The linear theory of fully electromagnetic plasma instabilities driven by currents flowing across a magnetic field is investigated, with applications to the laminar perpendicular bow shock. The theory utilizes the local approximation, assumes unmagnetized ions and magnetized electrons, and includes the effects of gradients in the magnetic field magnitude and density. Oblique propagation is considered, and wave numbers may be of the order of or larger than the reciprocal electron Larmor radius. An increase in the electron beta does not significantly affect the ion acoustic instability but does reduce the growth rates of the Buneman and the modified two-stream instabilities. If Te≫Ti within the shock, results indicate that the ion acoustic instability is the most important growing mode, for any reasonable beta. If Te<Ti throughout the shock, further work is necessary to determine which instability is most important.