Jason is right. Here in the USA, not likely to be worth it to just walk out to any cultivated field, and expect to be worth it. There simply has to be some reason for you to hunt it. Eg.: a camp was there, a house used to be there (cellar hole, etc...), a fort, a stage stop, a carnival used to set up there, etc...
About the only place where it might pay to just hit random fields, is a 2000+ yr. old place like some European countries. There, they've seen thousands of years of continuous cultivation of the same fields. So ... yeah.... even if there were no actual habitations or specific usage, yet odds are, with that many years of field hands coming and going, stuff eventually adds up. But here in our relatively young USA, you're talking needles in hay-stacks with our fields that are, at most, 200-ish years old of crop-usage. *Maybe* some possible exceptions in super old areas of the older eastern colonial areas? Still though, even there, I'm sure they still research what was in fields, when picking fields, so they're not just "random".