Respuesta :
Answer:
The magnitude of the magnetic field at the origin is [tex]2.56\times 10^{-6}\ T[/tex].
Explanation:
Given :
50-A wire is in the x-z plane and is 5 m from the z axis.
Also , 40-A wire is in the y-z plane and is 4 m from the z axis.
Now , since both the wire are perpendicular to each other .
Therefore , magnetic field are also perpendicular to each other .
Magnetic field at origin due to wire 1 is :
[tex]B_1=\dfrac{\mu_oI_1}{2\pi R_1}\\\\B_1=\dfrac{(50)\mu_o}{2\pi( 5)}\\\\B_1=\dfrac{5\mu_o}{\pi}[/tex]
Magnetic field at origin due to wire 2 is :
[tex]B_2=\dfrac{\mu_oI_2}{2\pi R_2}\\\\B_2=\dfrac{(40)\mu_o}{2\pi( 4)}\\\\B_2=\dfrac{4\mu_o}{\pi}[/tex]
Now , therefore net magnetic field is :
[tex]B=\sqrt{B_1^2+B_2^2}\\\\B=\sqrt{(\dfrac{5\mu_o}{\pi})^2+(\dfrac{4\mu_o}{\pi})^2}\\\\B=\dfrac{\sqrt{41}\mu_o}{\pi}[/tex]
Putting value of [tex]\mu_o=4\pi \times 10^{-7}\ H/m[/tex]
We get ,
[tex]B=\sqrt{41}\times 4\times 10^{-7}\\B=2.56\times 10^{-6}\ T[/tex]
Therefore, the magnitude of the magnetic field at the origin is [tex]2.56\times 10^{-6}\ T[/tex].
