This can be viewed from other term too. As we know the average power consumed by a inductor or a capacitor over a complete cycle is zero.During the first half cycle a field builds up across the inductor and during the second half cycle the field collapses. So power has to be returned back to source
A bit of correction! It is not between the two half cycles. Even in the same half cycle, the charge builds up from zero to maximum in the first half of the half cycle and then from the peak to zero of the same half cycle, the built-up charge would discharge back to the source. Again, in the next half cycle, the same process is repeated albeit in the reverse polarity.