What will happen to miners once Bitcoins reaches to its limit?
The miners won't so much become obsolete as their incentives will be based on transaction fees. Their primary job is to keep the Bitcoin network running smoothly and Bitcoin mining could still be profitable in regions where the cost of electricity is low or Bitcoin miners can generate their own power for not a lot of money. (It's doable. There's one kid who figured out how to build wind turbines out of junk and he's kind of a hero in his community.)