Electromagnetic problem by a plane angular sector is studied. The perfectly conducting sector is illuminated by a plane electromagnetic wave. The scattered wave field consists of several components at large distances from the vertex of the sector. In the framework of the consequent and mathematically justified procedure, based on the Watson-Bessel and Sommerfeld integral representations of the electromagnetic Debye potentials, we develop expressions for the electromagnetic diffraction coefficients of the spherical wave from the vertex. To that end, we carefully study analytic properties of the Sommerfeld transformants and give a new procedure of analytic continuation for them. Like in the acoustic problem, the singularities of the Sommerfeld transformants on the real axis are responsible for the different components in the far field asymptotics. The expressions for the diffraction coefficients are specified in the form of integrals depending on the so called spectral functions, i.e. solutions of the boundary