20 Netting
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What is the net magnetic field 20.0cm due west of the wire if the Earth's magnetic feid points down 40 degree
A long horizontal wire carries 22.0 A of current due north. What is the net magnetic feild 20.0 cm due west of the wire if the Earth's field there points downward, 40 degrees below the horizontal, and has magnitude 5.0X10^-5 T.
How should I go about solving the problem if the answer is 4.0x10^-5T, 15 degrees below the horizontal.
The net magnetic field is the vector sum of the magnetic fields due to the current in the wire and the Earth.
You are told the magnetic field vector due to the Earth, so you only need to find the magnetic field due to the wire now.
The magnetic field produced by an infinitely long current carrying wire is:
B = (μ * I) / (2 * π * d)
Where μ is the magnetic permeability of free space (1.2566 E-6 Wb / A m), I is the current through the wire, π is the ratio of the circumference of a circuit to its diameter (3.1415…..), and d is the distance away from the wire that you wish to measure its magnetic field.
This will give us the magnitude of the magnetic field, but we also need the direction in order to properly add the two magnetic field vectors.
Using the right-hand-rule, one can determine the way the magnetic field will wrap around the wire.
Point your hand-hand thumb in the direction of the current and your other 4 fingers will wrap around the wire in the same direction as the magnetic field will point. At a position which is on the same plane as the wire, the magnetic field will either be pointing entirely out of (upward) or into the (downward) plane.
Once you get the magnetic field vector, simply add it to the Earth’s magnetic field to get the net magnetic field at that point. (Remember to break the Earth’s magnetic field up into its components since it is not acting totally in a single direction, but at an angle)