Library / Foundations: Physics / FPH-27
Foundations: Physics
Electric field of a point charge
Field strength at a distance from a point charge.
- Ref
- FPH-27
- Rev
- v1
- Field
- Foundations: Physics
- Result
- E [kV/m]
For a point charge in vacuum. Force on a charge q is q times the field vector. ε₀ = 8.854×10⁻¹² F/m.
A charge creates an electric field that weakens with the square of the distance.
Calculator
kV/m
nC
cm
- Force on a 1 nC test charge8.988 µN
- Field in V/m8,988 V/m
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 strength (kV/m) current value 8.988 kV/m
QChargeKey driver
0.0899899
rDistance
0.0899899
- Air breaks down at about 3 MV/m, which sets how close high-voltage parts can be.
- The same inverse-square form applies to gravity.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing (kV/m) | Local step | Change in result |
|---|---|---|---|---|---|---|
| Q Charge | 0.1 to 1,000 nC | 0.08988 | 898.8 | 898.7 | +10% | +10 % |
| r Distance | 1 to 100 cm | 0.08988 | 898.8 | 898.7 | +10% | −17.4 % |
Sweep of Distance
| Distance (cm) | Field strength (kV/m) |
|---|---|
| 1 | 898.8 |
| 1.778 | 284.2 |
| 3.162 | 89.88 |
| 5.623 | 28.42 |
| 10 | 8.988 |
| 17.78 | 2.842 |
| 31.62 | 0.8988 |
| 56.23 | 0.2842 |
| 100 | 0.08988 |
Sweep one variable
Field strength (kV/m)Hover, touch, or use the arrow keys on the chart
Variables and how each one contributes
E
Field strength
What the equation gives you. Everything else feeds it.
Q
Charge
Magnitude of the charge. Directly proportional.
r
Distance
Distance from the charge. Inverse square.
Worked example with the values above
- 4πε₀ = 1.113×10−10 F/m; r = 0.1 m.
- E = 1×10−8 / (1.113×10−10 × 0.01) = 8,988 V/m.
- In kV/m 8.988 kV/m.
Assumptions and limits
- Point charge in vacuum (air is very close).
- Distance measured from the charge.
Common mistakes
- Using cm instead of m.
- Forgetting the direction of the field.
Statistics and uncertainty
Distance is squared, so a 2% error in r gives about 4% error in the field.
Where it is used
- Insulation spacing for high-voltage equipment.
- Static charge hazards.
Maths you need
- Charge: coulombs
- Inverse square law: 1/r²