in the stationary system or in the moving system, we obtain

which equation, if φ = 0, simplifies into

It follows from these results that to an observer approaching a source of light with the velocity c, this source of light must appear of infinite intensity.

^†Editor’s note: Erroneously given as “l'” in the 1923 English translation, propagating an error, despite a change in symbols, from the original 1905 paper.

On The Electrodynamics Of Moving Bodies Part:7

2019-07-19T08:31:00.000-07:00

On The Electrodynamics Of Moving Bodies Part:7

II. ELECTRODYNAMICAL PART

§ 6. Transformation of the Maxwell-Hertz Equations for Empty Space. On the Nature of the Electromotive Forces Occurring in a Magnetic Field During Motion

Let the Maxwell-Hertz equations for empty space hold good for the stationary system K, so that we have

where (X, Y, Z) denotes the vector of the electric force, and (L, M, N) that of the magnetic force.

If we apply to these equations the transformation developed in § 3, by referring the electromagnetic processes to the system of co-ordinates there introduced, moving with the velocity v, we obtain the equations ^†

where

Now the principle of relativity requires that if the Maxwell-Hertz equations for empty space hold good in system K, they also hold good in system k; that is to say that the vectors of the electric and the magnetic force—(X', Y', Z' ) and (L', M, N')—of the moving system k, which are defined by their ponderomotive effects on electric or magnetic masses respectively, satisfy the following equations:—

^†Editor’s note: In the 1923 English translation, the quantities “ζ” and “ξ” were interchanged in the second equation. They were given correctly in the the original 1905 paper.

Evidently the two systems of equations found for system k must express exactly the same thing, since both systems of equations are equivalent to the Maxwell-Hertz equations for system K. Since, further, the equations of the two systems agree, with the exception of the symbols for the vectors, it follows that the functions occurring in the systems of equations at corresponding places must agree, with the exception of a factor ψ(v), which is common for all functions of the one system of equations, and is independent of ξ, η, ζ and τ but depends upon v. Thus we have the relations

If we now form the reciprocal of this system of equations, firstly by solving the equations just obtained, and secondly by applying the equations to the inverse transformation (from k to K), which is characterized by the velocity −v, it follows, when we consider that the two systems of equations thus obtained must be identical, that ψ(v)ψ(−v) = 1. Further, from reasons of symmetry⁸ and therefore

and our equations assume the form

As to the interpretation of these equations we make the following remarks: Let a point charge of electricity have the magnitude “one” when measured in the stationary system K, i.e. let it when at rest in the stationary system exert a force of one dyne upon an equal quantity of electricity at a distance of one cm. By the principle of relativity this electric charge is also of the magnitude “one” when measured in the moving system. If this quantity of electricity is at rest relatively to the stationary system, then by definition the vector (X, Y, Z) is equal to the force acting upon it. If the quantity of electricity is at rest relatively to the moving system (at least at the relevant instant), then the force acting upon it, measured in the moving system, is equal to the vector (X', Y', Z'). Consequently the first three equations above allow themselves to be clothed in words in the two following ways:—

1. If a unit electric point charge is in motion in an electromagnetic field, there acts upon it, in addition to the. electric force, an “electromotive force” which, if we neglect the terms multiplied by the second and higher powers of v/c, is equal to the vector-product of the velocity of the charge and the magnetic force, divided by the velocity of light. (Old manner of expression.)

⁸If, for example, X=Y=Z=L=M=0, and N 6≠ 0, then from reasons of symmetry it is clear that when v changes sign without changing its numerical value, Y' must also change sign without changing its numerical value.

2. If a unit electric point charge is in motion in an electromagnetic field, the force acting upon it is equal to the electric force which is present at the locality of the charge, and which we ascertain by transformation of the field to a system of co-ordinates at rest relatively to the electrical charge. (New manner of expression.)

The analogy holds with “magnetomotive forces.” We see that electromotive force plays in the developed theory merely the part of an auxiliary concept, which owes its introduction to the circumstance that electric and magnetic forces do not exist independently of the state of motion of the system of co-ordinates.

Furthermore it is clear that the asymmetry mentioned in the introduction as arising when we consider the currents produced by the relative motion of a magnet and a conductor, now disappears. Moreover, questions as to the “seat” of electrodynamic electromotive forces (unipolar machines) now have no point.

On The Electrodynamics Of Moving Bodies Part:6

2019-07-18T14:51:00.000-07:00

On The Electrodynamics Of Moving Bodies Part:6

§ 5. The Composition of Velocities

In the system k moving along the axis of X of the system K with velocity v, let a point move in accordance with the equations

where w_ξ and w_η denote constants.

Required: the motion of the poinrelatively to the system K. If with the help of the equations of transformation developed in § 3 we introduce the quantities x, y, z, t into the equations of motion of the point, we obtain

Thus the law of the parallelogram of velocities is valid according to our theory only to a first approximation. We set

⁷Not a pendulum-clock, which is physically a system to which the Earth belongs. This case had to be excluded.

^†Editor’s note: This equation was incorrectly given in Einstein’s original paper and the 1923 English translation as a = tan⁻¹ w_y/w_x

a is then to be looked upon as the angle between the velocities v and w. After a simple calculation we obtain

It is worthy of remark that v and w enter into the expression for the resultant velocity in a symmetrical manner. If w also has the direction of the axis of X, we get

It follows from this equation that from a composition of two velocities which are less than c, there always results a velocity less than c. For if we set v = c − κ, w = c − λ, κ and λ being positive and less than c, then

It follows, further, that the velocity of light c cannot be altered by composition with a velocity less than that of light. For this case we obtain

We might also have obtained the formula for V, for the case when v and w have the same direction, by compounding two transformations in accordance with § 3. If in addition to the systems K and k figuring in § 3 we introduce still another system of co-ordinates k' moving parallel to k, its initial point moving on the axis of Ξ^† with the velocity w, we obtain equations between the quantities x, y, z, t and the corresponding quantities of k', which differ from the equations found in § 3 only in that the place of “v” is taken by the quantity

from which we see that such parallel transformations—necessarily—form a group. We have now deduced the requisite laws of the theory of kinematics cor- responding to our two principles, and we proceed to show their application to electrodynamics.

On The Electrodynamics Of Moving Bodies Part:5

2019-07-17T23:49:00.000-07:00

On The Electrodynamics Of Moving Bodies Part:5

§ 4. Physical Meaning of the Equations Obtained in Respect to Moving Rigid Bodies and Moving Clocks

We envisage a rigid sphere⁶ of radius R, at rest relatively to the moving system k, and with its centre at the origin of co-ordinates of k. The equation of the surface of this sphere moving relatively to the system K with velocity v is

⁶That is, a body possessing spherical form when examined at rest.

The equation of this surface expressed in x, y, z at the time t = 0 is

A rigid body which, measured in a state of rest, has the form of a sphere, therefore has in a state of motion—viewed from the stationary system—the form of an ellipsoid of revolution with the axes

Thus, whereas the Y and Z dimensions of the sphere (and therefore of every rigid body of no matter what form) do not appear modified by the motion, the X dimension appears shortened in the ratio 1 : i.e. the greater the value of v, the greater the shortening. For v = c all moving objects—viewed from the “stationary” system—shrivel up into plane figures.^† For velocities greater than that of light our deliberations become meaningless; we shall, however, find in what follows, that the velocity of light in our theory plays the part, physically, of an infinitely great velocity.

It is clear that the same results hold good of bodies at rest in the “stationary" system, viewed from a system in uniform motion.

Further, we imagine one of the clocks which are qualified to mark the time t when at rest relatively to the stationary system, and the time τ when at rest relatively to the moving system, to be located at the origin of the co-ordinates of k, and so adjusted that it marks the time τ . What is the rate of this clock, when viewed from the stationary system?

Between the quantities x, t, and τ, which refer to the position of the clock, we have, evidently, x = vt and

Therefore,

whence it follows that the time marked by the clock (viewed in the stationary system) is slow by seconds per second, or—neglecting magni tudes of fourth and higher order—by

From this there ensues the following peculiar consequence. If at the points A and B of K there are stationary clocks which, viewed in the stationary system, are synchronous; and if the clock at A is moved with the velocity v along the line AB to B, then on its arrival at B the two clocks no longer synchronize, but the clock moved from A to B lags behind the other which has remained at B by (up to magnitudes of fourth and higher order), ^t being the time occupied in the journey from A to B

^†Editor’s note: In the 1923 English translation, this phrase was erroneously translated as “plain figures”. I have used the correct “plane figures” in this edition.

It is at once apparent that this result still holds good if the clock moves from A to B in any polygonal line, and also when the points A and B coincide.

If we assume that the result proved for a polygonal line is also valid for a continuously curved line, we arrive at this result: If one of two synchronous clocks at A is moved in a closed curve with constant velocity until it returns to A, the journey lasting t seconds, then by the clock which has remained at rest the travelled clock on its arrival at A will be second slow. Thence we conclude that a balance-clock⁷ at the equator must go more slowly, by a very small amount, than a precisely similar clock situated at one of the poles under otherwise identical conditions.

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On The Electrodynamics Of Moving Bodies part:11

§ 10. Dynamics of the Slowly Accelerated Electron

9The definition of force here given is not advantageous, as was first shown by M. Planck. It is more to the point to define force in such a way that the laws of momentum and energy assume the simplest form.

On The Electrodynamics Of Moving Bodies Part:10

§ 9. Transformation of the Maxwell-Hertz Equations when Convection-Currents are Taken into Account

On The Electrodynamics Of Moving Bodies Part:9

§ 8. Transformation of the Energy of Light Rays. Theory of the Pressure of Radiation Exerted on Perfect Reflectors

On The Electrodynamics Of Moving Bodies Part:8

§ 7. Theory of Doppler’s Principle and of Aberration

†Editor’s note: Erroneously given as “l'” in the 1923 English translation, propagating an error, despite a change in symbols, from the original 1905 paper.

On The Electrodynamics Of Moving Bodies Part:7

II. ELECTRODYNAMICAL PART

§ 6. Transformation of the Maxwell-Hertz Equations for Empty Space. On the Nature of the Electromotive Forces Occurring in a Magnetic Field During Motion

†Editor’s note: In the 1923 English translation, the quantities “ζ” and “ξ” were interchanged in the second equation. They were given correctly in the the original 1905 paper.

8If, for example, X=Y=Z=L=M=0, and N 6≠ 0, then from reasons of symmetry it is clear that when v changes sign without changing its numerical value, Y' must also change sign without changing its numerical value.

On The Electrodynamics Of Moving Bodies Part:6

§ 5. The Composition of Velocities

7Not a pendulum-clock, which is physically a system to which the Earth belongs. This case had to be excluded.

†Editor’s note: This equation was incorrectly given in Einstein’s original paper and the 1923 English translation as a = tan−1 wy/wx

On The Electrodynamics Of Moving Bodies Part:5

§ 4. Physical Meaning of the Equations Obtained in Respect to Moving Rigid Bodies and Moving Clocks

6That is, a body possessing spherical form when examined at rest.

⁹The definition of force here given is not advantageous, as was first shown by M. Planck. It is more to the point to define force in such a way that the laws of momentum and energy assume the simplest form.

^†Editor’s note: Erroneously given as “l'” in the 1923 English translation, propagating an error, despite a change in symbols, from the original 1905 paper.

^†Editor’s note: In the 1923 English translation, the quantities “ζ” and “ξ” were interchanged in the second equation. They were given correctly in the the original 1905 paper.

⁸If, for example, X=Y=Z=L=M=0, and N 6≠ 0, then from reasons of symmetry it is clear that when v changes sign without changing its numerical value, Y' must also change sign without changing its numerical value.

⁷Not a pendulum-clock, which is physically a system to which the Earth belongs. This case had to be excluded.

^†Editor’s note: This equation was incorrectly given in Einstein’s original paper and the 1923 English translation as a = tan⁻¹ w_y/w_x

⁶That is, a body possessing spherical form when examined at rest.