Explore Westonci.ca, the top Q&A platform where your questions are answered by professionals and enthusiasts alike. Join our platform to connect with experts ready to provide accurate answers to your questions in various fields. Join our Q&A platform to connect with experts dedicated to providing accurate answers to your questions in various fields.
Sagot :
The question is incomplete. The complete question is :
A long, straight wire lies along the z-axis and carries a 3.90-A current in the + z-direction. Find the magnetic field (magnitude and direction) produced at the following points by a 0.600 mm segment of the wire centered at the origin.
A) x=2.00m,y=0, z=0
Bx,By,Bz = ? T
Enter your answers numerically separated by commas.
B) x=0, y=2.00m, z=0
C) x=2.00m, y=2.00m, z=0
D) x=0, y=0, z=2.00m
Solution :
The expression of the magnetic field using the Biot Savart's law is given by :
[tex]$d \vec B=\frac{\mu_0 I\vec{dl} \times \vec r}{4 \pi r^3}$[/tex]
a). The position vector is on the positive x direction.
[tex]$\vec r = (2 \ m) \ \hat i$[/tex]
[tex]$|r| = 2 \ m$[/tex]
The magnetic field is
[tex]$d \vec B=\frac{\mu_0 I\vec{dl} \times \vec r}{4 \pi r^3}$[/tex]
[tex]$d \vec B=\frac{4 \pi \times 10^{-7} \times 3.9 \times 0.6 \times 10^{-3} \times\hat k \times (2 ) \hat i }{4 \pi \times (2)^3}$[/tex]
[tex]$d \vec B=(5.85 \times 10^{-11} \ T)\hat j$[/tex]
The magnetic field is [tex]$(0, \ 5.85 \times 10^{-11} \ T, \ 0).$[/tex]
b). The position vector is in the positive y-direction.
[tex]$\vec r = (2 \ m) \ \hat j$[/tex]
[tex]$|r| = 2 \ m$[/tex]
The magnetic field is
[tex]$d \vec B=\frac{\mu_0 I\vec{dl} \times \vec r}{4 \pi r^3}$[/tex]
[tex]$d \vec B=\frac{4 \pi \times 10^{-7} \times 3.9 \times 0.6 \times 10^{-3} \times\hat k \times (2 ) \hat j }{4 \pi \times (2)^3}$[/tex]
[tex]$d \vec B=(5.85 \times 10^{-11} \ T)(-\hat{i})$[/tex]
The magnetic field is [tex]$(- 5.85 \times 10^{-11} \ T, \ 0, \ 0).$[/tex]
c). The position vector is :
[tex]$\vec r = (2)\hat i + (2)\hat j$[/tex]
[tex]$|\vec r| = \sqrt{(2)^2+(2)^2}$[/tex]
[tex]$=2.828 \ m$[/tex]
The magnetic field is
[tex]$d \vec B=\frac{\mu_0 I\vec{dl} \times \vec r}{4 \pi r^3}$[/tex]
[tex]$d \vec B=\frac{4 \pi \times 10^{-7} \times 3.9 \times 0.6 \times 10^{-3} \times\hat k \times ((2)\hat i + (2) \hat j) }{4 \pi \times (2.828)^3}$[/tex]
[tex]$=(4.13\times 10^{-11})\hat j+(4.13\times 10^{-11})(-\hat i)$[/tex]
The magnitude of the magnetic field is :
[tex]$|d\vec B|=\sqrt{(4.13\times 10^{-11})^2+(4.13\times 10^{-11})^2}$[/tex]
[tex]$=5.84 \times 10^{-11} \ T$[/tex]
Therefore, the magnetic field is [tex]$(-4.13 \times 10^{-11}\ T, \ 4.13 \times 10^{-11}\ T, \ 0 )$[/tex]
d). The position vector is in the positive y-direction.
[tex]$\vec r = (2 \ m) \ \hat k$[/tex]
[tex]$|r| = 2 \ m$[/tex]
The magnetic field is
[tex]$d \vec B=\frac{\mu_0 I\vec{dl} \times \vec r}{4 \pi r^3}$[/tex]
[tex]$d \vec B=\frac{4 \pi \times 10^{-7} \times 3.9 \times 0.6 \times 10^{-3} \times\hat k \times (2 ) \hat k }{4 \pi \times (2)^3}$[/tex]
= 0 T
The magnetic field is (0, 0, 0)
Visit us again for up-to-date and reliable answers. We're always ready to assist you with your informational needs. We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. Thank you for using Westonci.ca. Come back for more in-depth answers to all your queries.
