Brushes of end-grafted, polar polymer chains in a good, nonpolar solvent are studied via molecular dynamics simulations of a bead-spring model. The monomers are connected by finitely extensible nonlinear springs. The springs connecting consecutive monomers in a chain are labeled with dipoles parallel to the chain contour. We consider the dipoles as limits of charge pairs, replacing each dipole by a pair of charges positioned at the centers of mass of two consecutive beads. Equilibrium simulations are performed, and the static and dynamic properties of the chains are related to the dipole magnitude. It was found that the electrostatic interactions lead to a shorter brush and the collapse becomes more pronounced with increasing segmental dipole moment. The dielectric relaxation of the tethered chains is studied, and the dielectric permittivity is obtained from equilibrium dipole moment correlation functions. Results on the dielectric relaxation of tethered chains from experiments conducted by Yao et al. exhibited a broader dielectric dispersion spectrum than that of free macromolecules in homogeneous solutions. These authors attributed the results to the thermodynamic confinement (to keep uniform segment density) and the spatial confinement that prohibits a chain to cross the tethering domain boundary. The simulations indicate that neither the spatial confinement nor the thermodynamic confinement lead to a broader dielectric dispersion spectrum for the tethered chains, and we attribute the discrepancies to the morphology differences between the experimental system and the simulated one. Weak electric fields parallel and perpendicular to the grafting surface are applied, and the system response is related to the equilibrium fluctuations. We also examine the structural properties of the brushes at steady state under the influence of external electric fields.