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Brooks coil

A Brooks coils has the shortest length of wire for a given inductance.

The radius, height and width of a brooks coil are all the same yielding a square section coil shown here.

L 0.025391 c N 2 μ Η

Where c is the width and height of the coil in cm and N is the number of turns.

Coil Height/Width
N (# of Turns)

L (Inductance)
Inner Radius
Mean Radius
Outer Radius