# electric field intensity question

Discussion in 'Homework Help' started by TheSpArK505, Mar 11, 2015.

1. ### TheSpArK505 Thread Starter Member

Sep 25, 2013
92
0
hi everyone
I'm having a problem with a small part of integrating a line of charges

the question is how did dp became d^2(p)

question is attached!

File size:
54 KB
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39
2. ### t_n_k AAC Fanatic!

Mar 6, 2009
5,448
782
This is an example of integration by parts. Are you familiar with the method?

Sep 25, 2013
92
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yup

4. ### TheSpArK505 Thread Starter Member

Sep 25, 2013
92
0
But what's the connection?? @t_n_k

5. ### WBahn Moderator

Mar 31, 2012
17,751
4,799
I don't see d²(p) in there.

I do see d(p²), which is NOT the same thing?

What's d(p²)? Does that look like anything familiar?

I also notice that z went to h. Why? I suspect I know, but without having the problem available it's impossible to be sure.

6. ### t_n_k AAC Fanatic!

Mar 6, 2009
5,448
782
Also shouldn't the first integral in the second line read...

$\frac{ h \rho_s}{4\epsilon_o}\int^{a}_{\rho=0}$$\rho^2 + h^2$$^{-\frac {3}{2}}d$$\rho^2$$$

The index negative sign is missing in the original equations..

7. ### MrAl Well-Known Member

Jun 17, 2014
2,438
492
Hi,

I would have liked to at least follow this thread, but unfortunately the original document in post #1 is in a strange .doc format which WordPad doesnt read. What kind of format is this and any way to convert this into a more common file format?
Thanks

8. ### DickCappels Moderator

Aug 21, 2008
2,656
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The .doc file contains the following:

9. ### MrAl Well-Known Member

Jun 17, 2014
2,438
492
Hello,

Thanks much for posting.
Do you know what kind of file format that was?

10. ### WBahn Moderator

Mar 31, 2012
17,751
4,799
Microsoft Word. It opened just fine on my machine. The equations appear to use MS Equation, which used to be an optional component but that I think is now part of the basic install.

11. ### MrAl Well-Known Member

Jun 17, 2014
2,438
492
Hi,

Oh i see, thanks for that info. I wonder why it did not open then, you mean with Wordpad ? That's the program i have.

Back to the integral...

It seems that the easiest way to solve that integral is to use the technique of integration by u substitution.
In this case u could be equal to p^2+h^2, and then we just have to integrate a typical power of a variable, u:
integrate 1/u^(3/2) du
and since u is as above then du is simply 2*p dp, so the entire integral becomes:
(1/2)*integrate 1/(u^(3/2)) du

and then use the definition of u to solve for the new integration limits.

This looks like the electric field on axis of a thickish ring ?

Last edited: Mar 14, 2015
12. ### WBahn Moderator

Mar 31, 2012
17,751
4,799
Word and Wordpad are two different programs. Wordpad is (or at least started out life as) a hybrid of Word and Notepad, hence the name. Word is a full-featured document editor, while Wordpad is a small subset of it. Originally Wordpad only worked with ASCII text files and, perhaps, RichText, but now it works with quite a bit more.

Apr 5, 2008
15,648
2,347
Hello,

If you do not have Microsoft Office, you can use LibreOffice.
It also opens fine in the free LibreOffice: http://www.libreoffice.org/

Bertus

14. ### MrAl Well-Known Member

Jun 17, 2014
2,438
492
Hi again,

Thanks to both of you, very interesting. I wonder why they went to an entirely different format.
Do you remember the old Win 3.1 app called, "Write" ?
I used to like that one a lot because it allowed true subscripts, but they stopped support on that, after i made quite a few documents with subscripts.
This is one thing that really bugs me about Microsoft, the way they handle changes in new versions of Windows. They even dont like the original Help file format anymore so the handler for that is now a separate download for Win 7. They say they feel it is not worthy of the new system.

One quick question left, is libreoffice similar to 'open office' or soemthiing like that? I think i used to have that a long time ago before i changed hard drives (several times over the years ha ha). Thanks much.

Back to the integration again...
Another thing that looks suspicious is the order of the variables in the numerator of the very first integral. The integration variables seem to be written in reverse order. That makes me suspicious of the whole text, as to whether or not any of it is riddled with typos.

Last edited: Mar 14, 2015
15. ### WBahn Moderator

Mar 31, 2012
17,751
4,799
There are definitely some typos as well as some things that are taken for granted. The order of the differentials doesn't matter in this case because the integrals specify what the variable of integration is for each one. Normally, this is not the case and so the order of the differentials has to supply the cues to know which integration limits go with which differential. Still, it's sloppy to not keep them consistent.

16. ### JoeJester AAC Fanatic!

Apr 26, 2005
3,373
1,159
open office also opens word files as well as excel and power points.

https://www.openoffice.org/

I use the Microsoft products at home and open office at work.

17. ### MrAl Well-Known Member

Jun 17, 2014
2,438
492
Hi Joe and WBahn,

Joe:
Thanks for the link. I downloaded it and installed so now i have the program that can read the documents again. Now i just have to remember that i have it
I had used it in the past but didnt have much use for it as most people were posting graphics or just regular pdf's.
I also see that there may be a slight conversion issue, because the graphics seem 'cut off' at the top, unless that was the way they were made in the first place. I see those graphics are not 'formula' strings, but are actual graphics, probably created in another application and then copy and pasted into the Open Office app. I tried the 'formula' thing and it seems to make perfect math text and symbols.

WBahn:
Yes, that's what seemed strange, that the order was mixed up, even though we all know how it should be. When i see something like that i check the rest more carefully.
At MIT I've seen other notations by noted physicists that swap the 'differential' and the 'body', for example:
We normally write (with the symbol for integration rather than the word 'Integral'):
Integral 2*x^3 dx

but they might write this as:
Integral dx 2*x^3

(also with the symbol for integration).

18. ### WBahn Moderator

Mar 31, 2012
17,751
4,799
The problem I would have with the notation

$
\int dx 2x^3
$

Is that identifying the integrand becomes problematic and ambiguous. For instance, it would not be hard to construct a problem for which the solution worked out to be

$
$$\int 2 dx$$ $$x^3$$
$

Which they would then write as

$
$$\int dx 2$$ $$x^3$$
$

and since they would probably leave off the parens, might easily write it as

$
\int dx 2x^3
$

A more likely case would be something like

$
\int $$2x^2 + 3$$ dx
$

which they might write as

$
\int dx 2x^2 + 3
$

But now we don't know if the 3 is part of the integrand or not.

If they use a rule that the integration operator is applied to the next factor, then the ambiguity goes away because they would need to write it as

$
\int dx $$2x^2 + 3$$
$

But the question is -- would they.

We see all the time where people write

$
\int 2x^2 + 3 dx
$

which would properly parse as

$
$$\int 2x^2$$ + $$3 dx$$
$

So it can be argued either way. Using the integral as a single unary prefix operator may make it more likely that people will properly delimit the integrand (since they have no choice) whereas using the integral sign and the differential as the delimiters for the integral make it more likely that you can figure out what was intended even with the write is sloppy with properly delimiting the integrand.

I prefer to use the integral and differential to delimit the integrand AND to properly integrate it one its own, too. But then, as a pilot, I believe in backup systems.

19. ### TheSpArK505 Thread Starter Member

Sep 25, 2013
92
0
@MrAl @WBahn @DickCappels Guys thanks for ur responces , I have no problem with u method I'm just asking about the method used in the questio n

20. ### WBahn Moderator

Mar 31, 2012
17,751
4,799
Look over my response in Post #5 and see if that helps, or at least lets you make some headway so that you can ask a more specific question.