Two long, parallel, current-carrying wires lie in an xy-plane. The first wire lies on the line y = 0.300 m and carries a current of 26.0 A in the +x direction. The second wire lies along the x-axis. The wires exert attractive forces on each other, and the force per unit length on each wire is 295 µN/m. What is the y-value (in m) of the line in the xy-plane where the total magnetic field is zero?

The y-value  is  z = 0.759 m

Explanation:

From the question we are told that

     The position of the first y-axis is  

     The current on the first wire is  

      The force per unit length on each wire is  

Generally the force per unit length on first wire is mathematically represented as

Where   is the permeability of free space with value  

    substituting values

Now the at the point where the magnetic field is zero the magnetic field of each wire are equal , let that point by z meters from the second wire on the y-axis  so

substituting values

         z = 0.759 m

distance = 150m

displ = root (50 ^2 + 100^2)

root(2500+10000)

root 125000