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I'm not sure what is meant by "the induced emf could be considered as towards the centre". The induced emf, as I understand it, is the result of integrating the induced electric field around a closed path encompassing a changing magnetic field. It doesn't really exist from point to point because magnetic flux cannot be defined relative to an open path.
I'm not sure the differential approach helps either, i.e., curl E = -dB/dt, because the integral of the curl from point to point along an open path doesn't have a physical meaning (that I am aware of).