Electrostatic Applications & Safety

Field means force per unit charge, F/q, measured in V m⁻¹ or equivalently N C⁻¹. Air conducts when that field is strong enough that a free electron, accelerated between two collisions, arrives with enough energy to knock an electron off the next molecule; each collision then makes two carriers, and the avalanche builds a channel in under a microsecond. For clean dry air in centimetre gaps the onset is about 3.0 × 10⁶ V m⁻¹. Put a charge Q on an isolated sphere of radius R and the field is largest right at the metal, E = kQ/R², so the sphere can hold at most Qₘₐₓ = E_break R²/k. For R = 0.25 m that is 2.1 × 10⁻⁵ C, reached at V = E_break R = 7.5 × 10⁵ V. Double the radius and the charge limit quadruples while the voltage limit only doubles — which is the whole reason a demonstration generator carries a large smooth dome rather than a small one.

Conductors joined by metal share one potential. For a sphere V = kQ/R, so at a common V the charge divides as Q ∝ R, and the surface field becomes E = kQ/R² = V/R. Halve a radius and you double its field at the same potential. Take a 0.20 m dome carrying a 1.0 mm burr on a bolt head: the burr's field is R/r = 200 times the dome's, so air fails at the burr when the whole assembly reaches only V = E_break r = 3.0 × 10³ V, while the bare dome would have held 6.0 × 10⁵ V. The burr carries just r/R = 0.5% of the charge and destroys 99.5% of the working range. Sometimes that is exactly the point: a lightning rod, an ioniser needle and a photocopier corona wire are sharpened on purpose so that they ionise air at a modest potential. Everywhere else it is a defect, which is why high-voltage hardware is deburred, rounded and polished.

A lightning rod neither repels the strike nor quietly drains the cloud; the corona current it emits is microamps against a stroke of tens of kiloamps. What it does is offer the most probable termination point and, behind it, a low-resistance route to earth that passes through nothing flammable. The resistance of the earth electrode then matters directly: a median 30 kA return stroke into a 10 Ω electrode lifts the whole down-conductor to 30 × 10³ A × 10 Ω = 3 × 10⁵ V above remote earth for the duration of the stroke. Anything metallic nearby but separately earthed is suddenly 300 kV away from it, and that difference is bridged by a side flash. This is why a protection system bonds pipework, cable armour and structural steel together instead of isolating them, and why a car or a steel-framed building protects the people inside: the current stays on the conducting shell around them.

Rub two dissimilar insulators together and they exchange charge, leaving flakes of one plastic with a positive charge-to-mass ratio and the other with a negative one. Drop them between two plates that make a uniform field E and each flake feels a sideways force F = qE while gravity pulls it down, so the horizontal acceleration is a = (q/m)E and the sorting is by charge-to-mass ratio. With q/m = 6.0 × 10⁻⁶ C kg⁻¹ and E = 3.0 × 10⁵ V m⁻¹ the acceleration is 1.8 m s⁻²; a 1.2 m fall takes t = √(2h/g) = 0.49 s, so the flake drifts x = ½at² = 0.22 m sideways and the two plastics land 0.44 m apart in different bins. Note the field chosen: a tenth of breakdown, because a spark would neutralise the very charge the machine runs on. Precipitators and powder coating live on the same two lines of algebra.

A standing person is modelled as a 100 pF capacitor with about 1.5 kΩ of body resistance. Walk across a nylon carpet in dry air and a field meter may read 8.0 kV: that is Q = CV = 0.80 μC and W = ½CV² = 3.2 mJ, delivered at a peak current of V/R = 5.3 A over a time constant RC = 150 ns. Now compare thresholds rather than adjectives. A person first feels a discharge at roughly 2 kV, which is 0.20 mJ. A hydrogen-air mixture ignites on 0.017 mJ, a typical solvent vapour on about 0.25 mJ, and a fine organic dust cloud on tens of millijoules. A thin gate oxide can fail at 100 V, which on 100 pF is 0.50 μJ — four hundred times below the faintest shock a human can detect. The nervous system is calibrated far too high to be used as an instrument.

Charge leaves along a resistance, and τ = RC says how fast. With the 100 pF body, a dissipative floor-and-footwear path of 1 MΩ to 1 GΩ gives τ between 1.0 × 10⁻⁴ s and 0.1 s, so a person is neutral again before reaching the bench; insulating shoes on a sealed floor can exceed 1 TΩ, where τ ≈ 100 s and the charge simply travels with them. A wrist strap is built around a 1 MΩ series resistor for both halves of that trade: fast enough to bleed static, high enough that touching 250 V would pass only 250 μA. Raising humidity above about 50% helps by making surfaces conduct, and an ioniser is the fallback where the charged object is an insulator that cannot be drained at all. Then verify rather than assume: a charged-plate monitor should fall from 1000 V to 100 V in a couple of seconds, and a field meter should read the process, not the specification sheet.