Yesterday, we mapped the magnetic field of a bar magnet and of the earth. We said the Earth was an extra influence and that the true map of a dipole could be obtained by removing the Earth Map from the Dipole Map. Unfortunately, the separation of the two contributions is not straightforward and enough information has not been gathered to fully separate the contributions. In particular, we have little information on the actual strength (magnitude) of the magnetic fields. We will use two different methods to get a sense of the relative strength of the dipole field in relation to the earth field. The second method will yield a numerical result but we note it is only valid (as done below) along the line of calculation.
The first method will be to overlay and compare the earth and bar magnet maps. We will reason about the combined image. We will note that far from the bar magnet, the earth dominates. The earth is less important as a contributor to the observation of the bar magnet map as we get closer to the bar magnet itself. This can be seen from the triangle inequality and/or the Pythagorean Theorem. To coordinate these differing regions of dominance, we must remind ourselves that the arrows we drew represent direction only and have no relationship to the strength of the magnetic influence. Thus, the visual subtraction is not as simple as subtracting a constant amount from every observation.
The second method allows a numerical calculation along the earth's north-south magnetic axis. The measurement of the magnitude of the magnetic field is difficult without modern equipment or a standardized reference value. We have neither. This lab allows students to calculate the change in strength of the bar magnetic field assuming a specific geometry relative to the earth field. The bar magnet will point East-West while measurements are taken along a line pointing magnetic north. From the observations, students will make a graph that shows the inverse power law behavior of the magnetic field strength (of a dipole) as a function of distance from the center of the magnet. Complicating this measurement is the fact that we are constantly immersed in the magnetic field of the Earth.
The suggested homework asks the students to PREDICT the map they would observe for
5 different arrangements of 2 bar magnets. The subsequent activity to this one will
involve testing the predictions.