Why are AP champions generally in mid lane instead of an AD carry? It should be possible for AD carry to be in mid-lane, however in competitive tournaments the general structure is bruiser top, AP mid, carry + support bot, and jungle.
AP champions scale best off of levels so by putting them in a solo lane they earn the most experience. Mid lane is the shortest lane so it is easy to escape compared to top, which is generally the realm of bruisers who can survive ganks and have gap-closers.
Some APs are excellent roamers and having them in mid allows them to influence the other lanes. Ahri, Sion, and Leblanc are all vicious roamers that can quickly get kills in other lanes due to their burst/CC.
AD champions scale best off of gold so they get a support to help them farm safely. A lot of the times the support gives sustain to make this farming easier.
Having two people in bottom lane also allows for control over dragon, which is a very important objective early on. Baron doesn't normally become an issue until well after laning phase is over.
However, sometimes you will see pro teams throwing a solo champion bottom if the champion can handle fighting two people at once and still farm. They do this so their AD carry can abuse the enemy top lane and free farm.
There was a time when you could often see AD carry mid. The current meta-game, which is guided by world top gamers optimisations proved that it's often the best composition (1 bruiser top / 1 AP Carry mid / 1 AD Carry + Support bot / 1 Jungler) but sometimes, with a good teamplay, luck, skill, playing with a weird composition works well (2 AD carry + fiddle jungler/karthus, AD carry top destroying the brawler and farming hard, double jungler + counter jungle, ...) There is a meta game, but please don't be too much formated by it and on blind normal game, embrace new way of playing on the Summoner rift :).