We set out to determine the ratio, qIR, of rest-frame 8-1000-μm flux, SIR, to monochromatic radio flux, S1.4 GHz, for galaxies selected at far-infrared (IR) and radio wavelengths, to search for signs that the ratio evolves with redshift, luminosity or dust temperature, Td, and to identify any far-IR-bright outliers - useful laboratories for exploring why the far-IR/radio correlation (FIRRC) is generally so tight when the prevailing theory suggests variations are almost inevitable. We use flux-limited 250-μm and 1.4-GHz samples, obtained using Herschel and the Very Large Array (VLA) in GOODS-North (-N). We determine bolometric IR output using ten bands spanning λobs = 24-1250 μm, exploiting data from PACS and SPIRE (PEP; HerMES), as well as Spitzer, SCUBA, AzTEC and MAMBO. We also explore the properties of an LIR-matched sample, designed to reveal evolution of qIR with redshift, spanning log LIR = 11-12 L&sun; and z = 0-2, by stacking into the radio and far-IR images. For 1.4-GHz-selected galaxies in GOODS-N, we see tentative evidence of a break in the flux ratio, qIR, at L1.4 GHz ~ 1022.7 W Hz-1, where active galactic nuclei (AGN) are starting to dominate the radio power density, and of weaker correlations with redshift and Td. From our 250-μm-selected sample we identify a small number of far-IR-bright outliers, and see trends of qIR with L1.4 GHz, LIR, Td and redshift, noting that some of these are inter-related. For our LIR-matched sample, there is no evidence that qIR changes significantly as we move back into the epoch of galaxy formation: we find qIR ∝(1+z)γ, where γ = -0.04±0.03 at z = 0-2; however, discounting the least reliable data at z < 0.5 we find γ = -0.26±0.07, modest evolution which may be related to the radio background seen by ARCADE 2, perhaps driven by <10-μJy radio activity amongst ordinary star-forming galaxies at z > 1. Herschel is an ESA space observatory with science instruments provided by European-led Principal Investigator consortia and with important participation from NASA.