From the Greek Solen "pipe, channel". Other name: cable.

 

For a central curve with current point and curvilinear abscissa s, parametrization of the solenoid with radius a: where and , the angle y being the angle of torsion (see the notations).

The solenoids with central curve (or "bore") a curve are the curves that coil evenly around tubes centered on .
 

The solenoid is right-handed for k > 0 and left-handed for k < 0.

The solenoidal curves with linear bore are the circular helices and the solenoidal curves with circular bore are the toric solenoids.

See also the rotoids, which are to the solenoids what the helicoids are to the circular helices.

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© Robert FERRÉOL  2018