Filamentary coil - a hypothetical coil in which the diameter of the wire is infinitesimal.¹⁾ Such “thin” coils are used for derivation of certain analytical equations, such as the intensity of magnetic field generated along the axis of a current loop or a solenoid.

However, for infinitely thin wire the the magnetic field on its surface as well as the associated inductance would become infinite.

Any real coil is “thick” because there is always some physical thickness of the current-carrying conductors, so the magnetic field at the surface of real conductors is finite.

“Thin” solenoid ($d≈D$) with a circular cross-section

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Solenoid as a source of magnetic field

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Rectangular current loop

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• Current loop
• Helmholtz coil