# Toroidal Helical Coils

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Toroidal helical coils have applications in electrical machinery such as transformers, motors, and antennas. This Demonstration shows some examples of the geometry of toroidal coils with helical windings.

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Contributed by: Erik Mahieu (August 2015)

Open content licensed under CC BY-NC-SA

## Snapshots

## Details

The parametric equations for the torus are

,

where is the radius of the torus ring and is the radius of the tube.

The parametric equation of a helix wound around the torus is

,

where is a constant defining the longitudinal offset of the helix from a zero reference, is the number of helical windings, and is the number of turns per winding.

The parameter is the winding direction: for right and for left.

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