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Consider the figure above in which there is an electric current (constant) in R1 (consider it to be made of a conductor). Obviously there will be a magnetic field induced in R2 (consider it to be made of a ferromagnetic material) due to the electric current in R1. (http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/curloo.html) R3 (consider it to be made of a conductor) is an open loop as shown in the figure.

Will there be any induced voltage across AB in R3 due to the magnetic field in R2?

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    $\begingroup$ If the electric current is constant no induction will occur in R2 nor R3. Now if it is variable, yes there will be induction in both. $\endgroup$
    – rmhleo
    Aug 2, 2014 at 13:53

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No, a current can only be driven by an electric field which in turn can only be generated by either charge or a time varying magnetic field. Since you say that the current is constant, the magnetic field is also constant, therefore no electrice field arises. Besides, I wouldn't say that there is a magnetic field induced in R2 (sounds strange to me). It might be amplified by R2 if R2 is made of some ferromagnetic material.

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