How and why is a magnetic field transmitted with alternating current?
Firstly, a point about the title of your question.

You initially ask why it is that a magnetic field is "transmitted" with alternating current.  In terms of transmission, electromagnetic radiation only occurs where a circuit has (or becomes) an antenna.  Otherwise, only an electromagnetic field is generated around the conductors.  This is called a "near-field" and it is not 'transmitted'.

With regard to magnetic fields, a magnetic field is generated when a current flows through a wire.  This current can be D.C. too - the phenomena is not limited to A.C. current.  The direction of the magnetic field depends upon the direction of current flow.  Therefore, if you connect a D.C. source a magnetic field is generated with a constant polarity.  If you connect an A.C. source the magnetic field alternates in polarity.

It is interesting to note that a magnetic field is only measured or observed when a charge moves relative to you as an observer.  It is a relative property! If you were able to move down the wire with the charge (or alongside the wire at the same speed as the charge), so that the charge is no longer moving relative to you, you would see that the magnetic field disappears completely!
The electric and magnetic fields are related in a peculiar way, similar in some sense as to space and time in that they are relative properties and depend entirely upon the observer.

Here's a really good book which I think you would enjoy:

[http://books.google.co.uk/books/about/Electromagnetics_Explained.html?id=MLzPNpJQz9UC&amp;redir_esc=y][1]