Acceleration, force and velocity gained by a charged particle in a uniform electric field.
Classical, non-relativistic model for a uniform field. If the velocity approaches a sizeable fraction of light speed, relativity takes over and this result overestimates.
Acceleration
How to use this tool
Type the charge in elementary charges — 1 for a proton, −1 magnitude for an electron (use 1 and read direction separately).
Type the mass in atomic mass units — 1.007276 for a proton, 0.00054858 for an electron.
Type the uniform electric field in volts per metre.
Type how long the particle spends in the field, in microseconds, to get the velocity gained.
Formula & worked example
A proton (charge 1 e, mass 1.007276 u) in a 100,000 V/m field feels 1.602 × 10⁻¹⁴ N and accelerates at about 9.58 × 10¹² m/s², gaining about 9.58 × 10⁶ m/s (3.2% of light speed) in 1 µs.
Limitations — read this before you rely on it
Classical model only: it ignores relativity, radiation reaction and field non-uniformity. Above roughly 10% of light speed, use relativistic dynamics. The sign of the charge sets the direction, not the magnitude shown.
Frequently asked questions
The magnitude of the electron charge, e = 1.602 × 10⁻¹⁹ C. Protons carry +1 e, electrons −1 e.
1 u = 1.6605 × 10⁻²⁷ kg, about the mass of one nucleon. A proton is 1.007276 u.
Positive charges accelerate along the field, negative charges opposite to it. The magnitude is the same.
When the velocity exceeds roughly 10% of light speed, the classical v = at result starts to overestimate badly.
Inkjet and CRT deflection, mass spectrometers, ion implanters, particle accelerators and plasma physics.