A long straight wire along the Z-axis carries a current I in the negative z-direction. The magnetic vector field B at a point having coodinates (x, y) in the z = 0 plane is

Explanation

The total magnetic field is the vector sum of the constant magnetic
field and the wire's magnetic field.
(a) At (0,0,1m):
`vecB=vecB_0-(mu_0I)/(2pir)hati=(1.50xx10^-6T)hati-(mu_0(8.00A))/(2pi(1.00m)) hati`
`=-(1.0xx10^-7T)hati`
(b) At (1m,0,0):
`vecB=vecB_0+(mu_0I)/(2pir)hatk`
`=(1.50xx10^-6T)hati +(mu_0(8.00A))/(2pi(1.00m))hatk`
`vecB=(1.50xx10^-6T)hati+(1.6xx10^-6T)hatk`
`=2.19xx10^-6T`
at `theta=46.8^@` from x to z.
(c) At (0,0,-0.25m):
`vecB=vecB_0+(mu_0I)/(2pir)hati`
`=(1.50xx10^-6T)hati +(mu_0(8.00A))/(2pi(2.5m))hati`
`=(7.9xx10^-6T)hati`