larmor theorem
C2Highly Technical / Academic
Definition
Meaning
A fundamental theorem in electromagnetism and quantum mechanics stating that the motion of a charged particle in a uniform magnetic field is equivalent to the same motion in a rotating frame of reference, with the rotation frequency given by the Larmor frequency.
In physics, the theorem provides a classical and quantum-mechanical framework for understanding magnetic resonance, precession of magnetic moments, and the behaviour of systems in magnetic fields. It's a cornerstone for understanding phenomena like NMR (Nuclear Magnetic Resonance) and electron spin resonance.
Linguistics
Semantic Notes
This is a proper noun referring to a specific, named theorem in physics. It is almost exclusively used within physics, particularly in electromagnetism, quantum mechanics, and magnetic resonance. It is not used metaphorically.
Dialectal Variation
British vs American Usage
Differences
No significant differences in usage, spelling, or meaning. The term is standardised in the global scientific community.
Connotations
None beyond its precise scientific meaning.
Frequency
Identically rare and specialised in both varieties, confined to advanced physics contexts.
Vocabulary
Collocations
Grammar
Valency Patterns
[Subject] applies/uses the Larmor theorem to [object/ phenomenon]The Larmor theorem provides/establishes/implies [result]Vocabulary
Synonyms
Strong
Weak
Usage
Context Usage
Business
Not used.
Academic
Exclusively used in advanced physics lectures, textbooks, and research papers on electromagnetism, quantum theory, and magnetic resonance.
Everyday
Never used.
Technical
Core term in physics and engineering disciplines involving magnetism, quantum computing (spin qubits), and medical imaging (MRI principles).
Examples
By Part of Speech
adjective
British English
- The Larmor-frequency shift was calculated.
- This is a Larmor-theorem-based explanation.
American English
- The Larmor frequency shift was calculated.
- This explanation is based on the Larmor theorem.
Examples
By CEFR Level
- Scientists use the Larmor theorem to explain why particles spin in magnetic fields.
- The Larmor theorem elegantly demonstrates that for a system of charged particles in a weak, uniform magnetic field, the first-order effect is a universal precession of the entire system.
- By applying the Larmor theorem, one can transform the problem into a rotating frame, thereby simplifying the equations of motion considerably.
Learning
Memory Aids
Mnemonic
Think of a LARge gyroscope's MORning spin in a magnetic field. LAR-MOR.
Conceptual Metaphor
A DANCING TOP: The theorem conceptualises the motion of a charged particle or magnetic moment as a precise, predictable spin or precession, like a top dancing in a circle under the influence of an invisible force (the magnetic field).
Watch out
Common Pitfalls
Translation Traps (for Russian speakers)
- Do not translate 'Larmor' (a proper name). It should be transliterated as 'Теорема Лармора'.
- Avoid confusing it with the related but distinct 'Larmor frequency' (частота Лармора) or 'Larmor precession' (прецессия Лармора), which are consequences of the theorem.
Common Mistakes
- Misspelling as 'Larmour theorem' (adding a 'u').
- Incorrectly referring to it in non-magnetic contexts.
- Using it as a common noun without the capital 'L'.
Practice
Quiz
The Larmor theorem is most directly applicable to which of the following phenomena?
FAQ
Frequently Asked Questions
It is named after the Irish physicist Sir Joseph Larmor (1857–1942), who formulated it.
It has both classical and quantum-mechanical formulations. The classical version describes charged particle motion, while the quantum version applies to intrinsic spin and magnetic moments.
The Larmor frequency is the angular frequency of precession derived from the Larmor theorem, given by ω = (qB)/(2m) for a classical charge or ω = γB for a magnetic moment, where γ is the gyromagnetic ratio.
MRI (Magnetic Resonance Imaging) relies on the precession of nuclear spins (like protons in water) in a magnetic field, which is precisely described by the quantum version of the Larmor theorem. The resonance condition at the Larmor frequency is what is detected to create images.