Electric Field of a Point Charge
E = k · q / r²
Quick answer
This calculator solves E = kₑ × q / r² for Electric Field. With Charge 10 µC, Distance 10 cm, the result is 8.988 MV/m. It solves in 3 directions, so you can enter the values you have and get the one you need.
Calculator
Formula
Description
The electric field around a point charge describes the force per unit charge that a test charge would feel at a given distance. It points radially outward from a positive charge and falls off as the inverse square of distance. The field is the cause; the force on any charge placed in it (F = qE) is the effect. Electric fields determine breakdown, corona, and the operation of every field-effect device.
Variables
- E — Electric field strength (V/m or N/C)
- q — Source charge (C)
- r — Distance from the charge (m)
- kₑ — Coulomb constant
Practical Notes
Air breaks down at about 3×10⁶ V/m (3 kV/mm). Field strength sets clearance and creepage requirements and the maximum voltage a dielectric can withstand.
Symbols and units
| Symbol | Meaning | Default unit | Accepted units |
|---|---|---|---|
| E | Electric Field | V/m | mV/m, V/m, kV/m, MV/m |
| q | Charge | µC | pC, nC, µC, mC, C |
| r | Distance | cm | mm, cm, m, km |
Step by step
- 1. What you know: Charge 10 µC, Distance 10 cm
- 2. The relation: E = kₑ × q / r²
- 3. Substitute: q = 10 µC, r = 10 cm
- 4. Result: Electric Field = 8.988 MV/m
Worked examples
Minimum range
Given: Charge 100 nC, Distance 1 mm
Result: Electric Field = 898.8 MV/m
Low range
Given: Charge 1 µC, Distance 10 mm
Result: Electric Field = 89.88 MV/m
Typical
Given: Charge 10 µC, Distance 10 cm
Result: Electric Field = 8.988 MV/m
High range
Given: Charge 100 µC, Distance 1 m
Result: Electric Field = 0.8988 MV/m
Maximum range
Given: Charge 1 mC, Distance 10 m
Result: Electric Field = 89.88 kV/m
Solving for each variable
Solve for Electric Field
Charge 100 nC, Distance 1 mm → 898.8 MV/m
Solve for Charge
Electric Field 10 V/m, Distance 1 mm → 0.001113 pC
Solve for Distance
Electric Field 10 V/m, Charge 100 nC → 9.48 m
How Electric Field changes with Charge
| Charge (input) | Electric Field (result) |
|---|---|
| 1 µC | 0.8988 MV/m |
| 2.5 µC | 2.247 MV/m |
| 5 µC | 4.494 MV/m |
| 7.5 µC | 6.741 MV/m |
| 10 µC | 8.988 MV/m |
| 15 µC | 13.48 MV/m |
| 20 µC | 17.98 MV/m |
| 40 µC | 35.95 MV/m |
| 70 µC | 62.91 MV/m |
| 100 µC | 89.88 MV/m |
The same result in other units
| Unit | Value |
|---|---|
| V/m | 8988000 |
| kV/m | 8988 |
| MV/m | 8.988 |
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<p><a href="https://vbatpower.com/formulas/electric-field-point/">Electric Field of a Point Charge</a> Calculator by vbatpower.com</p>Frequently asked questions
How do you calculate Electric Field of a Point Charge?
Use E = kₑ × q / r². With Charge 10 µC, Distance 10 cm, Electric Field works out to 8.988 MV/m.
What is the formula for Electric Field of a Point Charge?
The formula is E = kₑ × q / r². The electric field around a point charge describes the force per unit charge that a test charge would feel at a given distance.
How do you find Charge when you know the other values?
Rearrange for Charge: with Electric Field 10 V/m, Distance 1 mm, Charge is 0.001113 pC.
How do you find Distance when you know the other values?
Rearrange for Distance: with Electric Field 10 V/m, Charge 100 nC, Distance is 9.48 m.
What units does Electric Field of a Point Charge use?
Electric Field is shown in V/m, kV/m, MV/m. Values are held in SI base units internally, so you can mix prefixes without converting by hand.
Related Concepts
All Fields & Electromagnetism formulas →Need more features?
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