In my physics lab class, we were allowed to come up with our own research question and then try to answer it. My question was whether permanent magnets (i.e., things like refrigerator magnets) would also have the characteristic that B decays with 1/distance as we see for the B created by current in a straight wire.
To answer this, I measured the magnetic field using a magnetometer at various distances from the magnet and then plotted 1/R vs. B in a linear fit, and B vs. R in a semi-log and log-log fit. For all the fridge magnets studied, the chi-square value of the best fit line in the semi-log plot was much closer to 1 than in the other fits and the residuals were all near zero, indicating that the semi-log was the best fit (and not only the best fit, but a very good fit over all) and the relationship between B and R was best modeled by an equation of the form B = Ae-CR. Why is this?
Why would permanent magnets have an exponential relationship with R? I don't need to know the answer to this question for my project. I just need to present the data, but I wondered if anybody knows why this might be.