How Acceleration in an Electric Field Works
A charged particle sitting in an electric field feels an electric force F = qE, where q is the particle's charge and E is the field strength. Newton's second law, F = ma, then gives the particle's acceleration directly: a = qE / m, where m is the particle's mass. In a uniform field this acceleration is constant, so the same constant-acceleration kinematics used for gravity or any other steady force apply to velocity and distance.
The formulas used
- Acceleration: a = qE / m
- Electric force: F = qE (equivalently F = ma)
- Velocity after time t: v = v0 + at
- Distance traveled in time t: d = v0t + ½at²
Typical particle charge and mass
- Electron: q = -1.602 × 10-19 C, m = 9.109 × 10-31 kg
- Proton: q = +1.602 × 10-19 C, m = 1.673 × 10-27 kg
- Alpha particle (helium nucleus): q = +3.204 × 10-19 C, m = 6.645 × 10-27 kg
Getting accurate results
- Keep the sign of the charge consistent with your intended direction: a positive charge accelerates in the direction of E, a negative charge (like an electron) accelerates opposite to E.
- Enter the electric field in N/C (equivalently V/m) and mass in kilograms — mixing unit systems is the most common source of errors of many orders of magnitude.
- This model assumes a uniform field and non-relativistic speeds (v much less than the speed of light). Near the speed of light, relativistic momentum makes a = qE / m inaccurate.
Frequently Asked Questions
What is the formula for acceleration in an electric field?
Acceleration comes from combining Newton's second law with the electric force: F = qE and F = ma, so a = qE / m. Here q is the particle's charge in coulombs, E is the electric field strength in newtons per coulomb (equivalently volts per meter), and m is the particle's mass in kilograms.
Why does a negative charge accelerate opposite to the field?
The electric force is F = qE, a vector equation. A positive charge feels a force in the same direction as the field and accelerates along the field lines. A negative charge, such as an electron, feels a force in the opposite direction and accelerates against the field. The sign you enter for charge sets that direction.
Is this calculation valid for speeds near the speed of light?
No. This calculator uses classical, non-relativistic kinematics, which assumes the particle's speed stays well below the speed of light. Once the computed velocity approaches roughly 10% of c (about 3 x 10^7 m/s), relativistic mass increase becomes significant and a = qE / m no longer gives an accurate result.
Are N/C and V/m the same unit for electric field?
Yes. Electric field strength can be expressed in newtons per coulomb (N/C) or volts per meter (V/m); both describe force per unit charge and are dimensionally equivalent, so 1 N/C equals 1 V/m. Either unit can be used for the electric field input.