The problem of the diffraction of electromagnetic waves by a small circular disk which is perfectly conducting along equiangular spirals is studied. The limiting cases where the spirals degenerate into circles and radial segments are also discussed. General modal excitation appropriate to the cylindrical geometry of the problem is assumed. The solution is expressed in the form of an integral representation, involving a pair of unknown functions, which is designed to satisfy Maxwell's equations, the continuity conditions outside the disk, the edge conditions and the radiation condition. The remaining conditions, specifically, that the current is directed along the spirals and that the total electric field in the direction of the spirals vanishes, lead directly to a pair of coupled integro-differential equations for the unknown functions. Formal power series solutions of this system are obtained for small values of ka (k is the wave number, a is the radius of the disk). Further, these formal power series solutions can be rigorously justified in the case where the conductivity is along circles. The results are employed to derive the leading terms in the power series expansions of the far fields, the total scattering cross-sections, the electric field on the disk, and the current density near the centre and edge of the disk. For a normally incident plane wave, it is shown that the scattering cross-sections of the perfectly conducting, circularly conducting and radially conducting disks are in the ratio of 2: 1: 0.0039.