The authors study a Dirac operator restricted to an open, smooth, simply connected domain in \(\mathbb{R}^2\) coupled to a magnetic field which is smooth and which points in the direction orthogonal to the plane. The focus is on the bag boundary condition, which physically says that no current flows through the boundary \(\partial\Omega\). When \(\Omega\) is bounded, the authors show the asymptotic behavior of the low-lying energies in the limit of a strong magnetic field (the semi-classical limit \(h\to 0\) corresponds to the strong magnetic field limit with \(h\) fixed). The problem is also studied on a half plane for a constant magnetic field, and it is shown in particular that the Dirac operator has continuous spectrum except for a gap of size \(a_0 \sqrt{B}\) where \(0<a_0<\sqrt{2}\) and \(B\) is the constant value of the magnetic field. This constant also characterizes the energies of the system if domain is bounded; numerically it is shown that \(a_0 \approx 1.312\).