A wire is an electric field with an electromagnetic field in the vacuum surrounding it. Chances are the same principle applies here: you'd have a magnetic wave in your tissues with a weak electromagnetic field around you. I'd assume that the "magnetic field" would be similar to (or the same as) the field present in ferromagnetic materials.

Remember electromagnetism isn't really a "thing:" it is not a distinct field, rather its two fields that interact with each other. The electric field and magnetic field are still distinct.

I think they may use near field rather than radiation for communication.