My kitchen currently consists of little more than an electric grill/hot plate combo, one wok and one non-stick pot/pan. Woks, it seems to me, were really designed for flame - either wood and coal fires or gas burners. The one time we tried with the wok (a round bottomed one) on the hot plate no heat seemed to be getting through. So my question is, were we just doin' it wrong? Or is it impossible to cook on a flat electric burner with a round bottomed wok?
Impossible is a strong word, but yes its near enough impossible as there is insufficient surface area touching to transfer the heat through, and hot plates do not have good heat .. not sure of the word, but they don't transfer heat well to things which are not touching them.
You can get flat bottomed woks which are more suited to this set up, but even then if you are moving the wok about a lot you still end up with the contact being lost quite a bit, and so not as much heat being transferred as you might want.
I've always found woks to work best on gas. In fact gas is just best, full stop.
Round bottom vs. flat bottom makes a difference, as Sam indicates. Another difference is wok type. You have really thin woks that really require a massive heat source, and you have thicker, cast-iron ("Chinese style") woks that you heat through-and-through before you start cooking. You might have a go with the latter type, but the wok will still probably be cooling faster than your heat source can match. If the wokking's short enough, perhaps you'll be able to pull it off.
You can get great results without gas and wok cooking, but a traditional round bottom will not work. The BEST wok to use is a good old Lodge cast iron 14" wok. It's flat on the bottom, and round inside. Do not waste time on other woks, in order to get it hot enough you will either warp the bottom and burn off the non stick coating. The Lodge is very thick and heavy and you need to heat it up slowly so that it's all hot, not just the bottom, and then still cook in batches.