A long, tightly wound solenoid of length \(L\) and radius \(R\) (where \(L \gg R\)) carries a steady current \(I\). Deep inside the solenoid near its geometric center, the magnetic field along the central axis is uniform with magnitude \(B_0 = \mu_0 n I\), where \(n\) is the number of turns per unit length. At the center of one of the open ends of the solenoid, the magnetic field magnitude on the axis is measured to be \(\frac{1}{2} B_0\). Which of the following provides the correct physical explanation for this measurement?