Current Density

In what context?

In UK home wiring, for example, copper twin-and-earth cable is typically rated around 10A for 1.0mm², 15A for 1.5mm² and 26A for 2.5mm².

Please elaborate.

From where did you ge these values (question to Edgar not PWS) already on this so editing, can not change the link

At this abnormally low values, you will land up in only copper and no iron on the machines.

As PWS correctly pointed out, the values are much much higher and the values given by PWS are with the factor of safety.

PS

a few links

http://wiki.answers.com/Q/Current_carrying_capacity_of_copper_in_terms_of_cross_sectional_area

http://www.seas.gwu.edu/~ecelabs/appnotes/PDF/techdat/CCCofCC.pdf

(look at the table in the end) the AWG of approx 18 is 1sqmm (I think, but you may calculate and see)

As other comments already mentioned the maximal current depends on the heat transfer capability of the zone where the conductor works. The data sheet concerns a conductor in free air. With those data one could compute back the convection factor used or which convection factor occurred during experiment and at which temperature the wire was heated. It is not the same if the conductor is horizontal or vertical. If the conductor is in an insulation then the current density has to be reduced accordingly. Further more if you consider a coil, a multilayer coil, then the conduction from the coil core to the outside is a lot reduced and the insulation of the wires has -depending on its type- a temperature limit to respect in order to assure the life expectancy. The current densities you found are usually considered for thick coils using a low grade wire insulation. The contact between layers is narrow so that the heat cannot travel easy from the inside to the outside.