Acceleration of a charged particle in an electric field
A particle carrying 0.000002 C with a mass of 0.001 kg in a 5000 N/C field accelerates at 10 m/s². Enter the charge, mass and field strength, signed for direction, and get charge times field divided by mass. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Worked example
- Q
- 0.000002
- M
- 0.001
- E
- 5,000
- Charge
- 0.000002
- Mass
- 0.001
- Electric field
- 5,000
- Field
- 5,000
A particle acceleration in an electric field calculator combines Newton's second law with the electric force F = qE to give a = qE/m for a charged particle in a uniform field. Signed charge and field values carry direction along your chosen axis, so negative electrons accelerate opposite to the field.
What a = qE/m means for a charged particle
In classical electrostatics a uniform electric field E exerts a force F equals q E on a point charge q, and Newton's second law F equals m a turns that force into an acceleration a equals q E divided by m. When charge is in coulombs, mass in kilograms, and field in newtons per coulomb or volts per meter, the result is in meters per second squared, the SI unit of acceleration.
The formula explains why subatomic particles pick up enormous accelerations in modest fields: an electron carries a tiny charge but an even tinier mass, so the quotient q E over m can reach ten to the fourteenth meters per second squared in a field of only one thousand newtons per coulomb. Direction follows the sign of the product: a positive charge accelerates along E, while a negative charge accelerates opposite to E, and a negative field flips both.
Zero charge or zero field yields zero acceleration, which is physically valid and not an error. A zero mass is rejected outright: division by zero has no physical meaning here and the model is purely classical, so relativistic massless particles are out of scope. The tool assumes a uniform field and non-relativistic motion; it does not integrate trajectories, handle non-uniform field maps, or apply relativistic corrections when speeds approach the speed of light.
Practical tips, limits, and related searches
Convert everything to base SI before calling if you want acceleration directly in meters per second squared: microcoulombs to coulombs, grams to kilograms, kilovolts per meter to volts per meter. Scientific notation is your friend for particle problems—an electron is about 1.602e-19 coulombs and 9.109e-31 kilograms, and a proton is the same charge magnitude with a mass near 1.673e-27 kilograms—so the quotient stays manageable.
If you need the force first, use an electric field force tool and divide by mass yourself; if you need velocity after some distance, combine the result with kinematics. Round-trip checks are easy: multiply the published acceleration by the mass and confirm it equals q times E within the same twelve-decimal rounding.
What you can do with it
Homework checks for a = qE/m
Students enter charge, mass, and field from textbook problems and compare hand-computed acceleration magnitude and sign against a deterministic result before submitting.
Back-of-envelope estimates for lab setups
Technicians estimate how hard a charged droplet, ion, or electron will accelerate in a known plate field before adjusting voltage or electrode spacing.
FAQ
What is the acceleration of a charged particle in an electric field?
The field exerts F = qE on the charge, and Newton's second law gives a = F/m, so a = qE/m. In SI units, q in coulombs, E in N/C (or V/m), and m in kilograms give a in m/s^2.
Does the sign of the charge matter?
Yes. A positive charge accelerates in the direction of E; a negative charge (like an electron) accelerates opposite to E. This tool returns a signed scalar along your chosen axis.
What happens if the mass is zero?
Division by zero is undefined and the classical model does not cover massless particles.
Does this handle relativistic speeds?
No. It is the classical a = qE/m. When the resulting motion approaches the speed of light, relativistic dynamics is needed and this result is only a first approximation.
Is the particle acceleration calculator free?
The browser tool is free and runs locally.
Related tools
For developers — API access
Everything on this page is available programmatically. This section is for teams who want to wire it into their own systems; everyone else can just use the tool above.
API endpoint
Prefer to automate it? One authenticated POST creates the task; the result comes back by webhook or a signed link. The same capability also runs here on the web, by email and from Telegram — and soon from our app too.
Call it from your stack
curl -X POST https://api.kit.forhosting.com/phys/acceleration-of-particle-in-electric-field \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"q":1.602e-19,"m":9.109e-31,"E":1000}'const res = await fetch("https://api.kit.forhosting.com/phys/acceleration-of-particle-in-electric-field", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"q": 1.602e-19,
"m": 9.109e-31,
"E": 1000
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/phys/acceleration-of-particle-in-electric-field",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"q": 1.602e-19,
"m": 9.109e-31,
"E": 1000
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/phys/acceleration-of-particle-in-electric-field", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"q":1.602e-19,"m":9.109e-31,"E":1000}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"q":1.602e-19,"m":9.109e-31,"E":1000}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/phys/acceleration-of-particle-in-electric-field", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"q": 1.602e-19,
"m": 9.109e-31,
"E": 1000
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "phys.acceleration_of_particle_in_electric_field",
"status": "queued",
"_links": {
"result": "/tasks/tsk_…/result"
}
}The API is asynchronous: the call returns a task_id immediately and the result arrives by webhook. Polling is capped at 1 req/s per task.
Pricing
Published price — no tokens, no invented credits. A failed task is never charged.
Limits
max_abs | 1000000000000 |
Errors
| HTTP | Code | Meaning |
|---|---|---|
401 | unauthorized | Missing or invalid API key. |
402 | insufficient_balance | Your balance doesn't cover the task price. |
404 | unknown_type | That task type doesn't exist. |
429 | rate_limited | Too many requests. Use the webhook instead of polling. |
Technical notes
A zero mass, a non-numeric string, or any non-finite input fails with invalid_input instead of inventing an answer.
How to call the API and what comes back
Prefer sending numbers rather than pre-formatted strings; string numbers are accepted only when they match a strict finite pattern including optional scientific notation such as 1.602e-19. Send a JSON body with three required finite numbers: q (aliases charge and Q) for charge in coulombs, m (aliases mass and M) for mass in kilograms, and E (aliases electric_field, field, and field_strength) for field strength in newtons per coulomb or volts per meter. Absolute input values must stay within one trillion, and the computed acceleration must remain finite and below one to the thirtieth so results stay representable in IEEE double precision on the Worker and in the browser. On success the response echoes rounded q, charge, m, mass, E, electric_field, and field; sets a and acceleration to the same rounded quotient; formula to the string a equals q E over m; equation to a human-readable substitution line; unit_acceleration to m/s^2 with the other SI units; message to a short English summary; and steps to an ordered array of given values, the formula, the substitution, a direction note, and the summary. Failed validation—missing fields, non-numeric strings, non-finite numbers, zero mass, or out-of-range values—returns invalid_input and is never charged. Pricing is a flat $0.002 per successful request with unit item.
Practical tips, limits, and related searches
When teaching, pair examples: a two-microcoulomb charge on a one-gram mass in a five-thousand-newton-per-coulomb field accelerates at ten meters per second squared; flipping the sign of the charge reverses the acceleration; zero field gives zero acceleration; a zero mass demonstrates the hard invalid_input path. This landing targets people searching for a particle acceleration in electric field calculator, a equals qE over m, or acceleration of a charged particle; it is not a trajectory integrator, not a relativistic accelerator model, and not a field-from-charges solver. Failed tasks returning invalid_input do not consume prepaid balance, which keeps exploratory scripts cheap when learners deliberately send bad values.
Integration use cases
Unit tests for physics solvers
Generate known-good positive, negative, and zero-acceleration cases plus deliberate zero-mass rejections as expected values for coding kata and CI fixtures.