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 wire 1

B1 = uo*i1/(2*pi*r1) k

B1 = 4*3.14*10^-7*53/(2*3.14*4.2) = (2.52*10^-6 T) k

Magnetic field due to wire 2

The distance from the second wire to the point where we are calculating net B
is r2 = 4.2 m - 1.2 m = 3 m.

B1 = uo*i2/(2*pi*r2) i

B1 = 4*3.14*10^-7*48/(2*3.14*3) = (3.2*10^-6 T) i

Bnet = sqrt(B2^2 + B1^2)

|Bnet| = 10^-6*sqrt(2.52^2 + 3.2^2) = 4.07*10^-6 T