A current running through a circular coil of wire produces a magnetic field B, which is directed along the axis perpendicular to the plane of the coil. This field is given by B_c=μ_0 NI/D, with N being the number of turns in the coil, I being the current of the coil, and D is the diameter of the coil. If the axis of this coil is oriented so that is in the magnetic East-West direction, if you calculate the magnitude of the coil’s field, then the horizontal component of the earth’s magnetic field B_h may be found from measuring the compass’s deflection through angle θ away from the magnetic north using the equation tanθ=B_c/B_h .
The purpose of this lab was to determine what the horizontal component of the earth’s total magnetic field is. The first step in the procedure was to determine the standard value of Earth’s magnetic field at Boise, ID, we did this by using the NOAA magnetic field calculator and entering the latitude, longitude and elevation of Boise, which were 43.6 degrees N, 116.2 degrees W and 850 m respectively. Then we placed our compass at the center of our coil such that it pointed in the plane of the coil, making the axis of the coil perpendicular to magnetic north. Then we turned the V coarse on the power supply to roughly ¼ of a turn, then we turned it on not exceeding 1 A of current aligning the compass with the resultant horizontal magnetic field due to both the earth and coil. Then we adjusted our current to around .7 amps, so that our compass needle would deflect from north by an angle between 30 and 60 degrees. We then recorded our offset which we got to be 78 degrees for a current of 0.67 A. Then we turned off the power supply and physically reverse our wires, reversing our current. Then we turned the power supply and recorded our offset for the reversed circuit which we found also equaled 78 degrees. Then we calculated B_c which we found equaled 6.31*〖10〗^(-5)T. The we plugged our average offset which was 78 degrees and our B_c into equation two a found that B_h=1.34221*〖10〗^(-5)T. Then we repeated the process to reach a total of 4 data points, each with varying values of I. The I values we chose were 0.18A, 0.34A and 0.55A which had average offsets of 49, 64, 72 degrees respectively, B_c values of 1.7*〖10〗^(-5)T, 3.2*〖10〗^(-5)T and 5.18*〖10〗^(-5)T respectively and B_h values of 1.47471*〖10〗^(-5)T, 1.5629*〖10〗^(-5)T and 1.68426*〖10〗^(-5)T respectively. Averaging these B_h values we got an experimental value of 1.52*〖10〗^(-5)T, which when compared to our actual B_h of 2.03*〖10〗^(-5)T gave us a percent error of 25.378%.
Using the equations B_c=μ_0 NI/D and tanθ=B_c/B_h we were able to calculate the horizontal component of the earth’s magnetic field, which for currents of 0.18A, 0.34A, 0.55A, and 0.67A we got B_h values of 1.47471*〖10〗^(-5)T1.5629*〖10〗^(-5)T, and 1.68426*〖10〗^(-5)T, and 1.34221*〖10〗^(-5)T and when average gave us an experimental B_h of 1.52*〖10〗^(-5)T. The actual B_h of the earth is 2.03*〖10〗^(-5)T, which gives us a percent error of 25.378%. One reason for the error we had was that all our measurements were taken by just looking at the compass, the lack of precise instruments to take measurements for meant less precise data and a higher error. Also the magnetic field of the wires interacted with the compass, causing the offset to be different then in if it was just the magnetic field of the coil, with the compass pointing more in the direction of the wire than it should.
The observations made in the experiment that the magnetic field of a coil will vary depending on what the current in that coil is. Having a higher magnetic field when the current is higher and vice versa, but the magnetic field of the earth is a constant. The percent error of 25.387% show that this experiment was not very accurate, with unprecise measurements and magnetic fields of the wire causing a significant change for the calculation of both B_c and B_h. The experiment demonstrated that you can change the magnetic field of a coil can be changed by changing the number of loops or the current of the coil, but the magnetic field of the earth stays the same causing an angle θ to formed between the two magnetic fields.
Both of the leads in this experiment will produce a magnetic field since they have a current running through them, and this magnetic field magnetic field will interact with our compass causing our results to not be as accurate. The reason they are twisted is the cause their magnetic field to overlap canceling them out for the most part. A real life application of earth magnetic field is in navigation especially that using a compass, the magnetic field of the compass when not acted on by other magnetic field will point straight towards the earth’s magnetic north allowing you know which direction you are headed and today magnetic compasses are still widely used on both ships and aircrafts as they are more reliable than other physical measurements.