Electric fields push charged particles, and because electrons are so light they accelerate enormously – 1.76 × 10¹⁴ m/s² in a field of just 1 kV/m. This is the principle behind cathode-ray tubes, particle accelerators and mass spectrometers.
How to use the Acceleration of a Particle in an Electric Field Calculator
- Particle
- Mass m
- Charge q
- Electric field E
Results update as you type, every field has its own unit menu, and everything is calculated in your browser.
How it works
Choose the particle or enter its mass and charge, then the electric field strength.
Inputs explained
| Field | What to enter |
|---|---|
| Particle | Choose one: Electron, Proton, Neutron (no charge), Alpha particle … |
| Mass m | Units: kg, u (Da), mₑ |
| Charge q | Units: e, C, nC |
| Electric field E | Units: V/m, kV/m, V/cm, MV/m, N/C |
What each result means
- Force F = [q]×[Electric field E]
- Acceleration a = abs([q]×[Electric field E]÷[m])
Example values
How the main result changes when Mass m changes and everything else stays at the example values above:
| Mass m (kg) | Acceleration a (m/s²) |
|---|---|
| 4.5547e-31 | 175,882,001,077,216.3 |
| 6.8320e-31 | 175,882,001,077,216.3 |
| 9.1094e-31 | 175,882,001,077,216.3 |
| 1.1387e-30 | 175,882,001,077,216.3 |
| 1.3664e-30 | 175,882,001,077,216.3 |
| 1.8219e-30 | 175,882,001,077,216.3 |
Formula
F = q·E, a = q·E / m
Worked example
Inputs — Particle: Electron; Electric field E: 1,000 V/m.
Results — Force F = -1.6022e-16 N; Acceleration a = 175,882,001,077,216.3 m/s²; Direction = Against the field.
Key terms
- Electric field
- Force per unit charge.
Frequently asked questions
Why do electrons accelerate so much?
Their charge-to-mass ratio is huge: 1.76 × 10¹¹ C/kg.
Which way does an electron move?
Opposite to the field direction, because its charge is negative.
Is gravity important here?
No – electric forces on particles are vastly stronger.
What happens at high speeds?
Relativity limits the speed below c, so a stops being constant.