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Abstract The time harmonic and transient analyses of axially symmetric mono¬poles of different geometries are considered. A general formulation of the scattering or radiation problem is first considered in terms of generalized and extended boundary conditions. Steady state and transient numerical re¬sults are obtained using the scalar potential axis extended boundary condi¬tion integral equation, the moment method and the Fourier transform. The equivalence theorem is used to derive novel generalized boundary condition (g.b.c.) integral equations for the tangential components of the electric and magnetic fields on the interfaces of a finite number of dielec¬tric or conducting scatterers with an arbitrary distribution of impressed sources. The uniqueness of the resulting integral equations is proved. Closed surface, plane and line type extended boundary conditions (e.b.c.) with regular kernels and equivalent to the g.b.c. are introduced. Two elec¬trostatic examples are given to demonstrate the method. Various integral equations are derived for an axially symmetric monopole fed by a coaxial line over a ground plane. Their numerical solution and details of the integral operator approximations are given. The axis ex¬tended boundary condition integral equation is used to study the steady-state behaviour of hemispherically capped thick cylindrical monopoles with or with¬out conical feed sections, the duo-conical monopole and the corrugated mono¬pole. The transient fields of an infinitely thin dipole and the relaxation of an initial charge distribution on a perfectly conducting sphere are stu¬died. The pulse response of the axially s~metric monopoles mentioned above is evaluated using the steady~state results and the Fourier transform. A qualitative physical description is also included. Their response to a |