Emf induced by a circular region of magnetic field on a variety of shapes

From Faraday's Law $\epsilon$ =- $\frac{d\phi}{dt}$ where $\phi$ is the flux Now this, does this induced emf only act circular,(i.e the current is flowing in a circular path.) Can it also be coerced to flow any path we choose(like place a hexagonal(closed) shaped wire in a region of magnetic field which is changing at the rate of $\frac{dB}{dT}$ and make the rest of the surface extremely resistive) and does the emf change or remain the same. To be explicit, consider this example Now say I consider three cases when no rectangular lop is present, when one loop(inside) is present and when only outerloop is present. Let current in the cases respectively be $I'$ $I''$ $I'''$ Is the emf same in all the cases? Note magnetic field is present in only circular region.