ATM-08

Larmor precession

ω_L = e B / (2 m). Orbital precession of a magnetic moment in B.

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StructureLarmor

Governing equation

\omega_L=eB/(2m)

$B \in \left[0.01, 12\right]$

where

B: Field (T)
\omega_L: Angular frequency (Grad/s)
f_L: Larmor frequency (GHz)

The figure, part by part

Each numbered marker wears the color of its card. Hover a card to light the marker. Tap a marker to jump to that card. The slider walks a red point along the curve; Animate drawing traces it like a pen.

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①

Governing law — red

\omega_L=eB/(2m)

$B \in \left[0.01, 12\right]$

$B = 0.01$ $\omega_L = 0.14$

Along the curve

②

Domain of the variable — blue

B_{\min} = 0.01,\quad B_{\max} = 12

$B \in \left[0.01, 12\right]$

$B = 0.01$ $B = 0.01$

Along the curve

③

Response curve — green

\omega_L=eB/(2m)

$B \in \left[0.01, 12\right]$

$B = 0.01$ $\omega_L = 0.14$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}\omega_L}{\mathrm{d}B}

$B \in \left[0.01, 12\right]$

$B = 0.085$ $\omega_L^{\prime} = 14$

Along the curve

Lecture brief

Historical brief

Balmer, Rydberg, Bohr (1913), fine structure, Zeeman and Stern–Gerlach built the spectrum of one atom. The lab computes levels, selection and magnetic splitting. This sheet (ATM-08 — Larmor precession) is the form associated with Larmor. Working symbols: $B$ $\rightarrow$ $\omega_L$ , $f_L$ . Spin precesses at g times this. NMR quotes γ = g μ_B / ħ for the nucleus.

Purpose

Purpose: compute

\omega_L

f_L

from

B

in Atomic physics via

\omega_L=eB/(2m)

ω_L = e B / (2 m). Orbital precession of a magnetic moment in B. Use it when a real atomic physics question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

B = 1.000\,\mathrm{T}

, the governing relation

\omega_L=eB/(2m)

yields

\omega_L = 87.941\,\mathrm{Grad/s}

f_L = 13.996\,\mathrm{GHz}

. A tiny loop, a B axis, a circling μ. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Field B1 T

Outputs

Angular frequency \omega_L87.941 Grad/s
Larmor frequency f_L13.996 GHz

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Narration of this film

A tiny loop, a B axis, a circling μ.

Spin precesses at g times this. NMR quotes γ = g μ_B / ħ for the nucleus.

Reading speed

Watch on YouTube