Answer
We can rank the circuits according to the net magnetic fields at the center:
$(c) \gt (a) \gt (b)$
Work Step by Step
We can write the expression for the magnetic field produced by an arc of current:
$B = \frac{\mu_0~i~\phi}{4~pi~r}$
It is given that $\phi$ and $i$ are equal for all three situations.
Since circuit (c) has most of the current moving around a smaller radius $r$, the magnetic field at the center will be the greatest.
Since circuit (b) has less current moving around the larger radius $R$ compared with circuit (a), the magnetic field at the center of circuit (b) will be less than the magnetic field at the center of circuit (a).
We can rank the circuits according to the net magnetic fields at the center:
$(c) \gt (a) \gt (b)$
