Extensional flows and magnetic fields induce similar steady alignment responses when applied to liquid crystals (LCs), liquid crystal polymers (LCPs) and nematic (rigid rod or platelet) suspensions. This observation is explained for LCs by a classical analogy, expressed as a symmetry, between hydrodynamic and magnetic fields in the Leslie-Ericksen theory [de Gennes and Prost, The Physics of Liquid Crystals (Oxford University Press, New York, 1993); Chandrasekhar, Liquid Crystals (Cambridge University Press, London, 1992)]. Our purpose here is to extend this analogy: first, to LCPs and nernatic suspensions where an excluded volume potential couples either to a linear flow [Hess, Z. Naturforsch. A 31a, 1034-1037 (1976); Doi and Edwards, The Theory of Polymer Dynamics (Clarendon, Oxford, 1986)] or to a magnetic field [Bhandar and Wiest, J. Colloid Interface Sci. 257, 371-382 (2003)]; and second, to the strong coupling of excluded volume interactions, planar linear flows, and a coplanar magnetic field. The general symmetries reveal parameter redundancies in the Doi-Hess kinetic theory, leading to a reduced model with significant computational savings. That is, a rotational planar linear LCP (or nernatic suspension) flow under an imposed coplanar magnetic field is reducible to a simple shear flow coupled with a transversely imposed magnetic field and negative anisotropy through an orthogonal transformation; whereas a magnetic field coupled linear, irrotational flow corresponds to a tri-directional elongation. We illustrate these results with a second-moment tensor model to predict how a variable strength, coplanar magnetic field may be used to alter or control flow-induced responses of LCPs or nematic suspensions. The illustrations are for sheared dynamic attractors (tumbling, kayaking and chaotic), extension-induced steady states, and four roll mill flows. (c) 2007 The Society of Rheology.