Single top quark events produced in the t channel are used to set limits on anomalous Wtb couplings and to search for top quark flavour-changing neutral current (FCNC) interactions. The data taken with the CMS detector at the LHC in proton-proton collisions at s=7 and 8 TeV correspond to integrated luminosities of 5.0 and 19.7 fb −1 , respectively. The analysis is performed using events with one muon and two or three jets. A Bayesian neural network technique is used to discriminate between the signal and backgrounds, which are observed to be consistent with the standard model prediction. The 95% confidence level (CL) exclusion limits on anomalous right-handed vector, and left- and right-handed tensor Wtb couplings are measured to be |f V R | < 0.16, |f T L | < 0.057, and − 0.049 < f T R < 0.048, respectively. For the FCNC couplings κ tug and κ tcg , the 95% CL upper limits on coupling strengths are |κ tug |/Λ < 4.1 × 10 − 3 TeV −1 and |κ tcg |/Λ < 1.8 × 10 − 2 TeV −1 , where Λ is the scale for new physics, and correspond to upper limits on the branching fractions of 2.0 × 10 −5 and 4.1 × 10 −4 for the decays t → ug and t → cg, respectively.[Figure not available: see fulltext.]