# length and area and volume

Discussion in 'Math' started by TimeZero, Oct 11, 2015.

1. ### TimeZero Thread Starter New Member

Sep 14, 2015
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hi

Who can explain to me how brief length and area and volume?

2. ### crutschow Expert

Mar 14, 2008
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And this is related to circuits how?
I think you are in the wrong forum.

TimeZero likes this.
3. ### TimeZero Thread Starter New Member

Sep 14, 2015
18
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LOL

do you have good forum for math ?

4. ### atferrari AAC Fanatic!

Jan 6, 2004
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Isn't one about math and science?

5. ### Papabravo Expert

Feb 24, 2006
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Ok. a couple of things you need to know first.
1. Do you know that ax, ay, and az are unit vectors in the direction of the x, y, and z axes respectively?
2. Do you know the × operation is the vector cross product?
3. Do you know how to evaluate a vector cross product?
When you can answer those three questions we can proceed.

Sep 14, 2015
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7. ### TimeZero Thread Starter New Member

Sep 14, 2015
18
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this is for electromagnetic

8. ### Papabravo Expert

Feb 24, 2006
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OK. So let us take the first one. A differential length dl is the summation of the length dx times the unit vector in the x direction ax, plus the length dy times the unit vector in the y direction ay, plus the length dz times the unit vector in the z direction. This vector sum produces a vector of the correct length with an orientation that depends on the magnitudes of the scaler quantities dx, dy, and dz. Are we OK with that?

RRITESH KAKKAR likes this.

Sep 14, 2015
18
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ok nice

10. ### Papabravo Expert

Feb 24, 2006
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The differential volume element is also pretty easy to grasp since it is just a cube of infinitesimally small size made up of sides with infinitesimally small lengths, namely dx, dy, and dz.

Area is the tough one to grasp, until you realize that the cross product of two vectors produces a pseudo vector that is perpendicular to both, and which has a magnitude proportional to the differential area with sides dx by dy, or dx by dz, or dy by dz.

Are you still with me?

https://en.wikipedia.org/wiki/Pseudovector
https://en.wikipedia.org/wiki/Poynting_vector

11. ### TimeZero Thread Starter New Member

Sep 14, 2015
18
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I do not understand the area , why ds1= dy dz ax?

ds2= dz dx ay?

ds3= dy dz az?

12. ### Papabravo Expert

Feb 24, 2006
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ds1 has a magnitude of dy dz and a direction of ±ax, where ax is the unit vector in the x direction. Similarly for the other two directions.

13. ### RRITESH KAKKAR Senior Member

Jun 29, 2010
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from what job?

14. ### Papabravo Expert

Feb 24, 2006
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Hardware design, firmware development, and financial planning.

15. ### jssamp New Member

Jun 19, 2014
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Wow. Interesting interplay in this thread. Makes me realize how hard it would be to be a calculus teacher. Once you have it and use it all the time it becomes second nature. It is in trying to explain ideas like curl that I am glad I chose engineering over education. Good job PapaBravo. In some forums people aren't always so patient and willing to stay with it.

16. ### Papabravo Expert

Feb 24, 2006
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To be fair, I didn't get many of the concepts with my first bite at the apple -- so to speak. It wasn't until I took Fluid Dynamics that these concepts became cemented inside my thick skull. I really really loved that class.

Jun 29, 2010
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18. ### jssamp New Member

Jun 19, 2014
3
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Do you have any insight into polarization density, permittivity, and the D-field that might help me to make it click? Getting bogged down in my E&M class.

19. ### Papabravo Expert

Feb 24, 2006
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Nothing comes to mind, except divide an conquer. More pointed questions would be helpful to understand what is giving you trouble.

20. ### Papabravo Expert

Feb 24, 2006
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I never did any projects on my own that I retained the rights to post and publish. Many of them were done in the era from 1969 to 1992 on paper which got left behind each time I changed employers.