Under the assumption of the low magnetic Reynolds number, the coupled model is established for the turbulent flow field and the externally applied magnetic field. The AUSMPW+ scheme and LUSGS method are used to solve turbulent magnetohydrodynamics (MHD) flow equations, in which the Spalart-Allmaras one-equation turbulence model is used. A series of numerical simulations over various geometry configurations, namely, a flat plate and a compression corner, is conducted by using an external electromagnetic field. Results show that the performance of MHD boundary layer flow control is determined mainly by the Lorentz force in the streamwise direction. With an external magnetic field used, the low velocity fluid in the boundary layer can decelerate and increase the static temperature locally. Moreover, the counter-flow Lorentz force always brings a negative effect on the turbulent skin friction coefficient, and the location for the MHD zone has a great influence on the control efficiency of the ramp-induced separation. A reasonable magnetic field layout scheme should be configured in practical engineering application.