Distribution of magnetic field strength H on the axis of round and rectangular solenoids with the same length L and similar diameters (d, D) or side widths (a, b), all values are plotted as relative to the “ideal” $H=N·I/L$.
For a “long” solenoid (such that L»d) the field is very uniform in the middle half of the length (from x=-0.25 to x=0.25). At the edges of the field reduces roughly to half of the value in the middle.
The data is generated by S. Zurek, using equations from:
solenoids_round_rectangular_magnetica.png
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S. Zurek, Encyclopedia Magnetica, CC-BY-4.0
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