A thin, nonconducting rod of length \(L\) lies along the \(z\)-axis, centered at the origin, and carries a total positive charge \(Q\) distributed uniformly along its length. A detector measures the electric field magnitude \(E(r)\) as a function of distance \(r\) along the positive \(x\)-axis, which forms the perpendicular bisector of the rod. The measured field magnitude is well approximated by a \(1/r\) dependence when \(r \ll L\), but transitions smoothly to a \(1/r^2\) dependence when \(r \gg L\). Which of the following statements provides the physically correct explanation for this transition?