An interstage seal for a turbine of a gas turbine engine, the interstage seal having a seal carrier with an axial extending seal tooth movable with a stator of the engine, and a rotor with a seal surface that forms the interstage seal with the seal tooth, where a magnetic force produced by two magnets and a gas force produced by a gas pressure acting on the seal carrier forms a balancing force to maintain a close clearance of the seal without the seal tooth contacting the rotor seal surfaces during engine operation. In other embodiments, two pairs of magnets produce first and second magnetic forces that balance the seal in the engine.