We have derived the theory for the electromagnetic transient response of metallic spheres, spherical shells, and composite spheres (composed of two materials with different conductivities). We have related the dominant time constant of the voltage at a secondary coil wound around the samples, with their physical characteristics: conductivity, permeability, and geometrical factors. We show that a thin spherical shell under certain conditions can be considered as one time constant system and we derive the values of the resistance and the inductance of the shell equivalent circuit. We have obtained experimental results for aluminum and brass spheres, and we have evaluated experimentally the effect of different primary coil designs.