From a circuit theory perspective, recall that the product of voltage and current is power:

$p(t) = v(t) \cdot i(t)$

Also, for the inductor:

$v_L(t) = L \dfrac{d}{dt}i_L(t)$

So, there is only a voltage across an inductor when the inductor current is changing with time.

It follows that *power (time rate of change of work) is supplied to or delivered from the inductor when the inductor current is changing with time.*

But, the magnetic field threading the inductor must be changing with time if the inductor current is changing with time.

Finally, recall that a changing magnetic field induces a non-conservative electric field and thus an emf *which can do work*.

Remember, for a *constant* current through an (ideal) inductor, there is no associated power as there is only a steady magnetic field and thus, no emf.