Discuss the implications of the theorem $\Phi_{12}=\Phi_{21}$ in the case of the large and small concentric rings in Fig. $7.20$. With fixed current $I_{1}$ in the outer ring, obviously $\Phi_{21}$, the flux through the inner ring, decreases if $R_{1}$ is increased, simply because the field at the center gets weaker. But with fixed current in the inner ring, why should $\Phi_{12}$, the flux through the outer ring, decrease as $R_{1}$ increases, holding $R_{2}$ constant? It must do so to satisfy our theorem.