An infinite number of conducting rings having increasing radii $$r_0, r_1, r_2, r_3$$ and so on, such that $$r_0 = r$$, $$r_1 = 2r$$, $$r_2 = 2^2r$$, $$r_3 = 2^3r$$ and so on up to infinity, have been placed concentrically on a plane. All the rings carry the same current $$i$$ but the current in consecutive rings is in opposite direction as shown.

The magnetic field produced at the common center of the rings is