The vector form of the Biot Savart equation is the
following:
![μοǐAS ที่)](//img.homeworklib.com/images/85c97769-4e6c-4fb1-9605-57f92647da66.latex?%5Cvec%7BB%7D%3D%5Cfrac%7B%5Cmu%20_%7B0%7Di%7D%7B4%5Cpi%7D%28%5Cfrac%7B%5Cvec%7B%5CDelta%7BS%7D%7D%5Ctimes%5Cvec%7Br%7D%7D%7Br%5E%7B3%7D%7D%29?x-oss-process=image/resize,w_560)
The first part of the right hand side of the equation is
constant:
![\vec{B}=4,1\times 10^{-7}N/A(\frac{\vec{\Delta{S}}\times\vec{r}}{r^{3}})](//img.homeworklib.com/images/24eeb913-1b26-4a8b-940a-725db29d11fb?x-oss-process=image/resize,w_560)
The length vector will also be constant:
![(0: 0. 0225m : 0)-(0:-0. 0225m: 0)-(0: 0. 045m : 0) ▲S](//img.homeworklib.com/images/0b057731-1bff-436c-8cd0-fc00406ad2b1.latex?%5Cvec%7B%5CDelta%20S%7D%3D%280%3B0%2C0225m%3B0%29-%280%3B-0%2C0225m%3B0%29%3D%280%3B0%2C045m%3B0%29?x-oss-process=image/resize,w_560)
a)
![(0: 0: 8m](//img.homeworklib.com/images/a18ac7a1-cb84-4b07-8e9b-0379184a5ab2.latex?%5Cvec%7Br%7D%3D%280%3B0%3B8m%29?x-oss-process=image/resize,w_560)
![AS0 0,045m 0(0, 36m2)i 0 0 8m](//img.homeworklib.com/images/828e6666-dd19-42bb-b0b3-551e786ca4ed.latex?%5Cvec%7B%5CDelta%20S%7D%5Ctimes%20%5Cvec%7Br%7D%3D%5Cbegin%7Bvmatrix%7D%20%5Cvec%7Bi%20%7D%26%5Cvec%7Bj%7D%26%5Cvec%7Bk%7D%20%5C%5C%200%260%2C045m%260%20%5C%5C%200%260%268m%20%5Cend%7Bvmatrix%7D%3D%280%2C36m%5E%7B2%7D%29%5Cvec%7Bi%7D?x-oss-process=image/resize,w_560)
![r^{3}=(\sqrt{0^{2}+0^{2}+(8m)^{2}})^{3}=512m^{3}](//img.homeworklib.com/images/0d482050-090b-40a1-977b-820cdd985426.latex?r%5E%7B3%7D%3D%28%5Csqrt%7B0%5E%7B2%7D+0%5E%7B2%7D+%288m%29%5E%7B2%7D%7D%29%5E%7B3%7D%3D512m%5E%7B3%7D?x-oss-process=image/resize,w_560)
![, 36m 512m3 --(2.88 × 10-10T)](//img.homeworklib.com/images/50b36505-92c2-4bc2-96e4-bd237ab230c4?x-oss-process=image/resize,w_560)
b)
![= (0: 8.2771:0)](//img.homeworklib.com/images/f61fafe3-0d02-4858-8e91-28d6fe318ae9.latex?%5Cvec%7Br%7D%3D%280%3B8%2C2m%3B0%29?x-oss-process=image/resize,w_560)
![ASXT.=|0 0|=0 0.045m 0 8,2m 0](//img.homeworklib.com/images/11a0cc59-be9a-4083-9a86-843bd0c4e2c9.latex?%5Cvec%7B%5CDelta%20S%7D%5Ctimes%20%5Cvec%7Br%7D%3D%5Cbegin%7Bvmatrix%7D%20%5Cvec%7Bi%20%7D%26%5Cvec%7Bj%7D%26%5Cvec%7Bk%7D%20%5C%5C%200%260%2C045m%260%20%5C%5C%200%268%2C2m%260%20%5Cend%7Bvmatrix%7D%3D0?x-oss-process=image/resize,w_560)
![\rightarrow B=0](//img.homeworklib.com/images/5b95746e-93c0-49f0-9ebb-9790e8cc9438.latex?%5Crightarrow%20B%3D0?x-oss-process=image/resize,w_560)
c)
![\vec{r}=(8,6m;7,3m;0)](//img.homeworklib.com/images/f8a542c4-44d8-49ba-8689-8ec86bc45bcd.latex?%5Cvec%7Br%7D%3D%288%2C6m%3B7%2C3m%3B0%29?x-oss-process=image/resize,w_560)
![\vec{\Delta S}\times \vec{r}=\begin{vmatrix} \vec{i }&\vec{j}&\vec{k} \\ 0&0,045m&0 \\ 8,6m&7,3m&0 \end{vmatrix}=(-0,387m^{2})\vec{k}](//img.homeworklib.com/images/5500d8bd-5a28-4748-8c9f-d926f62844b8.latex?%5Cvec%7B%5CDelta%20S%7D%5Ctimes%20%5Cvec%7Br%7D%3D%5Cbegin%7Bvmatrix%7D%20%5Cvec%7Bi%20%7D%26%5Cvec%7Bj%7D%26%5Cvec%7Bk%7D%20%5C%5C%200%260%2C045m%260%20%5C%5C%208%2C6m%267%2C3m%260%20%5Cend%7Bvmatrix%7D%3D%28-0%2C387m%5E%7B2%7D%29%5Cvec%7Bk%7D?x-oss-process=image/resize,w_560)
![r^{3}=(\sqrt{(8,6m)^{2}+(7,3m)^{2}+0^{2}})^{3}=1435,445m^{3}](//img.homeworklib.com/images/2a6aff24-3276-4378-8cd7-51c9f6802d16.latex?r%5E%7B3%7D%3D%28%5Csqrt%7B%288%2C6m%29%5E%7B2%7D+%287%2C3m%29%5E%7B2%7D+0%5E%7B2%7D%7D%29%5E%7B3%7D%3D1435%2C445m%5E%7B3%7D?x-oss-process=image/resize,w_560)
![(-0.387m2)k) = (-1. 105 × 10-10T)k 1435,445m3 4, 1](//img.homeworklib.com/images/c0c2b9f3-3f81-407f-a6dc-22cb7231317f?x-oss-process=image/resize,w_560)
d)
![\vec{r}=(-5,3m;-5,6m;0)](//img.homeworklib.com/images/bcb841b6-5ceb-4e2b-aad2-ab35f7bbc610.latex?%5Cvec%7Br%7D%3D%28-5%2C3m%3B-5%2C6m%3B0%29?x-oss-process=image/resize,w_560)
![\vec{\Delta S}\times \vec{r}=\begin{vmatrix} \vec{i }&\vec{j}&\vec{k} \\ 0&0,045m&0 \\ -5,3m&-5,6m&0 \end{vmatrix}=(0,2385m^{2})\vec{k}](//img.homeworklib.com/images/5439cdb9-d524-40f9-b7e6-1820a9dd5273.latex?%5Cvec%7B%5CDelta%20S%7D%5Ctimes%20%5Cvec%7Br%7D%3D%5Cbegin%7Bvmatrix%7D%20%5Cvec%7Bi%20%7D%26%5Cvec%7Bj%7D%26%5Cvec%7Bk%7D%20%5C%5C%200%260%2C045m%260%20%5C%5C%20-5%2C3m%26-5%2C6m%260%20%5Cend%7Bvmatrix%7D%3D%280%2C2385m%5E%7B2%7D%29%5Cvec%7Bk%7D?x-oss-process=image/resize,w_560)
![r^{3}=(\sqrt{(-5,3m)^{2}+(-5,6m)^{2}+0^{2}})^{3}=458,38m^{3}](//img.homeworklib.com/images/19168915-a6e6-4ab3-a5de-f8eee700b499.latex?r%5E%7B3%7D%3D%28%5Csqrt%7B%28-5%2C3m%29%5E%7B2%7D+%28-5%2C6m%29%5E%7B2%7D+0%5E%7B2%7D%7D%29%5E%7B3%7D%3D458%2C38m%5E%7B3%7D?x-oss-process=image/resize,w_560)
![\vec{B}=4,1\times 10^{-7}N/A(\frac{(0,2385m^{2})\vec{k}}{458,38m^{3}})=(2,13\times 10^{-10}T)\vec{k}](//img.homeworklib.com/images/17342eea-ca78-42a2-9c99-b97f91d5c39d?x-oss-process=image/resize,w_560)
μοǐAS ที่)
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(0: 0. 0225m : 0)-(0:-0. 0225m: 0)-(0: 0. 045m : 0) ▲S
(0: 0: 8m
AS0 0,045m 0(0, 36m2)i 0 0 8m
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, 36m 512m3 --(2.88 × 10-10T)
= (0: 8.2771:0)
ASXT.=|0 0|=0 0.045m 0 8,2m 0
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(-0.387m2)k) = (-1. 105 × 10-10T)k 1435,445m3 4, 1
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