Particle Acceleration in Electric Field Calculator

Calculate the acceleration of a charged particle in a uniform electric field based on charge, mass, and field strength.

PARTICLE ACCELERATION
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Force
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Acceleration
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Speed after 1 ns
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KE after 1 cm
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Charged Particles in Electric Fields

When a charged particle is placed in an electric field, it experiences an electrostatic force that accelerates it. Positive charges accelerate in the field direction; negative charges accelerate opposite. This principle is fundamental to particle accelerators, cathode ray tubes, mass spectrometers, and electron microscopes.

In a uniform electric field, the acceleration is constant, making the motion analogous to a projectile in gravity. This allows the use of standard kinematic equations to predict trajectory, velocity, and kinetic energy of charged particles under electromagnetic influence.

Force and Acceleration Formulas

F = qE     a = qE / m
KE = qEd (work done over distance d)

Where F is force in newtons, q is charge in coulombs, E is electric field in V/m, m is mass in kg, and d is distance in meters. The kinetic energy gained equals the work done by the electric field on the particle.

Common Particle Properties

ParticleCharge (C)Mass (kg)q/m Ratio
Electron1.602 × 10-199.109 × 10-311.759 × 1011
Proton1.602 × 10-191.673 × 10-279.578 × 107
Alpha3.204 × 10-196.646 × 10-274.822 × 107

Frequently Asked Questions

Why do electrons accelerate faster than protons?

Although both carry the same charge magnitude, the electron is about 1,836 times lighter than the proton. Since a = F/m, the electron experiences about 1,836 times greater acceleration in the same field. This is why electrons reach near-light speeds in relatively modest electric fields.

What happens at relativistic speeds?

When speed approaches the speed of light, Newtonian mechanics breaks down. The effective relativistic mass increases, so additional energy goes into mass rather than speed. Particle accelerators like the LHC require enormous energies to push particles closer to light speed due to this relativistic effect.

What is an electron-volt?

An electron-volt (eV) is the kinetic energy gained by an electron accelerated through 1 volt of potential difference. It equals 1.602 × 10-19 joules. It is a convenient unit in atomic and particle physics. Accelerators are rated in MeV, GeV, or TeV to describe the energies particles achieve.