Lorentz Force Calculator

The magnetic Lorentz force acts perpendicular to both velocity and magnetic field, causing circular motion. It powers electric motors, particle accelerators, and mass spectrometers.

⚡ Electromagnetism📐 F = qvB sinθ⚛️ Particle Physics
Charge q (C)
Velocity v (m/s)
Magnetic Field B (T)
Angle θ (deg)
Please enter valid values.

Formula & Reference

VariableSymbolFormulaUnits
Magnetic ForceFF = qvB sinθN
Velocityvv = F/(qB sinθ)m/s
ChargeqC
B FieldBT
AngleθBetween v and Bdeg

Step-by-Step Examples

Example 1
Electron in B field

Electron q=1.6e-19 C, v=2e6 m/s, B=0.05 T, theta=90.

  • F = 1.6e-19 * 2e6 * 0.05 * sin90
  • F = 1.6e-14 N
✓ 1.6e-14 N — causes circular orbit
Example 2
Proton in cyclotron

Proton q=1.6e-19, v=1e7 m/s, B=1.5 T.

  • F = 1.6e-19 * 1e7 * 1.5 = 2.4e-12 N
✓ 2.4e-12 N — steers proton in circle
Example 3
Zero force case

Particle moves parallel to B (theta=0).

  • F = qvB sin(0) = 0
  • No force — particle goes straight
✓ Zero magnetic force when v parallel to B

Real-World Applications

⚙️
Electric Motors
Current in magnetic field experiences Lorentz force — creates rotation.
💺
CRT Displays
Lorentz force steered electron beams to different screen positions.
⚛️
Particle Accelerators
Magnetic fields steer particle beams in the LHC via Lorentz force.
🧭
Mass Spectrometers
Radius r=mv/(qB) identifies ions by mass-to-charge ratio.

Common Mistakes to Avoid

⚠️
Forgetting sine factor

F = qvB sin(theta). Zero force when v parallel to B. Maximum when perpendicular.

⚠️
Magnetic force does zero work

Force is perpendicular to v — changes direction not speed.

⚠️
Direction requires right-hand rule

This calculator gives magnitude only. Use right-hand rule for direction.

Frequently Asked Questions

Why does magnetic force cause circular motion?
Force is always perpendicular to velocity — it deflects without speeding up. This results in uniform circular motion with radius r = mv/(qB).
What is the Larmor radius?
r = mv/(qB). Heavier or faster particles curve less. Basis of cyclotrons and mass spectrometers.
Why can the magnetic force not do work?
Work = F dot v. Since F is always perpendicular to v, the dot product is zero. No energy transfer.
How do electric motors use Lorentz force?
Current-carrying wire in magnetic field: F = IL x B. Force on wire segment causes rotation of motor coil.
What is the Hall effect?
Lorentz force on carriers in conductor creates transverse Hall voltage V_H = IB/(nqt), used to measure B fields and carrier density.

Related Physics Calculators

Formula Explorer connections

Interpretation: This relationship connects motion, force, momentum, work or energy in a mechanical system. Assumption: Choose a consistent reference direction and unit system. The model may assume constant acceleration, rigid bodies, negligible losses or an isolated system.

Lorentz Force & Particle Motion Calculator →Magnetic Force on Moving Charge Calculator →Mass-Energy Calculator →Physics Formula Explorer →