A long, straight wire lies along the y-axis and carries a current `I=8A` in the y-direction (as shown in Fig) In addition to the magnetic field due to the current in the wire, a uniform magnetic field `vecB_0` with magnitude `1.50xx10^-6T` is in the +x direction. What is the total field (magnitude and direction ) at following points in the plane?
(a)`x=0,z=1.00m`
(b) `x=1.00m,z=0`
(c) `x=0, z=-0.25m`

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`