🧲 Lorentz Force Calculator

Calculate magnetic forces on moving charges and current-carrying conductors. Analyze electromagnetic interactions with detailed vector analysis and direction determination.

Calculation Type

Input Parameters

Lorentz Force on Moving Charge
F = q × v × B × sin(θ)
Force on a charged particle moving in a magnetic field
Right-Hand Rule:
👍 Thumb: velocity (v)
🤏 Fingers: magnetic field (B)
🖐️ Palm: force direction (F)
(For positive charges)

Results & Analysis

Enter values and click Calculate to see Lorentz force analysis results

Electromagnetic Force Theory

Lorentz Force

The force experienced by a charged particle moving in an electromagnetic field.

  • F = q(E + v × B) (full form)
  • F = qvB sin(θ) (magnetic only)
  • Force perpendicular to both v and B
  • Right-hand rule determines direction

Cyclotron Motion

Charged particles move in circular paths in uniform magnetic fields.

  • Radius: r = mv/(qB)
  • Frequency: f = qB/(2πm)
  • Period independent of velocity
  • Used in mass spectrometry

Applications

  • Electric Motors: Force on current-carrying wires
  • Mass Spectrometry: Particle separation
  • Hall Effect Sensors: Magnetic field detection
  • Particle Accelerators: Beam steering

HOW TO USE

Enter the charge value, velocity, magnetic field strength, and the angle between velocity and field vectors. Click Calculate to find the magnetic force on the moving charge.

FORMULA USED

F = q × v × B × sin(θ)
For a current-carrying conductor: F = I × L × B × sin(θ)
Direction: Right-hand rule

WORKED EXAMPLE

An electron (q=1.6×10⁻¹⁹C) moving at 10⁶ m/s perpendicular to a 0.1T field: F = 1.6×10⁻¹⁹ × 10⁶ × 0.1 = 1.6×10⁻¹⁴ N.

FREQUENTLY ASKED QUESTIONS

Q: What is the Lorentz Force?

A: The Lorentz Force is the combined electric and magnetic force on a charged particle: F = q(E + v × B).

Q: What is the right-hand rule?

A: Point fingers in the direction of velocity, curl toward the magnetic field — your thumb points in the force direction (for positive charges).

Q: Why does the Lorentz Force do no work?

A: The magnetic force is always perpendicular to velocity, so it changes direction but not speed — thus doing no work.

Q: Where is Lorentz Force applied?

A: Electric motors, cathode ray tubes, mass spectrometers, particle accelerators, and MRI machines all use Lorentz Force.