For a charged particle to move strictly in a plane with a curved but non-circular path, the magnetic field must have both an in-plane component (along the initial velocity direction) and a component perpendicular to the plane. The perpendicular component alone would give pure circular motion; a component along the velocity contributes nothing initially but affects the dynamics as the velocity direction changes, producing a non-circular (e.g. cycloid-like) trajectory confined to the plane.