Here is a reference that has the correct expressions for the E and
B fields radiated by a vertical lightning channel above a flat
perfectly conducting ground surface: Thottappillil,
R.,
V.A. Rakov, and M.A. Uman, "Distribution of charge along the
lightning channel: Relation to remote electric and magnetic fields and
to return stroke models," J. Geophys. Res., 102, 6987-7006, 1997.
A figure showing the channel geometry and defining some of the
variables is shown below.
