The resolution parameter
A key parameter in BiotSavart is the resolution of a conductor. This is how finely the conductor is to be subdivided in order to calculate the magnetic field generated by the conductor. A ten thousand turn solenoid is not recommended to be calculated by summing ten thousand loops. Sufficient accuracy for most purposes is obtained by approximating the solenoid by a smaller number of loops (called elements) that each represent many of the real loops in the solenoid.
The figures below show the elements of a solenoid for several resolutions. The solenoid is 20mm long, 3mm inner radius, and 10mm outer radius. With a wire diameter of 150 micron, packed hexagonally, the number of turns is 7184. The resolutions used in the figures below give a much smaller number of elements. While many people might prefer the very finely divided solenoid, or something even finer, the coarsest solenoid (30 loops) is already a good enough approximation for most purposes, allowing one to calculate fields near the axis of the solenoid to within 0.2%. The main effect of decreasing the resolution is to increase the computation time.
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| Resolution 2mm | Resolution 1mm | Resolution 0.5mm |
The moral of this story: choose the resolution wisely.
