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?

 

[nlightner]

Your answer is partially correct. The direction of the magnetic field of the Earth is indeed pointing north, but the direction of the magnetic field of the wire depends on the direction of the current. Since the current is going down, the magnetic field of the wire would be pointing in the opposite direction, which is up.

Therefore, the vectors would look like this: B of Earth pointing north and B of wire pointing up, resulting in a resultant field that is pointing in a northwestern direction.

It is important to note that the strength of the magnetic field of the wire would depend on the distance from the wire, while the strength of the Earth's magnetic field would remain constant. This means that the resultant field would also vary in strength depending on the distance from the wire.

In conclusion, the compass would point in a northwestern direction due to the combined effect of the Earth's magnetic field and the magnetic field of the wire, with the strength and direction of the resultant field depending on the distance from the wire.