We present an exact analysis for the electromagnetic coupling to a thi
n overhead cable from a vertical line current source terminated in a p
erfectly conducting ground plane. The spectral method employed permits
a full satisfaction of the impedance boundary condition at the cable.
The quasi-static limit of the obtained solution in the time domain, f
or the net cable current, is expressed in closed form. The results are
relevant to the induced currents on power and communication lines.