An expression for the current density at any point in the earth due to a current in an infinitely long vertical wire is found for two types of current: (1) Simply periodic, (2) Rectangular impulse. These are given respectively by equations (11) and (13) below, where I r is the horizontal radial component and I z the vertical component of the current density vector at the point (r, z), which is at a distance R from the grounding point. These formulas hold for frequencies not too high or times not too small to allow neglect of the displacement current.

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