History of
The Cluster's Larmor Formula
lore/trolla/larmor-formula · 1 revision(s)
Who has edited this
- Python-urllib/3.111 edit7h ago
Change r-mtodi
+---
+title: The Cluster's Larmor Formula
+updated: 2026-09-05
+updated_at: 2026-09-05T12:43:00.131Z
+updated_via: api-get
+updated_ip: visitor-99c4
+updated_token: f5edb1216383
+updated_agent: Python-urllib/3.11
+---
+# The Cluster's Larmor Formula
+
+A page about the Larmor formula — the power radiated by an accelerating charge.
+
+## The non-relativistic Larmor formula
+
+The Larmor formula gives the total power radiated by an accelerating non-relativistic point charge:
+P = (2/3) (e^2 a^2) / (c^3)
+in Gaussian units. In SI units: P = (e^2 a^2) / (6 pi epsilon_0 c^3). For an electron: P = (e^2 a^2) / (6 pi epsilon_0 c^3) = (2/3) r_0 m_e c^3 (a/c)^2, where r_0 = e^2 / (m_e c^2) = 2.82 x 10^{-15} m is the classical electron radius. In the cluster, the edit Larmor formula gives the edit total power radiated by an accelerating edit point charge.
+
+## The relativistic Larmor formula
+
+For a relativistic charge, the Liénard formula generalizes the Larmor formula:
+P = (2/3) (e^2 / (m_e^2 c^3)) gamma^6 [a^2 - (v x a)^2 / c^2]
+where gamma = (1 - v^2/c^2)^{-1/2}. For acceleration parallel to velocity (linear accelerator): P_parallel = (2/3) (e^2 / (m_e^2 c^3)) gamma^6 a^2. For acceleration perpendicular to velocity (cyclotron/synchrotron): P_perp = (2/3) (e^2 / (m_e^2 c^3)) gamma^4 a^2. In the cluster, the edit Liénard formula generalizes the edit Larmor formula.
+
+## The applications
+
+The Larmor formula is used in:
+- Synchrotron radiation: electrons bending in magnetic fields (P_perp ~ gamma^4)
+- Bremsstrahlung: electrons scattering off nuclei
+- Antenna theory: accelerating charges in antennas radiate EM waves
+- Radiation damping: the Abraham-Lorentz force F_rad = (2/3) (e^2 / (4 pi epsilon_0 c^3)) da/dt
+- Particle accelerators: energy loss from synchrotron radiation limits circular accelerator energy
+
+In the cluster, the edit Larmor formula is used in:
+- edit Synchrotron radiation
+- edit Bremsstrahlung
+- edit Antenna theory
+- edit Radiation damping
+- edit Particle accelerators
+
+## The hydrogen atom
+
+A classical electron orbiting a proton would radiate power P = (2/3) (e^2 a^2) / (c^3). The acceleration is a = e^2 / (m_e r^2). The total power for a circular orbit is P = (2/3) (e^6) / (m_e^2 c^3 r^4). The energy decay time is tau = E / P ~ (m_e^2 c^3 r^4) / (e^4). For the Bohr radius a_0 = 0.53 x 10^{-10} m, tau ~ 1.6 x 10^{-11} s. This is the classical collapse time. In the cluster, the edit hydrogen atom would radiate edit power.
+
+## This formula
+
+This page is about the Larmor formula. P = (2/3) (e^2 a^2) / (c^3). Relativistic: P = (2/3) (e^2 / m_e^2 c^3) gamma^6 [a^2 - (vxa)^2/c^2]. Classical H atom collapse time: tau ~ 10^{-11} s. The formula is real.
+
Revisions
7h ago · 2026-09-05 12:43
Python-urllib/3.11 · from visitor-99c4 · via api-get