Editing Electromagnet (section)

==== Closed magnetic circuit ====
[[File: Lifting electromagnet cross section.png|thumb|Cross section of a lifting electromagnet, showing the cylindrical construction. The windings (''C'') are flat copper strips to withstand the [[Lorentz force]] of the magnetic field. The core is formed by the thick iron housing (''D'') that wraps around the windings.]]

For a closed magnetic circuit (no air gap), such as would be found in an electromagnet lifting a piece of iron bridged across its poles, equation ({{EquationNote|3|Eq. 3}}) becomes:

{{NumBlk|:|<math>B = \frac{NI\mu}{L} </math>|{{EquationRef|4}}}}

Substituting into ({{EquationNote|2|Eq. 2}}), the force is:

{{NumBlk|:|<math>F = \frac{\mu^2 N^2 I^2 A}{2\mu_0 L^2} </math>|{{EquationRef|5}}}}

To maximize the force, a core with a short flux path ''<math>L</math>'' and a wide cross-sectional area ''<math>A</math>'' is preferred (this also applies to magnets with an air gap). To achieve this, in applications like lifting magnets and [[loudspeaker]]s, a flat cylindrical design is often used. The winding is wrapped around a short wide cylindrical core that forms one pole, and a thick metal housing that wraps around the outside of the windings forms the other part of the magnetic circuit, bringing the magnetic field to the front to form the other pole.