The interactions between a permanent magnet (PM) and a coated conductor tape lies at the heart of several types of high-temperature superconducting (HTS) devices, including the HTS dynamo. The applied magnetic field from a PM is typically highly spatially inhomogeneous with large field gradients occurring near the edges of the PM. This situation differs substantially from the well known Brandt analytical model, which describes flux penetration and current behaviour of type-II superconducting strips in a spatially-homogeneous applied magnetic field. The Brandt model also assumes the superconductor exhibits a constant critical current (Jc) throughout, and hence does not take into account the more complex behaviour of practical HTS tapes which exhibit an angular magnetic field-dependence of the critical current, Jc(B, θ). In this work, a finite-element model is developed to include such considerations and describe the interaction between a permanent magnet and an HTS coated-conductor wire at small flux gap distances similar to those used in the HTS dynamo. The effect of varying key parameters is studied including: (1) changing the critical current, (2) including an anisotropic magnetic field dependence to the critical current density, (3) changing the relative width of the PM to the coated conductor tape, and (4) changing the flux gap between the magnet and the HTS tape. The effects on the flux penetration and current behaviour of the HTS tape are calculated and compared to the Brandt model. Of particular interest are the key differences in the flux penetration profile which are observed when the magnet width is much smaller than the width of the coated conductor tape.