A long, straight solid cylindrical wire of radius \(R\) carries a steady current \(I_0\) that is uniformly distributed across its cross section. A student considers a circular Amperian loop of radius \(r\) centered on the axis of the wire, where \(r > R\). If the radius of the loop is increased from \(r = 2R\) to \(r = 4R\), which of the following correctly describes what happens to the value of the line integral \(\oint \vec{B} \cdot d\vec{\ell}\) around the loop and gives the correct justification?