I'm working on a science fiction story idea, and trying to make sure I get all of the physics right. One of the concepts I'm using is superconducting coils as "batteries," because they can store huge amounts of energy indefinitely. However, most of what I've read about superconductors (mostly Wikipedia) seems to indicate that this would give off an extremely powerful magnetic field, proportional to the amount of energy stored.
How significant is this magnetic field, and would there be any effective way to cancel it out (with the shape of the coil, etc)? I should probably know that last part, but it's been forever since I took a class on electromagnetism. Would it be practical to have a portable computer, robot, etc. with superconductive energy storage, or would the magnetic field cause too many problems?