A physical dipole consists of two point charges, \(+q\) and \(-q\), fixed at a distance \(d\) apart, giving a dipole moment of magnitude \(p = qd\). The dipole is centered at position \(x = x_0\) in a region with an electric field directed along the \(x\)-axis given by \(E(x) = E_0 + bx\), where \(E_0\) and \(b\) are positive constants. Initially, the dipole is oriented parallel to the field, with \(+q\) at \(x = x_0 + \dfrac{d}{2}\) and \(-q\) at \(x = x_0 - \dfrac{d}{2}\). The dipole is then rotated by \(180^\circ\) about its center \(x_0\) so that it is oriented antiparallel to the field. What is the change in electric potential energy \(\Delta U\) of the dipole system resulting from this rotation?