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Consider an infinite solenoid (ideal solenoid) with n turns per length unit, through which a current () flows. The magnetic field inside the solenoid is, The magnetic field inside the solenoid is, B = μ n I ( t ) {\displaystyle \mathbf {B} =\mu nI(t)} (1)
Figure 1: An infinite solenoid with three arbitrary Ampèrian loops labelled a, b, and c. Integrating over path c demonstrates that the magnetic field inside the solenoid must be radially uniform. An infinite solenoid has infinite length but finite diameter.
Of course, the ideal case of infinite length is not realizable, and in practice the finite length of the cylinders produces end effects, which introduce non-uniformities in the field. [ 12 ] [ 13 ] The difficulty of manufacturing a cylinder with a continuously varying magnetization also usually leads to the design being broken into segments.
A solenoid is a one-dimensional homogeneous indecomposable continuum that has the structure of an abelian compact topological group. Solenoids were first introduced by Vietoris for the n i = 2 {\displaystyle n_{i}=2} case, [ 2 ] and by van Dantzig the n i = n {\displaystyle n_{i}=n} case, where n ≥ 2 {\displaystyle n\geq 2} is fixed. [ 3 ]
The strength of the magnetic field decreases with distance from the wire. (For an infinite length wire the strength is inversely proportional to the distance.) A Solenoid with electric current running through it behaves like a magnet. Bending a current-carrying wire into a loop concentrates the magnetic field inside the loop while weakening it ...
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