Sorry, but it has to be rigid to be a sphere. Angular momentum is a bitch!
PS: Dyson Spheres is misnomer, Olaf Stapledon should be credited for this idea (Star Maker 1937)
PS: Dyson Spheres is misnomer, Olaf Stapledon should be credited for this idea (Star Maker 1937)
The result may not be literally a rigid sphere as people think of it, but if the orbits are packed tightly together enough it'll look plenty "sphere-like" from the next star system over.
A rigid Dyson sphere is probably impossible, and its utility is not entirely clear. Making a Dyson swarm around a star is merely a lot of work, and also has the advantage of immediately paying benefits as soon as the very first satellite is launched.
Collisions between orbital junk are most likely to happen between objects in the same orbit. And most junk is in some roughly equatorial orbit. So I'd expect the resulting debris to end up in roughly the same orbit, so that the debris would form a sort of fuzzy disk - not a sphere. I wouldn't expect to observe much debris over the North Pole.