Table of Contents
| Stan Zurek, Cross-sectional area, Encyclopedia Magnetica,
The amount of cross-sectional area is typically important for maintaining flux of a given quantity, such such electric current or magnetic flux. In order to maintain the same flux within a smaller area the flux density must increase proportionally.
In technical texts, cross-sectional area is often simply referred to as “area”, but the difference from a generic “surface area” is usually clear from the context.
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For a conducting wire there is a maximum current that can be carried under given cooling conditions. Higher current density can be maintained for the same area if cooling is improved, for example by using forced or liquid cooling.
Limitation of maximum current density also applies to superconducting wires, but arises from the critical magnetic field limit (Silsbee's rule), because resistive losses are negligible in a superconductor, so no heat is dissipated as a result of the current flow.
Total cross-sectional area of a typical electric wire comprises the area of the conductor and the insulation. Hence, the effective cross-sectional area (the area available for conducting current) is appropriately smaller, related to the thickness of insulation. This less-than ideal amount of active area is related to window utilisation and fill factor.4)5)
In a magnetic core, a sufficient cross-sectional area is required so that the magnetic flux density does not reach saturation. For this reason, for power applications the cores are typically designed so that the cross-sectional area is roughly constant throughout the magnetic path, such as in ETD cores.
Conversely, sensors such as fluxgate, rely on local saturation of the magnetic material, which can be achieved by using “magnetic probe”, whose cross-sectional area is smaller than the rest of the core, and therefore easier to saturate.6)
Other types of circuits
For example, in the illustration on the right, a capacitor formed from two flat charged plates has a high-permittivity dielectric with changing cross-sectional area. The resulting electric flux density D increases in the part which has smaller cross-sectional area.
The flux of heat follows similar principles.