Using a 2005 Student Version of Maxwell ™ 2-D electromagnetic field software, I generated field plots for single magnetic pickup poles in cylindrical coordinates (r, z). The left side of the plot is r = 0, the center of the pole. So a rectangle to the right represents 1/2 of a rod or disk. The major grid marks are 0.5 inch, and the minor grid marks are 0.1 inch. Be aware that this does not take into account the influence of adjacent poles in a 6-pole pickup. But as I recall, where one field overlaps another, field strengths add linearly in air or vacuum.
The plots on the left are flux line, 40 per graph, in linear mode. They do not show the absolute strength of the field so much as its relative distribution. Where lines are closer together, the field is stronger.
Magnetic B Field
The plots on the right show the magnetic B field. I am not prepared to explain that; it’s been a very long time since I took those courses, and the textbooks are lost in storage. Suffice it to say that this shows a measure of absolute strength. The lines are strength in 40 logarithmic steps from 0.001 to 2 (units of Tesla, I think). The equation for the multiplier from one line to the next should be somethink like:
0.001 x r^(40) = 2, or ln(r) = ln(2000)/40, or r = 1.20928
So if the farthest line out from the pole is of strength 0.001, the next line in is 0.00121, followed by 0.00146, 0.001768, 0.002138, etc. If a plot has 5 lines that extend farther out than a second plot, then the relative increase in magnetic field of the first plot over the second at the outermost line of the second should be about r^5 = 2.586 times
Steel pole with Ceramic 8D magnet in the base
ALNICO 5 pole
The Alnico 5 magnetic pole is the same size as the steel pole in the previous plot. Note that the flux lines are concentrated at the ends of the Alnico pole, and closer to the pole in the middle than for the steel pole with the ceramic magnet. The field extends farther up, about 3 lines in the right-hand plot, for an increase in strength of about 1.77 times. One might expect this pole to produce a more sensitive pickup.
ALNICO 5 pole with steel base plate
In this example, a 1008 steel base plate of 1.0″ dia x about 1/16″ thick has been added to the bottom of the Alnico 5 pole. It moves the concentration of flux lines away from the bottom of the Alnico pole. Note that in effect, the plate pushes the field up slightly, so that it is about 1.209 times stronger where the pole without the plate has a field strength of about 0.001.
This raises a question: should the pickup coil be wound with the most turns where the field is strongest (the flux lines thickest)? Without much more expensive simulation software, it can only be answered by experiment. Even with software that takes account of dynamic fields and currents, it would still have to be verified by experiment.