Electric Potential of a Point Charge
V = k · q / r
Quick answer
This calculator solves V = kₑ × q / r for Potential. With Charge 10 µC, Distance 10 cm, the result is 898.8 kV. It solves in 3 directions, so you can enter the values you have and get the one you need.
Calculator
Formula
Description
Electric potential is the electrostatic potential energy per unit charge at a distance r from a point charge. Unlike the field, potential is a scalar and falls off as 1/r rather than 1/r². The difference in potential between two points is the voltage that drives current. Setting the potential to a reference defines the voltage that appears across capacitors and in any electrostatic problem.
Variables
- V — Electric potential (V)
- q — Source charge (C)
- r — Distance from the charge (m)
- kₑ — Coulomb constant
Practical Notes
Potential is taken as zero at infinity. The work to bring a charge q′ from infinity to this point is q′·V. The electric field is the negative gradient of potential, E = −dV/dr.
Symbols and units
| Symbol | Meaning | Default unit | Accepted units |
|---|---|---|---|
| Vp | Potential | V | pV, nV, µV, mV, V, kV |
| 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: V = kₑ × q / r
- 3. Substitute: q = 10 µC, r = 10 cm
- 4. Result: Potential = 898.8 kV
Worked examples
Minimum range
Given: Charge 100 nC, Distance 1 mm
Result: Potential = 898.8 kV
Low range
Given: Charge 1 µC, Distance 10 mm
Result: Potential = 898.8 kV
Typical
Given: Charge 10 µC, Distance 10 cm
Result: Potential = 898.8 kV
High range
Given: Charge 100 µC, Distance 1 m
Result: Potential = 898.8 kV
Maximum range
Given: Charge 1 mC, Distance 10 m
Result: Potential = 898.8 kV
Solving for each variable
Solve for Potential
Charge 100 nC, Distance 1 mm → 898.8 kV
Solve for Charge
Potential 0.33 V, Distance 1 mm → 0.03672 pC
Solve for Distance
Potential 0.33 V, Charge 100 nC → 2.724 km
How Potential changes with Charge
| Charge (input) | Potential (result) |
|---|---|
| 1 µC | 89.88 kV |
| 2.5 µC | 224.7 kV |
| 5 µC | 449.4 kV |
| 7.5 µC | 674.1 kV |
| 10 µC | 898.8 kV |
| 15 µC | 1348 kV |
| 20 µC | 1798 kV |
| 40 µC | 3595 kV |
| 70 µC | 6291 kV |
| 100 µC | 8988 kV |
The same result in other units
| Unit | Value |
|---|---|
| V | 898800 |
| kV | 898.8 |
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<p><a href="https://vbatpower.com/formulas/electric-potential-point/">Electric Potential of a Point Charge</a> Calculator by vbatpower.com</p>Frequently asked questions
How do you calculate Electric Potential of a Point Charge?
Use V = kₑ × q / r. With Charge 10 µC, Distance 10 cm, Potential works out to 898.8 kV.
What is the formula for Electric Potential of a Point Charge?
The formula is V = kₑ × q / r. Electric potential is the electrostatic potential energy per unit charge at a distance r from a point charge.
How do you find Charge when you know the other values?
Rearrange for Charge: with Potential 0.33 V, Distance 1 mm, Charge is 0.03672 pC.
How do you find Distance when you know the other values?
Rearrange for Distance: with Potential 0.33 V, Charge 100 nC, Distance is 2.724 km.
What units does Electric Potential of a Point Charge use?
Potential is shown in V, kV. 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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