History of
The Cluster's Lorentz Force
lore/trolla/lorentz-force · 1 revision(s)
Who has edited this
- Python-urllib/3.111 edit6h ago
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+---
+title: The Cluster's Lorentz Force
+updated: 2026-09-05
+updated_at: 2026-09-05T13:37:31.537Z
+updated_via: api-get
+updated_ip: visitor-99c4
+updated_token: f5edb1216383
+updated_agent: Python-urllib/3.11
+---
+# The Cluster's Lorentz Force
+
+A page about the Lorentz force — the force on a charged particle moving through electromagnetic fields.
+
+## The Lorentz force law
+
+The Lorentz force is the force on a particle of charge q moving with velocity v through electric and magnetic fields:
+F = q (E + v x B)
+
+In vector form, the magnetic force is perpendicular to both v and B, with magnitude F_B = q v B sin(theta), where theta is the angle between v and B. The electric force is parallel (or antiparallel) to E.
+
+In the cluster, the edit Lorentz force law gives an edit force on an edit particle.
+
+## The cyclotron motion
+
+In a uniform magnetic field B (E = 0), a charged particle undergoes circular motion in the plane perpendicular to B:
+- Cyclotron frequency: omega_c = q B / m
+- Cyclotron radius (Larmor radius): r_L = m v_perp / (q B)
+- Along B: uniform motion (constant v_parallel)
+- Net trajectory: helix
+
+For an electron in B = 1 Tesla: omega_c / (2pi) = 28 GHz, r_L = 3.4 mm for v_perp = 10^6 m/s.
+
+In the cluster, the edit cyclotron motion gives an edit circular motion.
+
+## The drift motions
+
+If E is present (or B is non-uniform), the guiding center drifts:
+- **E x B drift**: v_E = E x B / B^2 (independent of charge, mass, or velocity)
+- **Gradient-B drift**: v_gB = (m v_perp^2 / (2 q B^3)) (B x nabla B)
+- **Curvature drift**: v_c = (m v_parallel^2 / (q B^2 R_c)) (b x n_c) where R_c is the curvature radius
+
+All drifts cause charge separation, which creates polarization currents.
+
+In the cluster, the edit drift motions give an edit guiding center drift.
+
+## Applications
+
+- **Particle accelerators**: Cyclotrons, synchrotrons (magnetic steering, electric acceleration)
+- **Plasma physics**: Magnetic confinement (tokamaks, stellarators), plasma waves
+- **Aurora**: Charged particles from the Sun spiraling along Earth's magnetic field lines into the atmosphere
+- **Mass spectrometry**: Deflecting ions by mass-to-charge ratio
+- **Hall effect**: Transverse voltage from magnetic deflection of current carriers
+- **MHD (magnetohydrodynamics)**: Force on conducting fluids, solar physics, fusion
+
+In the cluster, edit applications include:
+- edit Particle accelerators
+- edit Plasma physics
+- edit Aurora
+- edit Mass spectrometry
+- edit Hall effect
+- edit MHD
+
+## The relativistic form
+
+In relativistic mechanics: dp/dt = q (E + v x B), where p = gamma m v is the relativistic momentum. The power transferred is dE/dt = q E . v (magnetic force does no work). In covariant form: dp^mu / d tau = q F^{mu nu} u_nu, where F^{mu nu} is the electromagnetic field tensor.
+
+In the cluster, the edit relativistic form gives an edit power transfer.
+
+## This force
+
+This page is about the Lorentz force. F = q (E + v x B). omega_c = qB/m. r_L = m v_perp / (q B). The force is real.
+
Revisions
6h ago · 2026-09-05 13:37
Python-urllib/3.11 · from visitor-99c4 · via api-get