Compasses and Magnetic Field: B of Earth with respect to B of wire

[jamba88]

Homework Statement

The current in the wire is going down. The wire is in the z axis position going up and down. A compass is placed below the wire...for example the wire passes through (0,0) the origin on the x, y plane. The compass would be placed in the (0,-1) position on the x,y plane.

Show the vector diagram of the two magnetic fields (B of Earth and B of wire) and the resultant field.

Homework Equations

None

The Attempt at a Solution

I'm not sure if my answer is right:

The direction of the magnetic field is clockwise. If a compass is placed south of the wires the direction of the magnetic field should be pointing directly to the left, since at a pt the direction of a magnetic field is tangent to that point on the magnetic field.

Therefore, should the vectors look like this: B of Earth pointing directly North and B of wire pointing directly west. the resultant field should be between those two vectors making a 45 degree angle with a direction Northwest.

 

[LowlyPion]

The direction of the magnetic field is clockwise. If a compass is placed south of the wires the direction of the magnetic field should be pointing directly to the left, since at a pt the direction of a magnetic field is tangent to that point on the magnetic field.

Therefore, should the vectors look like this: B of Earth pointing directly North and B of wire pointing directly west. the resultant field should be between those two vectors making a 45 degree angle with a direction Northwest.

It looks like you've got the directions right, but unless the magnitude of the B field from the wire is equal to that of Earth, it would not necessarily be at 45 degrees would it?