OK, so this is a hideously pointless question. I’m thinking of something like a mug full of water for tea. Do you put it in the center or on the edge of the rotating tray in the microwave? Which is “better”?
Lacking any other info, put it on the center.
Ideally, you’d run a couple of tests by covering the microwave tray with bread covered in unmelted cheese, and nuking it to see where your hotspots are (it should only take 10 seconds or so to start melting the cheese). If you are truly bored try repeating at 1 inch intervals from the floor to the ceiling of the microwave, to create a 3D map 
You’ll get hot “circles” instead of bands, since you’ve got a rotating tray.
Arjuna34
First let me say that I’m quite intrigued by the proposition of making a 3-D map of the hot spots in a microwave. (Let’s hope I don’t have some free time this weekend…)
But, I’d think putting something off-center would be better (lacking any dead-spot info). Since the boundary conditions are Cartesian (i.e., the waves are in a box), you wouldn’t get rings of dead spots. Instead, your mug of water would move in and out of dead spots – dead spots lying on a grid. Your mug will always get some average amount of nuke. Of course, there’s a 50% chance that the power right at the center is more than this average (in which case the center is better), but there’s also a 50% chance that it’s less. I guess, then, it doesn’t matter where you put it unless you’re risk averse.
Maybe, then, you should factor in the probability that the designers thought to ensure that the center was a hot spot.
Some of us have WAY to much time on our hands.
You guys are overlooking one important fact: there is no single “beam” of microwaves. Every microwave oven has two essential features: a microwave emitter, and a “stirrer.” The microwaves hit the stirrer, which is nothing more than a slowly moving fan-blade mechanism. The metal of the blades bounces the microwaves into different positions throughout the oven interior. If you didn’t have a stirrer, there would be hot spots in the oven that got all the energy, while other spots receive relatively little energy.
The correct answer to the question “where do I put a small object in the microwave” is, “anywhere except right next to the walls.”
Even with a stirrer, the distribution isn’t perfectly even through the microwave- that’s the reason the tray rotates.
You’d get rings of hot and cold spots, but probably no completely dead spots. If you put something off-center, say 3 inches from center, it will rotate around, moving in and out of local hot spots. It will receive an average energy that will depend on the exact path (I suppose you’d integrate over the absorbed microwave curve). An object at 4 inches will travel through different hot spots, and have a different average energy.
You could remove the rotating tray and truly map the 3D field, for completeness, but this would only be necessary if you plan on nuking things for less than tray revolution time.
Arjuna34
IANA microwave engineer, but I do know that with mine, if you put the mug full of water on the outside rim of the glass plate, the carousel doesn’t have enough “oomph” to convey it around and around without grumbling. It’s only happy if you put a fairly heavy object directly in the middle, over the gizmo that grabs onto the glass plate.
Anyway, the whole point of the carousel is, first, to rotate the food item itself, so as to get more even heating, and second, to move the food around through the microwaves bouncing off the sides of the tank, so as to avoid the problem of hot spots. Even something small, like a single taco, would be heated just the same, whether you put it on the edge or in the middle. It’s still going to be rotated while it’s being bathed in microwaves. It’ll just rotate around itself in little teeny circles, rather than in big sweeps.
And actually, I would assume that if there is a difference in where you put the food, it would be better to put it in the middle, because the engineers who design the things are probably assuming that the user is going to put the food in the middle. So they’d design the microwave mechanism with “food in the middle” in mind, and therefore “food in the middle” will give you optimal results.
In other words, what Arjuna said.
The first - and only - time I put Mrs. O’s coffee in the dead center of the carousel (for the household standard of 1 minute) it boiled over out of the cup. The consumer reaction was also negative: “You only need to put the coffee in for a minute!”
Placing it about halfway out from the center of the carousel tray seems to yield optimum results; any further out and the coffee stands a chance of getting heated again after the first sip.
YMMV, of course, depending on the make and model of oven you’re using.
The Unwise Microwave Oven Experiments website (which is quite amusing) says that ovens with turntables typically do not have a stirrer.
They also pass along that slightly-moistened fax paper can be used to map your oven’s hotspots.
Microwave ovens support a lot of resonant modes, so the center won’t tend to have more energy than away from the center. It’s as likely to be a cold spot as a hot spot. Also, any hot or cold spots are only going to be maybe an inch or so across, less than the size of you mug of tea. So it probably doesn’t much matter where you put it, but personally, I would put it off-center (not necessarily right at the edge), just in case.