A current-carrying wire is placed directly across of a compass along the north south line as shown. The current flows north along the wire and produces a magnetic field of 3.25X10^-5T. Calculate the compass angle of deflection from north. The earth's magnetic field is 5X10^-5T.
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. (Note scale may be skewed)
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))`
`theta=tan^(-1)((3.25times10^(-5) T)/(5.00times10^(-5) T))~~33^@`
Physics 6th Ed. Giancoli