Ampère's Law in its integral form (ignoring the term Maxwell introduced for capacitors) essentially says that the total magnetic field directed around a closed loop is proportional to the current flowing in it. This carries the implication that any loop of creates a corresponding magnetic field (the basis of solenoids etc). Please do correct anything incorrect in the above! My question is this: does the converse of the above work (i.e.: does a magnetic field create a current in a wire). My intuition says this is wrong since in most of EM you need some notion of a changing field for any effect to be produced. Thanks for any help!
You are right in your description and intuition of Ampère's law - the presence of a magnetic field does not imply a current will be created in a nearby wire. However, there are two things to note:
- The presence of the magnetic field implies there is a current somewhere (no current = no magnetic field).
- If you start in a situation with a superconducting loop of wire and no magnetic field, and they you create a magnetic field (by sending current through a loop somewhere), then you will indeed get a corresponding current in the superconducting loop (so as to keep the flux through the loop unchanged). But as you say, at some point during the experiment this required a changing field (but after that, it can remain static and the current will continue).