Thoughts on the Magnetic Field in a Toroid

There has been some discussion on whether it is better to wind inductors as a torroid or as a solenoid on non magnetic material.

Magnetic lines of force add vectorially. They do not influence one another. Hence:
In a long close-wound solenoid, (i.e. l » d), the magnetic field from “near” turns i.e. within a length equivalant to ‘d’ leak out from the cross-section of the solenoid through neighbouring turns and similarly return externally to their coil. The result of this is that the field near the centre of the solenoid is proportional to the number of turns per unit length rather than to the total number of turns*. I.e. The field doesn’t get stronger as the solenoid gets longer .

Near the centre of a long solenoid, the field is uniform across the cross-sectional area of the solenoid*.

The field across the area at the end of a solenoid, (which can be regarded as a “half solenoid”), is half that at its centre*.

These observations are also true for a toroid if its diameter is » than the diameter of its cross section*.

The leakage of magnetic flux is therefore thought to be greater for a toroid than for a solenoid of the same number of turns, because of the angle of each turn to its neighbour, (resulting on poorer coupling), and because of the space between the outer edges of the turns, and thus its inductance is thought to be less. (Inductance confirmed by experiment Oct 2011).

*Principles of Electricity and Electro-Magnetism, Harnwell, p314.


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