Online Lorentz Force Calculator

Calculate the magnetic force exerted on a charged particle traveling through a magnetic field B. Essential for electromagnetism, particle physics, and cyclotron kinematics.

Lorentz Force Calculator

Calculate Lorentz magnetic force F = q·v·B·sin(α), orbital radius in magnetic field, and crossed field drift velocity

90°

Calculation Results

Lorentz Force (F)
8.0109e-14 Н (N)
F = |q|·v·B·sin(90°) = 1.602e-19 × 1000000 × 0.5 × 1.000
Cyclotron Orbital Radius (r)
1.1371e-5 м (m)
r = (m · v · sin α) / (|q| · B)
Direction Rule

Left-hand rule applies for negative charges (e.g., electrons), reversing the vector product direction.

How to use

  1. Input electric charge magnitude q in Coulombs.
  2. Enter particle velocity v in meters per second.
  3. Specify magnetic flux density B in Teslas (T).
  4. Enter angle α between velocity vector and magnetic field vector (degrees).
  5. View resulting Lorentz force in Newtons (N).

Calculation Example

For an electron (charge e ≈ 1.6 × 10⁻¹⁹ C) moving at 10⁶ m/s perpendicular to a 0.5 T magnetic field (α = 90°, sin(90°) = 1):

Lorentz force: F = q * v * B * sin(α) = 1.6 × 10⁻¹⁹ * 10⁶ * 0.5 * 1 = 8.0 × 10⁻¹⁴ N.

Calculation Methodology

The magnetic component of Lorentz force obeys F = |q| * v * B * sin(α). Direction follows the right-hand rule for positive charges (F = q * [v × B]).

Frequently Asked Questions

What is Lorentz Force?

The force exerted by an electromagnetic field on a charged particle in motion.

When is Lorentz force equal to zero?

When charge is stationary (v = 0), uncharged (q = 0), or moving parallel to magnetic field lines (angle α = 0° or 180°).

When is Lorentz force maximized?

When velocity vector is perpendicular to magnetic field lines (α = 90°).

Does the magnetic Lorentz force do work?

No, because the force is always perpendicular to velocity, doing zero work and altering only trajectory direction without modifying kinetic energy.

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