**Answer** 33° West of North

**Approach** Magnetic fields can be simplified as a vector. The two magnetic fields will superimpose using vector addition. The compass needle will point in the direction of the net magnetic field. Find the angle using trigonometry.

**Assumptions** The current-carrying wire is on top of the...

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**Answer** 33° West of North

**Approach** Magnetic fields can be simplified as a vector. The two magnetic fields will superimpose using vector addition. The compass needle will point in the direction of the net magnetic field. Find the angle using trigonometry.

**Assumptions** The current-carrying wire is on top of the compass (based on the description you gave). Right-Hand-Rule for magnetic field current in a wire suggests that the magnetic field underneath the wire is directed West. Thus, the two magnetic fields are at right angles to each other.

**Plan** Draw a picture to identify the angle in question.

Red represents the Earth's magnetic field, Blue represents the magnetic field due to the wire. Purple is the net magentic field. The angle in question is the angle made by the red and purple vectors.

`tan(theta)=B_(wire)/B_(earth)` so `theta=tan^(-1)(B_(wire)/B_(earth))`

**Calculate**

`theta=tan^(-1)((3.25times10^(-5) T)/(5.00times10^(-5) T))~~33^@`

**References**

Physics 6th Ed. Giancoli