Transient electromagnetic response of a permeable and conducting ground to a linear current ramp switch-off

The asymptotic representation for late times of the transient electric field above and on a uniform permeable and conducting ground is derived with the hitherto untreated effects of a ramp switch-off source current. The source is a vertically oriented finite loop placed on the ground. Certain response functions are defined and the results are compared directly to those of a Heaviside switch-off. The authors show that the ramp-time dependence is given by certain well-defined functions multiplying the respective terms of the series for the field produced by a Heaviside switch-off source. They also show that for late times t , the first term shows an enhancement of the ramp switch-off field relative to the Heaviside of the order of 1+5t₀/4t, where t₀ is the ramp time