# Acceleration in the Electric Field Calculator

Created by Dominik Czernia, PhD
Reviewed by Bogna Szyk and Adena Benn
Last updated: Jun 05, 2023

There are two main types of fields that act on the charged particles: electric and magnetic. In our acceleration in the electric field calculator, we have focused on the former. If you want to learn more about the latter, check out our Lorentz force calculator. In the text below, we explain what the force acting on the charged particle in the electric field is and how you can compute the acceleration of this particle.

## Charged particle in an electromagnetic field

One of the fundamental forces of nature, the electromagnetic force, consists of the electric and magnetic fields. On the one hand, the electric field always acts on the charged particle, and on the other hand, the magnetic field acts only when this particle is moving.

The magnitude of force $F$, which is exerted on the charged particle in the electric field $E$, can be described with Coulomb's law which we explore further in our Coulomb's law calculator. It states that $F = q E$, where $q$ is the particle's charge. You can see that particles with a higher charge will always be attracted (or repelled) stronger.

## Acceleration in the electric field

If we also take into account the mass of the particle, we will be able to calculate its acceleration. For this purpose, we can use the following formula:

$a = \frac{qE}{m},$

where:

• $a$ – Acceleration of the particle;
• $q$ – Charge of the particle;
• $m$ – Mass of the particle; and
• $E$ – Electric field.

The default weight and charge units used in our calculator are, respectively, the weight $\small m_{\rm e} = 9.1 \times 10^{-31}\ \rm kg$ and the charge $\small \rm e = 1.6 \times 10^{-19}\ C$ of a single electron.

The above equation can be easily derived from Newton's second law: $F = ma$. We just have to combine it with the electrostatic force $F = q E$ described in the previous section.

## Acceleration of electrons

What is the magnitude of the acceleration of an electron in a typical electric field? Is it similar to the gravitational force of our Earth?

Let's check it with our calculator, assuming that we have the electron with the mass $m_{\rm e}$ and charge $e$ in the relatively weak electric field $\small E = 1\ \rm N/C$.

The result is astonishing! The electron accelerates almost 20 billion times faster than the average acceleration of gravity on Earth.

Dominik Czernia, PhD
Mass
me
Charge
e
Electric field
N/C
Acceleration
m/s²
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