F=qvBMagnetic Force Calculator (Lorentz Force)
90° = maximum force
The magnetic force on a moving charge is given by the Lorentz force law: F = qvB sinθ. This force is always perpendicular to both the velocity and the magnetic field, causing charged particles to move in circular or helical paths. The Lorentz force is the working principle behind particle accelerators, mass spectrometers, electric motors, and MRI machines.
- 1F = |q| × v × B × sin(θ)
- 2q = charge (coulombs), v = velocity (m/s), B = magnetic field (tesla)
- 3θ = angle between velocity vector and B field
- 4Maximum force when θ = 90° (perpendicular to field)
- 5Zero force when θ = 0° (parallel to field — charge moves along field lines)
Electron (q=1.6×10⁻¹⁹ C) at 10⁷ m/s, B=0.5 T, θ=90°=F = 1.6×10⁻¹⁹ × 10⁷ × 0.5 = 8×10⁻¹³ N
Proton in LHC (B≈8 T, v≈c)=F ≈ enormous — required to keep proton on circular track
| Application | Principle | Magnetic Field |
|---|---|---|
| Electric motor | F = qvB bends current-carrying wire | 0.1–2 T (permanent magnet) |
| MRI scanner | Proton spin alignment | 1.5–7 T (superconducting) |
| Mass spectrometer | Different masses curve differently | ~0.1–1 T |
| Particle accelerator (LHC) | Circular orbit of protons | 8.3 T (superconducting) |
| CRT monitor (historical) | Electron beam deflection | ~1 mT |
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