Magnetic field from a current carrying wire + earth's field

[Jacob87411]

A long horizontal wire carries a 12.0 A of current due north. What is the net magnetic field 20.0 CM due west of the wire if the Earth's field there points downward 40 degrees below the horizontal, and has a magnitude of 5.0x10^-5


Unsure on how to start...Do you find the magnetic field produced by the wire and combine it with the Earth's? If so, I did that and found the field produced by the wire to be 1.2 x 10^-5, so how do you combine fields.

 

[HallsofIvy]

But remember that the magnetic field is a VECTOR quantity- that's why they told you that, at that point on the earth, the Earth's magnetic field pointed downward at 40 degree. Assuming that "due west" of the wire means at the same height as the wire, in which direction is the wire's magnetic field pointing? After you have both magnetic fields as vectors, add vectorially.

 

[Jacob87411]

So 20 cm west of the wire...find the magnetic field from the wire at that point, then add that vectorially with the Earth's..

20 CM due west would mean there is no angle so the magentic field should equal:

B=(2 * 10^-7) ( 12A/.2M)

Then add that vectorially with the Earth's field?