This work is focused on the propagation of electromagnetic waves in $R^3$ described by Maxwell`s equation with large wave number and Silver-Muller radiation condition. The model problem is approximated by truncating the exact Dirichlet-to-Neumann (DtN) operator into a finite sum of vector spherical harmonics. We prove the well-posedness and wave-number-explicit H(curl)-stability of the solution to truncated problem by assuming that the truncation number N satisfies $N\le akR$ for some a> 1, where k represents the wave number and R is the radius of the physical domain. Additionally, we demonstrate that the truncated solution is exponentially close, in terms of N, to the true scattering solution. Finally, we present the hp-finite element method (hp-FEM) for the truncated problem, along with its asymptotic error estimate. Some numerical experiments are provided to validate the theoretical findings.