Two identical inductors are connected in parallel. If the parallel...

Let the self-inductance of each coil be $L$.

Since the two identical inductors are connected in parallel, their equivalent inductance $L_{eq}$ is given by:

$L_{eq} = \dfrac{L}{2}$

The magnetic potential energy stored in the equivalent inductor is:

$U = \dfrac{1}{2} L_{eq} I^2$

Given $U = 40\ \text{J}$ and total current $I = 2\ \text{A}$, substituting these values:

$40 = \dfrac{1}{2} \left(\dfrac{L}{2}\right) (2)^2$

$40 = \dfrac{L}{4} \times 4$

$L = 40\ \text{H}$

Answer: $40\ \text{H}$