A proton located several proton diameters away from a small charged object carrying charge \(q\) is subject to an electric field of magnitude \(E\). As the proton moves a distance \(d\) along the \(x\) axis away from the object, the electric field magnitude drops to \(E / 4\). If the charged object had instead been an electric dipole (with a charge of magnitude \(q\) on each end) oriented in the \(z\) direction, by what factor would the initial electric field magnitude \(E\) have dropped as the proton receded by distance \(d\) along the \(x\) axis?