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Electric field across a gap

How strong is the field between two electrodes at this voltage and spacing?

The formula
E=Vd
E
Electric field, V/m
V
Voltage, V
d
Gap, m
LaTeX 
E = \frac{V}{d}

Work it out

V

The potential difference across the gap.

mm

The electrode separation.

Compare with a variation

Result

E Electric field 2500 V/cm

The field strength between the plates, uniform in this model.

With your numbers
2500 V/cm=500 V2 mm
LaTeX 
2500\,\mathrm{V/cm} = \frac{500\,\mathrm{V}}{2\,\mathrm{mm}}

This result is a link — the address bar holds your numbers, so it can be pasted into a post and opened to the same answer.

What this looks like

Electric field against voltage Voltage swept from 250 V to 750 V with everything else held at your numbers. The dashed lines cross where you are.
Electric field against voltageElectric field rises from 1250 V/cm to 3750 V/cm as voltage rises from 250 V to 750 V. At your voltage of 500 V it is 2500 V/cm.1000200030004000200400600800500 V2500 V/cmVoltage (V)Electric field (V/cm)
The formula behind the curve
E=Vd
E
Electric field, V/m
V
Voltage, V
d
Gap, m
LaTeX 
E = \frac{V}{d}
What moves the answer Each input moved 10% either way, with the others held still, and the effect on electric field.
What moves the answerElectric field is most sensitive to Gap, which moves it by about 11.1% for a 10% change. It is least sensitive to Voltage, at about 10%.Change in the answer when each input moves by 10%-20%-10%10%20%Gap±11.1Voltage±10
The formula behind the curve
E=Vd
E
Electric field, V/m
V
Voltage, V
d
Gap, m
LaTeX 
E = \frac{V}{d}

Method

  1. Convert the gap to metres.
  2. Divide the voltage by the gap. This is the field for a uniform, parallel-plate gap — the same relation the cell capacitance calculations use for the field across the water.

Assumptions

  • The electrodes are parallel plates with the field uniform between them and zero outside — a real point, wire or irregular electrode concentrates the field near sharp features far above this average figure.
  • No space charge. A gas gap that is already partly ionised distorts the field it sits in, which this static picture does not capture.