  This paper provides a rigorous analysis on boundary element methods for the
magnetic field integral equation on Lipschitz polyhedra. The magnetic field
integral equation is widely used in practical applications to model
electromagnetic scattering by a perfectly conducting body. The governing
operator is shown to be coercive by means of the electric field integral
operator with a purely imaginary wave number. Consequently, the continuous
variational problem is uniquely solvable, given that the wave number does not
belong to the spectrum of the interior Maxwell's problem. A Galerkin
discretization scheme is then introduced, employing Raviart-Thomas basis
functions for the solution space and Buffa-Christiansen functions for the test
space. A discrete inf-sup condition is proven, implying the unique solvability
of the discrete variational problem. An asymptotically quasi-optimal error
estimate for the numerical solutions is established, and the convergence rate
of the numerical scheme is examined. In addition, the resulting matrix system
is shown to be well-conditioned regardless of the mesh refinement. Some
numerical results are presented to support the theoretical analysis.
