If you consider Grover's expression as bounding your desired
inductance from above, I think I can bound it from below --
by the case where the plane carries the return current. The
expression for this inductance comes from the following trick:
the fields are the same as for two identical wires (carrying
equal and opposite currents) spaced twice as far apart as the
wire is from the plane. For this case, the formula is:
L(wire-wire) = 4e-7 * ln(separation/radius) Henries/Meter
So for the wire "height" above ground plane, the current is
the same but the voltage (and so the inductance) is halved:
L(wire-plane) = 2e-7 * ln(2*height/radius) Henries/Meter
Hope that helps you (and that I haven't lost a factor of two
somewhere). I suspect the actual answer is an ugly finite
element problem.
Regards,
Mike Jenkins
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