Solenoid Magnetic Field Calculator

The formula

wire B = µ₀I ÷ 2πr; solenoid B = µ₀nI; L = µ₀N²A ÷ l

Line sources fall off more slowly

A long straight wire's field falls as 1/r, not as an inverse square. That is not an exception to anything — it follows from the source being a line rather than a point, and integrating the contributions along it. A point source in three dimensions gives 1/r²; a line gives 1/r; an infinite sheet gives a field that does not fall off at all.

Inside a long solenoid the field depends only on the turn density and the current — not on the radius, and not on the total number of turns. Two solenoids of very different diameters with the same turns per metre produce identical interior fields. Inductance is different: it goes as the square of the total turns and with the cross-sectional area, so a fat coil stores far more energy at the same field.

The formula assumes a long solenoid. Below a length-to-diameter ratio of about five the ends leak appreciably and the real field is lower than calculated.

An iron core multiplies the field by its relative permeability, which can reach several thousand — but only until the core saturates, typically around 1.5 to 2 tesla, beyond which further current buys almost nothing. Note that µ₀ has been a measured quantity since the 2019 SI redefinition; it is no longer exactly 4π×10⁻⁷.