Acceleration in Electric Field Calculator
Calculate the acceleration of charged particles in electric fields using fundamental physics
Calculate Particle Acceleration
Mass of the charged particle
Electric charge of the particle
Electric field strength
Calculation Results
Acceleration
Force & Comparison
Formula used: a = qE/m
Where: a = acceleration, q = charge, E = electric field, m = mass
Force: F = qE (Coulomb's law)
Example: Electron in Electric Field
Standard Electron Example
Particle: Single electron
Mass: mₑ = 9.109 × 10⁻³¹ kg
Charge: e = 1.602 × 10⁻¹⁹ C
Electric field: E = 1 N/C (relatively weak field)
Calculation
a = qE/m = (1.602 × 10⁻¹⁹ C)(1 N/C) / (9.109 × 10⁻³¹ kg)
a = 1.602 × 10⁻¹⁹ / 9.109 × 10⁻³¹
a = 1.759 × 10¹¹ m/s²
Comparison: ~1.79 × 10¹⁰ times Earth's gravity!
Physical Constants
Electron
Mass: 9.109 × 10⁻³¹ kg
Charge: -1.602 × 10⁻¹⁹ C
q/m: -1.759 × 10¹¹ C/kg
Proton
Mass: 1.673 × 10⁻²⁷ kg
Charge: +1.602 × 10⁻¹⁹ C
q/m: +9.576 × 10⁷ C/kg
Other Constants
Earth gravity: 9.807 m/s²
Elementary charge: 1.602 × 10⁻¹⁹ C
Atomic mass unit: 1.661 × 10⁻²⁷ kg
Electric Field Examples
Note: Higher fields produce dramatically higher accelerations for charged particles
Understanding Acceleration in Electric Fields
Fundamental Physics
When a charged particle is placed in an electric field, it experiences a force described by Coulomb's law: F = qE. According to Newton's second law (F = ma), this force causes the particle to accelerate with a = qE/m.
Key Relationships
- •Acceleration is proportional to charge (q)
- •Acceleration is proportional to field strength (E)
- •Acceleration is inversely proportional to mass (m)
- •Direction depends on the sign of the charge
The Physics Equations
F = qE
F = ma
a = qE/m
- F: Force acting on the particle (N)
- q: Electric charge of the particle (C)
- E: Electric field strength (N/C or V/m)
- m: Mass of the particle (kg)
- a: Acceleration of the particle (m/s²)
Important: This formula assumes the electric field is uniform and the particle starts from rest or has constant velocity in the absence of the field.
Electrons
Due to their small mass and unit charge, electrons achieve enormous accelerations even in weak electric fields - billions of times Earth's gravity.
Applications
This principle is used in CRT displays, electron microscopes, particle accelerators, and mass spectrometers to control charged particle motion.
Charge-to-Mass Ratio
The q/m ratio is crucial in particle physics. Particles with higher q/m ratios are easier to accelerate and deflect in electric fields.