Motivated by results derived from chiral phenomenological Lagrangian field theories encompassing low-energy strong interactions and current-algebra PCAC aspects, one formulates a definite spinor quark model with attending magnetic pointlike charge. From this approach, the anomalous contribution to baryon magnetic moments can be evaluated and suppression of electric-dipole moments with time reversal invariance understood. In this paper, the different parts of the interaction Hamiltonian are discussed and the equations for the potentials are obtained explicitly. Simpler solutions showing magnetic polarizations are derived and shown to exist. Mellin transform techniques are set up to treat more general cases.