Help please A long straight wire lies along the yaxis and ca

A long, straight wire lies along the y-axis and carries a current I = 7.50 A in the -y-direction (see the following figure). In addition to the magnetic field due to the current in the wire, a uniform magnetic field B_0 with magnitude 1.20 Times 10^-6 T is in the +x-direction. What is the total field (magnitude and direction) at the following points in the xz-plane. (Give the smallest such angles.) x = 0, z = 5.00 m x = 5.00 m, z = 0 x = 0, z = -1.25 m

Solution

1. Given B0 = 1.2*10^-6 T (+x direction)

Bi = uo*i/2*pi*r = 4*pi*10^-7*7.5/(2*pi*5.00)

Bi = 3*10^-7 T (in -x drection)

Bt = Bi - B0 = 0.3*10^-6 - 1.2*10^-6 = 0.9*10^-6 (in + x direction)

2.

Given B0 = 1.2*10^-6 T (+x direction)

Bi = uo*i/2*pi*r = 4*pi*10^-7*7.5/(2*pi*5.00)

Bi = 3*10^-7 T (in +z drection)

Bt = sqrt(Bi^2+ B0^2) = sqrt(0.3^2*10^-12 + 1.2^2*10^-12) = 1.23*10^-6

direction = arctan(0.3/1.2) = 14.03 deg

3.

Given B0 = 1.2*10^-6 T (+x direction)

Bi = uo*i/2*pi*r = 4*pi*10^-7*7.5/(2*pi*1.25)

Bi = 1.2*10^-6 T (in +x drection)

Bt = Bi + B0 = 1.2*10^-6 + 1.2*10^-6 = 2.4*10^-6 (in + x direction)

Let me know if you have any doubt.