No, or not really.
https://www.google.com/search?q=%281mA+%2F+elementary+charge%29+*+sqrt%282+*+9.1093837e-31+kilograms+*+100+electron+volts%29I *think* that's right... the number of electrons, times the momentum of an electron at that energy. Taking 1mA and 100V as very typical values.
IIRC, µN are just measurable, maybe nN for small things, but you'll have a hard time making mA in things that small, so, it seems unlikely. Meanwhile the electric field is huge:
https://www.google.com/search?q=%28%28100V%2Fmm%29%5E2+*+electric+constant+%2F+2%29+*+1cm%5E2The field could be balanced by placing symmetrical electrodes while having asymmetrical electron flow, but are you really going to balance that to within a percent,
while the balance is moving? It'll just unbalance, swing around and short out.
Well, motion is manageable: one would employ a differential field plate/set, and control arm motion based on laser reflection, servoing it stationary. This also removes the spring-mass complex pole, allowing the control loop to assert a lower mechanical impedance, faster control, and doing the test at different frequencies may allow separation of interfering effects like adsorption and expansion.
An electron beam welder might be more promising: currents are comparable, but the energy is much higher (10s keV). But as the name suggests, this is likely to melt the target, so, that's a bit of a non-starter.
Note also, everything in here is going to be hot, and is surrounded by just a little bit of gas -- heat means emission of adsorbed and chemically-bound gases, and convection of what remains in the chamber. That too will dominate the errors.
Making the EBW plate as an electric "catcher" (have an outer grid (ring, or tube, more like) set to ground potential, inner plate set to -V), might have some merit -- most energy gets recycled into electric current, rather than dissipated as heat, and only two connections up the torsion filament are needed, versus 3+ for a heated cathode with grid. Albeit at high voltage (the insulation up the torsion filament might be worse than using thicker wires for heater power, lol).
Tim