Answer:
The y-value of the line in the xy-plane where the total magnetic field is zero [tex]U = 0.1355 \ m[/tex]
Explanation:
From the question we are told that
The distance of wire one from two along the y-axis is y = 0.340 m
The current on the first wire is [tex]I_1 = (27.5i) A[/tex]
The force per unit length on each wire is [tex]Z = 295 \mu N/m = 295*10^{-6} N/m[/tex]
Generally the force per unit length is mathematically represented as
[tex]Z = \frac{F}{l} = \frac{\mu_o I_1I_2}{2\pi y}[/tex]
=> [tex]\frac{\mu_o I_1I_2}{2\pi y} = 295[/tex]
Where [tex]\mu_o[/tex] is the permeability of free space with a constant value of [tex]\mu_o = 4\pi *10^{-7} \ N/A2[/tex]
substituting values
[tex]\frac{ 4\pi *10^{-7} 27.5 * I_2}{2\pi * 0.340} = 295 *10^{-6}[/tex]
=> [tex]I_2 = 18.23 \ A[/tex]
Let U denote the line in the xy-plane where the total magnetic field is zero
So
So the force per unit length of wire 2 from line U is equal to the force per unit length of wire 1 from line (y - U)
So
[tex]\frac{\mu_o I_2 }{2 \pi U} = \frac{\mu_o I_1 }{2 \pi(y - U) }[/tex]
substituting values
[tex]\frac{ 18.23 }{ U} = \frac{ 27.5 }{(0.34 - U) }[/tex]
[tex]6.198 -18.23U = 27.5U[/tex]
[tex]6.198=45.73U[/tex]
[tex]U = 0.1355 \ m[/tex]
