The field dependence of the magnetic susceptibility and collective mode frequencies of superfluid 3He-B are calculated perturbatively in (γH/Δ) using the quasiclassical theory. With the aid of this perturbation theory, we interpret the gap distortion, nonlinear susceptibility, and collective excitations of the order parameter in terms of additional correlations between Cooper pairs that are induced by a magnetic field. We also calculate the dispersion splittings of the real squashing modes in a magnetic field. In addition to the nonlinear Zeeman shifts of these modes, which occur in strong magnetic fields (γH≈0.1Δ) there are low-field [γH≈(qvf)2/Δ] nonlinearities of the collective mode frequencies resulting from the field dependence of the quantization axis. Our results for all of these response properties of 3He-B depend upon a small number of material parameters; thus measurements of these properties can provide detailed information on the quasiparticle interactions.