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Yea, thats a good explanation. I was trying to think when to use же and ж. But yea that sounds about right.

Где ж он?
- Он же здесь!

ALso i think 'Лето ж.' sounds funny. U need the EEE sound.

Since noone has given you a straight answer, here you might find this of interest.

Же emphasizes the previous word, so the effect is like pronouncing "Where is she?" with extra emphasise on 'is'...