Lorentz Force Calculator

Calculate the magnetic force on charged particles using the Lorentz force equation

Calculate Lorentz Force

Electric charge of the particle

Velocity of the charged particle

Strength of the magnetic field

degrees (°)

Angle between velocity and magnetic field (0-180°)

Lorentz Force Results

0.000e+0
Lorentz Force (N)
0.000e+0
Maximum Force (at 90°)

Formula used: F = q × v × B × sin(α)

Input values: q = 0.000e+0 C, v = 0.000e+0 m/s, B = 0.000e+0 T

Force direction: Perpendicular to both velocity and magnetic field (use right-hand rule)

Force Analysis

Example Calculation

Electron in Earth's Magnetic Field

Electron charge: -1.602 × 10⁻¹⁹ C

Velocity: 10⁶ m/s (relativistic effects negligible)

Earth's magnetic field: ~50 μT

Angle: 90° (perpendicular motion)

Calculation

F = |q| × v × B × sin(90°)

F = 1.602 × 10⁻¹⁹ × 10⁶ × 50 × 10⁻⁶ × 1

F = 8.01 × 10⁻¹⁸ N

Right-Hand Rule

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Thumb

Point in direction of velocity (v)

☝️

Index Finger

Point in direction of magnetic field (B)

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Middle Finger

Points in direction of force (F)

For positive charges only

Applications

Electric motors and generators

🔬

Mass spectrometers

🌀

Cyclotrons and particle accelerators

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Loudspeakers

🧭

Magnetic deflection systems

Railguns

Understanding the Lorentz Force

What is the Lorentz Force?

The Lorentz force is the electromagnetic force experienced by a charged particle moving through electric and magnetic fields. In this calculator, we focus on the magnetic component of the force, which occurs when a charged particle moves through a magnetic field.

Key Characteristics

  • Force is perpendicular to both velocity and magnetic field
  • Maximum force occurs when motion is perpendicular to field
  • No force when motion is parallel to magnetic field
  • Causes charged particles to move in circular or helical paths

Formula Explanation

F = q × v × B × sin(α)

  • F: Lorentz force (Newtons)
  • q: Electric charge (Coulombs)
  • v: Velocity of particle (m/s)
  • B: Magnetic field strength (Tesla)
  • α: Angle between velocity and field

Note: The force magnitude depends on sin(α), making it zero when α = 0° or 180°, and maximum when α = 90°.