One long wire lies along an x axis and carries a current of

One long wire lies along an x axis and carries a current of 53 A in the positive x direction. A second long wire is perpendicular to the xy plane, passes through the point (0, 4.2 m, 0), and carries a current of 48 A in the positive z direction. What is the magnitude of the resulting magnetic field at the point (0, 1.2 m, 0)?

Solution

Magnetic field due to the wire on the x-axis is calculated as follows:
      B = µ₀I/2*pi*r

         =(4*pi*x10^-7*53)/(2)*pi*1.2

         = 8.83x10^-6 T in +z-axis

Magnetic field due to wire on the +z-axis is,

      B = µ₀I/2*pi*r

        = (4*pix10^-7*48)/(2)*pi*(4.2-1.2)

       = 3.2x10^-6 T       in +x-axis

The net magnetic field is,
B = sqrt((8.83x10^-6 )^2+(3.2x10^-6 )^2)

   = 9.39x10^-6 T

   = 9.4 uT