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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!

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    $\begingroup$ You're right throughout – including your intuition about requiring a $changing$ magnetic field (or motion of a conductor through a field). [Faraday didn't know this when he first started looking for an electrical effect of magnetic fields to partner the recently discovered magnetic effect of an electric current.] $\endgroup$ – Philip Wood Jun 28 '17 at 12:29
  • $\begingroup$ "total magnetic field directed around a closed loop is proportional to the current flowing in it." - it's proportional to the current through the surface bounded by the loop. Is this what you mean? $\endgroup$ – Hal Hollis Jun 28 '17 at 14:08
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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:

  1. The presence of the magnetic field implies there is a current somewhere (no current = no magnetic field).
  2. 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).
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