Modelling an STM Tip current
Capacitance of a parallel_plate capacitor is

C = E0 * Er * Area/Distance

You can insert values for area and distance.
The Er of air is 1, as is vacuum.
Eo is apbut 8.89e-12 farad/meter.
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You might get better accuracy by using formula for round_surface (your needle) to a plane.