Re: Biot-Savart Law - Electromagnetics - Unanswered Question
I don't think I can help too much, though can hopefully shed some light on your problem:
1) The Biot Savart Law is only strictly true for time steady currents. When you look at currents that change in time you have to take into account fields that are referred to as "retarded". This is because the changes in electric and magnetic fields only travel at a finite speed, namely the speed of light, c. However, for circuits that are small in size and for low frequencies, people usually ignore retardation effects (referred to as the "quasi-static approximation").
2) This probably has to be done numerically unless there are some special assumptions that you can make, eg the steel plate is of infinite extent, it has a special set up with respect to the current flowing in the conductor. You don’t specify many details about the steel plate.
>I am assuming that a Mag Field generated by a DC source will induce a DC .
>current and Vice-versa.
3) If the current is DC then the magnetic field may be influenced by the position of the steel plate , but no current will be induced since currents are only induced by changing magnetic fields. It may be that you are thinking of the transitory currents that flow when (eg) the current through the conductor is first switched on or when the steel plate is first brought near to the curremt carrying conductor.
Sorry I couldn't have given some of the answers you want,
Jim