A uniform magnetic field is confined to a circular region of radius ‘a’. A thin metallic ring of radius r (r > a) is concentrically placed around the circular region as shown in figure. If the magnetic field in the circular region increases at a constant rate, then 

The magnetic flux associated with the circular region is increasing with time. So at a radial distance r, an emf ($\epsilon$) is induced which is given by 

$\epsilon =\mathrm{E}.2\mathrm{\pi r}=-\frac{\mathrm{d}}{\mathrm{dt}}\left({\mathrm{\pi a}}^2\mathrm{B}\right)$

Where E is the intensity of electric field.

The electric field is produced by a variable magnetic field, so it is non-conservative in nature. Also the field lines form closed curves.