Library / Electrical / ELE-11
Electrical
Electric field strength
Uniform electric field between parallel plates, or across an insulator, from the voltage and the gap.
- Ref
- ELE-11
- Rev
- v1
- Field
- Electrical
- Result
- E [kV/mm]
E in volts per metre (V/m), V in volts, d in metres. The calculator takes V in kV and d in mm, so the field comes out in kV/mm, which is the same number as MV/m.
The field between two plates is the voltage divided by the gap. Squeeze the same voltage into a smaller gap and the field rises. If the field exceeds the dielectric strength of the material between the plates, the insulation breaks down.
Calculator
- Field in V/m2,000,000 V/m
- Fraction of the breakdown field of air (about 3 kV/mm)66.67 %
What drives the result
Each variable is moved across its typical range while the others stay at the values above. The longest bar is the key driver.
- Field is voltage per unit gap. Halving the gap doubles E, which is why a thin gap or a sharp point flashes over first.
- Air breaks down at about 3 kV/mm in a uniform field at standard conditions. Many solid insulating materials withstand much more, in the range of tens of kV/mm.
- E = V/d holds for a uniform field. Near sharp points and edges the real field is much higher than V/d, so breakdown occurs below the calculated value.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing (kV/mm) | Local step | Change in result |
|---|---|---|---|---|---|---|
| d Gap | 0.1 to 50 mm | 0.2 | 100 | 99.8 | +10% | −9.09 % |
| V Voltage across the gap | 0.1 to 100 kV | 0.02 | 20 | 19.98 | +10% | +10 % |
Sweep of Gap
| Gap (mm) | Electric field (kV/mm) |
|---|---|
| 0.1 | 100 |
| 0.2175 | 45.99 |
| 0.4729 | 21.15 |
| 1.028 | 9.725 |
| 2.236 | 4.472 |
| 4.862 | 2.057 |
| 10.57 | 0.9457 |
| 22.99 | 0.4349 |
| 50 | 0.2 |
Sweep one variable
Variables and how each one contributes
Electric field
What the equation gives you. Everything else feeds it.
Voltage across the gap
Potential difference between the two plates or electrodes. Directly proportional: doubling the voltage doubles the field.
Gap
Distance between the plates, or the thickness of the insulator. Inversely proportional: halving the gap doubles the field, so thin insulation is highly stressed.
Worked example with the values above
- Check the units: kV divided by mm is kV/mm, which equals MV/m.
- E = V/d = 10 / 5 = 2 kV/mm.
- Air breaks down at roughly 3 kV/mm in a uniform field at normal pressure, so this gap is at about 66.67% of that value.
Assumptions and limits
- Uniform field between parallel plates or across a uniform thickness.
- The gap d is the true distance across the insulator or air.
- Breakdown values are for standard conditions. Altitude, humidity, temperature and contamination reduce them.
Common mistakes
- Mixing mm and m, or kV and V, in the same line.
- Using the formula for a sharp point or a non-uniform gap, where the field peaks well above V/d.
- Using an RMS voltage when the peak voltage sets the stress. Use the peak.
Statistics and uncertainty
Breakdown is statistical, not a sharp threshold. The dielectric strength is quoted as a typical or minimum value, with a spread that depends on thickness, temperature, humidity, surface condition and how long the voltage is applied. Designers use a safety factor, and test results are often fitted with a Weibull distribution.
Where it is used
- Checking clearance and insulation thickness in high-voltage equipment.
- Capacitor dielectric thickness and voltage rating.
- Estimating the risk of arcing across a gap.
Maths you need
- Units and prefixes: kV/mm = MV/m = 106 V/m
- Ratios: field is voltage per unit distance