Respuesta :
Answer:
The value of y is 0.136 m
Explanation:
Given that,
Y = 0.330 m
Current I₁= 26.5 A
Force per unit length [tex]\dfrac{F}{l}= 300\ \mu N/m[/tex]
We need to calculate the current of second wire
Using formula of magnetic force
[tex]\dfrac{F}{l}=\dfrac{\mu I_{1}I_{2}}{2\pi d}[/tex]
[tex]300\times10^{-6}=\dfrac{4\pi\times10^{-7}\times26.5\timesI_{2}}{2\times\pi\times0.330}[/tex]
[tex]I_{2}=\dfrac{300\times10^{-6}\times2\times\pi\times0.330}{4\pi\times10^{-7}\times26.5}[/tex]
[tex]I_{2}=18.68\ A[/tex]
We need to calculate the value of y where the total magnetic field is zero
Using formula of magnetic field
[tex]\dfrac{\mu_{0}I_{2}}{2\pi y}=\dfrac{\mu_{0}I_{1}}{2\pi(0.330-y)}[/tex]
Put the value in the equation
[tex][tex]\dfrac{4\pi\times10^{-7}\times18.68}{2\pi y}=\dfrac{4\pi\times10^{-7}\times26.5}{2\pi(0.330-y)}[/tex]
[tex]\dfrac{0.330-y}{y}=\dfrac{26.5}{18.68}[/tex]
[tex]\dfrac{0.330-y}{y}=1.4186[/tex]
[tex]0.330=1.4186y+y[/tex]
[tex]2.4186y=0.330[/tex]
[tex]y=\dfrac{0.330}{2.4186}[/tex]
[tex]y=0.136\ m[/tex]
Hence, The value of y is 0.136 m.
