Charge in an Electric Field Calculator
What a uniform electric field does to a charged particle: the force on it, its acceleration, the speed and energy it gains crossing a distance from rest, and how long that takes.
A charge q in a field E feels a force qE, so it accelerates at qE ÷ m — enormously for an electron, whose mass is tiny.
How the charge in an electric field calculator works
A charge q in a field E feels a force qE, so it accelerates at qE ÷ m — enormously for an electron, whose mass is tiny. Over a distance d from rest it gains kinetic energy qEd, which in electronvolts is simply the voltage crossed times the charge in units of e. Speeds are non-relativistic; the calculator warns when they are not.
Formula: F = qE; a = qE ÷ m; v = √(2ad); KE = qEd
Worked examples
| Inputs | Acceleration (m/s²) | Note |
|---|---|---|
| Electron in 1,000 V/m over 1 cm | 1.759e+14 | 1.759 × 10¹⁴ m/s², 10 eV |
| Proton in the same field | 9.579e+10 | 9.579 × 10¹⁰ m/s² |
| Alpha particle across 1 MV/m for 10 cm | 4.822e+13 | 200 keV |
FAQFrequently asked questions
Why is the energy in electronvolts so simple?
An electronvolt is the energy one elementary charge gains crossing one volt. A uniform field of E volts per meter over d meters is a potential difference of E × d volts, so a particle of charge n·e gains n × E × d electronvolts.
Why does the electron go so much faster than the proton?
Same force, 1,836 times less mass — so 1,836 times the acceleration. Over the same distance it gains the same energy, but that energy is all speed for the light particle.
When does relativity matter?
Once the speed approaches a tenth of c the kinetic energy is no longer ½mv² and the particle gains less speed than this predicts. For an electron that happens above a few kilovolts; for a proton above a few megavolts.
What if the field is not uniform?
Then the force changes along the path and the energy gained is the charge times the potential difference actually crossed. The uniform-field case describes parallel plates and the gaps in accelerators well.
Where these figures come from
- NIST — CODATA 2018 fundamental physical constants — G, g₀, R, c
- NIST Special Publication 811 — Guide for the use of the International System of Units — unit conversions
- The Engineering ToolBox — material properties — specific heats, expansion coefficients, densities
- National Institute of Standards and Technology — the US measurement authority
Last checked: September 2026. Constants are the CODATA 2018 values; formulas are the standard textbook forms.