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.