Equations e = 1 2πε0 qd z3 and e = 1 2πε0 p z3 are approximations of the magnitude of the electric field of an electric dipole, at points along the dipole axis. consider a point p on that axis at distance z = 4.50d from the dipole center (where d is the separation distance between the particles of the dipole). let eappr be the magnitude of the field at point p as approximated by e = 1 2πε0 qd z3 and e = 1 2πε0 p z3 (electric dipole). let eact be the actual magnitude. by how much is the ratio eappr/eact less than 1?