Linking current-carrying wires to magnets

[Cluelessness]

This may be an obvious question but I have no idea:
How can anyone link current-carrying wires (solenoids) and its formulae, to magnets?!
All I've researched so far points out that magnets have their own stable magnetic field, attributed to the alignment of spins of the electrons of the atoms which the magnet is composed of. But is that all to it? Are there any other relationships, anything that I'm missing?

 

[tiny-tim]

Welcome to PF!

Hi Cluelessness! Welcome to PF!

How can anyone link current-carrying wires (solenoids) and its formulae, to magnets?!
…
But is that all to it?

Basically, yes.

The only thing that causes magnetic fields is the movement of electric charge.

Even a charge moving with uniform velocity has a magnetic field.

Mechanically useful magnetic fields come from circular motion or spin of charges.

There's no essential difference between the tiny circular motion or spin of electrons in a magnet and the large-scale circular motion of electrons in a solenoid.

 

[Cluelessness]

Thanks a lot tiny-tim! :D
Does that mean magnets exhibit magnetic properties solely due to synchronised movement of electrons i.e aligned domains? So this means that a current is not required like a solenoid? Or do aligned domains produce a current?
Sorry, I'm nearly there...I think :)

 

[tiny-tim]

i'm really not familiar with magnetic domains, or magnetisable material generally

i think that if there was a current, it would be called a polarisation current, rather than something to do with magnetism

 

[Bob S]

This may be an obvious question but I have no idea:
How can anyone link current-carrying wires (solenoids) and its formulae, to magnets?!
All I've researched so far points out that magnets have their own stable magnetic field, attributed to the alignment of spins of the electrons of the atoms which the magnet is composed of. But is that all to it? Are there any other relationships, anything that I'm missing?

There is no link between electron spin, and the currents in a (air core) solenoidal coil producing a magnetic field. The magnetic field is due to Ampere's Law. http://en.wikipedia.org/wiki/Ampère's_circuital_law.
Electrons do have orbital and intrinsic spin dipole fields, which do impact magnetic materials and EPR (electron paramagnetic resonance).

The on-axis field in a solenoid is given in http://www.phys.uri.edu/~gerhard/PHY204/tsl215.pdf

 

[Cluelessness]

Sorry for replying so late! ><
Thanks guys! I really appreciate it :D