FWIW, tau=sqrt(L*C); Z0=sqrt(L/C); L=3.86e-5; tau=4e-8
(Please note: That is NOT!! a lumped model!)

implies that C= 41pF and Z0=965ohms

(v.f. = 0.058 is left as an exercise for the reader.)

But if the coil's axis is parallel to a ground plane, that 6" diameter
coil must be spaced about a quarter inch away from the ground plane
(axis 3.25" from ground plane) to get that 41pF capacitance, and that's
assuming a solid tube 3" in radius as a quick model .(An
approximation!)

Cheers,
Tom