electromagnetism - How does inductor store energy in the magnetic field?

I learnt from book that magnetic field does no work because the force is proportional to $\vec{v}\times\vec{B}$ where $\vec{v}$ is the particle velocity. That vector cross product is always at right angles to $\vec{v}$, so that $\vec{F}\cdot\vec{v}=0$, i.e. no work is done on the particle. But then how come does an inductor store energy in the magnetic field?

Answer

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 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 induced electric field.