Two distinct inductors store the exact same amount of magnetic...

Let the inductances be $L_1 and L_2$, and the currents be $i_1 and i_2$.

The magnetic energy stored in an inductor is given by $U = \dfrac{1}{2} L i^2$.

Since the energies are equal:
$U_1 = U_2$
$\dfrac{1}{2} L_1 i_1^2 = \dfrac{1}{2} L_2 i_2^2$

Rearranging for the ratio of currents:
\left(\dfrac{i_1}{i_2}\right)^2 = \dfrac{L_2}{L_1}$<br><br>Given that$L_1 : L_2 = 1 : 4$, we have$\dfrac{L_2}{L_1} = \dfrac{4}{1}$.<br><br>\left(\dfrac{i_1}{i_2}\right)^2 = 4$
$\dfrac{i_1}{i_2} = \dfrac{2}{1}$

Therefore, the ratio of the currents is $2:1$.

Answer: $2:1$