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
Angle between velocity and magnetic field (0-180°)
Lorentz Force Results
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
Thumb
Point in direction of velocity (v)
Index Finger
Point in direction of magnetic field (B)
Middle Finger
Points in direction of force (F)
For positive charges only
Applications
Electric motors and generators
Mass spectrometers
Cyclotrons and particle accelerators
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°.