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Re: Integrating over 3D vector

  • To: mathgroup at smc.vnet.net
  • Subject: [mg128384] Re: Integrating over 3D vector
  • From: pw <p.willis at telus.net>
  • Date: Thu, 11 Oct 2012 02:10:28 -0400 (EDT)
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  • References: <20121004033915.2CDC06871@smc.vnet.net> <513F5F84AADF427991A95D687F8E5492@JEROMEPC> <20121005064847.53C5C6858@smc.vnet.net> <DD5AE69A35CE44D89F02E6C12507EC1D@JEROMEPC> <20121009043627.6A017685B@smc.vnet.net> <80FE834A8C554DEF886678E43F0BF4D4@JEROMEPC>

Hello,

I see what you are getting at.
You have demonstrated the vector direction and force along
the 3D wire path according to biot-savart.

I took the liberty of rewriting the code sections from the
notebook you sent so that I could rearrange things and
enter (iterate) more numbers.

This is very close to what I was looking for.
I have not had much chance to do much more than look at
your notes and rearrange your code into programmatic space.

I will attempt to rearrange the code to allow me to make
a volumetric plot with a series of fixed distances from the wire.

What I hope is that I can ultimately step my way along
equally spaced positions along the (any) path and
iterate through a series of radial distances from those.



Peter



On 10/09/2012 05:09 PM, mathgroup wrote:
> Here are 2 examples of a odd wire shape for 2D and 3D geometries......
>
> I used the parameter 's' to define  x,y,z of the wire......and than
> performed an integration over the variable 's'.....assumed CCW current....
>
> here are the results...I tested them with several  locations along the x
> and y axes  that would tell me if my results were correct and they seem
> correct.....I made the H vectors larger than the actual values to make
> it easier to see the vectors.......unfortunately, I had to use
> NIntegrate because dH was too complicated....
>
>
> jerry b.....
>
> -----Original Message----- From: pw
> Sent: Monday, October 08, 2012 11:36 PM
> To: mathgroup at smc.vnet.net
> Subject: Re: Integrating over 3D vector
>
> Hello,
>
> The attachment is interesting in the linearity of the procedure
> used to solve the problem.
>
> I am, however, thinking that it may be more efficient to simply
> calculate a linear integral over the full calculated length
> (straight length) of the wire, and then simply transform the
> results into the direction and 3D position of each point
> on the wire. Then simply perform integration of the 3D
> results by position within the volume of the winding space.
>
>
> Peter
>
>
>
> On 10/06/2012 08:52 AM, mathgroup wrote:
>> I don?t know you're background, so don?t know if this is of value to you
>> or not....
>>
>> here are 2 examples of biot savart calculations for a triangle and a
>> loop.....it's interesting that, unfortunately,in each case I had to use
>> Integrate with GenerateConditions->False, otherwize it took forever to
>> do the integrals...this often happens with definite integrals...
>>
>>
>> jerry b
>>
>> -----Original Message----- From: pw
>> Sent: Friday, October 05, 2012 1:48 AM
>> To: mathgroup at smc.vnet.net
>> Subject: Re: Integrating over 3D vector
>>
>>
>> Hello,
>>
>> I think I need to do a line integral like NIntegrate[].
>>
>> I think I may just need to collect single position integrals
>> and then transform the integrals using the 3D coordinates...
>>
>> Thank you for mentioning the Classroom Assistant Palette,
>> that was very useful.
>>
>> Current linux distro is Ubuntu PP . Mathematica distro is 8.04.
>>
>> I am looking to integrate magnetic flux along a series of curved
>> windings.
>>
>>
>> Peter
>>
>>
>> On 10/04/2012 02:33 PM, mathgroup wrote:
>>> several questions....
>>>
>>> 1.  of course, you can nest integrals....I personally use the Classroom
>>> Assistant palette and put together the number of integrals I want....
>>>
>>> 2.  sometimes getting vector potential A is easier....etc..
>>>
>>> 3.  could you tell me exactly what the current distribution is.....I'm
>>> assuming from what you say that there isnt any symmetry to break it down
>>> into one integral only, e.g. circular loop....
>>>
>>>
>>> If you are interested, I can send you a double integral example to
>>> calculate the force between a wire along the z axis and a square loop
>>> positioned away from it....this involves double integrals....
>>>
>>> jerry blimbaum
>>>
>>> -----Original Message----- From: pw
>>> Sent: Wednesday, October 03, 2012 10:39 PM
>>> To: mathgroup at smc.vnet.net
>>> Subject: Integrating over 3D vector
>>>
>>> Hello,
>>>
>>> Biot?Savart Law is used to calculate the magnetic field strength
>>> at some vector location relative to the path of a conductor.
>>>
>>> The function of the law requires integration along the path of the
>>> current in 3 dimensions which indicates 3D displacement.
>>>
>>> QUESTION: Is it possible to 'nest' a series of integrals
>>> that follow the series of XYZ coordinates.
>>>
>>> ie: Integrate[{x1,x2,x3},
>>>        Integrate[{y1,y2,y3},
>>>          Integrate[{z1,z2,z3},
>>> ....
>>>          ]
>>>        ]
>>>      ];
>>>
>>>
>>> Thanks for any interest,
>>>
>>> Peter
>>>
>>>




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