Acceleration in Electric Field Calculator

When a charged particle enters an electric field, it experiences a force that causes it to accelerate — the Acceleration in Electric Field Calculator works out exactly how much. Enter the particle charge (q), particle mass (m), and electric field strength (E) — or select a preset for an electron, proton, or alpha particle — to get the particle acceleration in m/s², plus the electric force (F = qE) and both values in scientific notation.

C

Charge of the particle in Coulombs. Use 1.6×10⁻¹⁹ C for a proton or electron.

kg

Mass of the particle in kilograms. Electron mass ≈ 9.109×10⁻³¹ kg, proton ≈ 1.673×10⁻²⁷ kg.

N/C

Magnitude of the uniform electric field in Newtons per Coulomb (equivalent to V/m).

Select a preset to auto-fill charge and mass for common particles.

Results

Particle Acceleration (a)

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Electric Force (F = qE)

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Acceleration (Scientific Notation)

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Force (Scientific Notation)

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Frequently Asked Questions

What is the formula for acceleration of a charged particle in an electric field?

The acceleration is calculated using a = qE/m, where q is the particle's charge in Coulombs, E is the electric field strength in N/C, and m is the particle's mass in kilograms. This formula comes from combining Coulomb's force law (F = qE) with Newton's second law (F = ma).

What is the difference between electric force and acceleration in this context?

The electric force (F = qE) is the force exerted on the charged particle by the electric field. The acceleration (a = F/m = qE/m) is how quickly that force changes the particle's velocity, and it depends on the particle's mass. A lighter particle like an electron accelerates far more than a heavier proton under the same force.

How fast does an electron accelerate in an electric field of 1000 N/C?

An electron (charge ≈ 1.6×10⁻¹⁹ C, mass ≈ 9.109×10⁻³¹ kg) in a 1000 N/C field experiences an acceleration of approximately 1.758×10¹⁴ m/s². This extraordinarily high value reflects how light the electron is compared to the force acting on it.

Does the direction of acceleration depend on the sign of the charge?

Yes. A positive charge accelerates in the same direction as the electric field, while a negative charge (like an electron) accelerates in the opposite direction. This calculator computes the magnitude of acceleration; the direction must be inferred from the charge sign and field orientation.

What is the SI unit of electric field strength?

The SI unit of electric field strength is Newtons per Coulomb (N/C), which is equivalent to Volts per meter (V/m). Both units are interchangeable and represent how much force is exerted per unit charge at a given point in the field.

Can this calculator be used for any charged particle?

Yes. You can enter any charge and mass values. The calculator includes presets for common particles — electrons, protons, and alpha particles — but you can enter custom values for ions, dust particles, or any other charged body in a uniform electric field.

Does the magnetic field also accelerate a charged particle?

A magnetic field can change the direction of a moving charged particle's velocity but does no work on it, so it does not change the particle's speed or kinetic energy. Only the electric field component accelerates (changes the speed of) the charged particle in the direction of the field.

What assumptions does this calculator make?

This calculator assumes a uniform electric field and ignores relativistic effects, gravity, and magnetic forces. For particles approaching the speed of light or in complex electromagnetic environments, more advanced models would be required.