# Exploring the Electromagnetic Triangle with Larmor Frequency

• FrankMak
In summary, the Electromagnetic Triangle uses the wavelength of the precession frequency of neutral hydrogen as a reference value to link physical constants. The relationships in the pdf article (9k) were identified when studying an unconventional cavity configuration and can be translated to a 45 degree triangle for various purposes. The ratio between the cosecants of the two angles represents the differences in the "time base". Increasing the wavelength multiplier by 10^2 creates a mathematically perfect triangle. The various characteristics associated with the precession of the magnetic moment of a proton are now being referred to as "Larmor", similar to the term "Hertz". However, many people are not familiar with transverse waveform notation as it applies to electromagnetic waves and

#### FrankMak

The Electromagnetic Triangle uses
the wavelength of the precession frequency of neutral hydrogen as a reference value and this provides a unique manner in linking physical constants.

The geometric-mathematical relationships in the pdf article (9k) were identified empirically when studying an unconventional cavity configuration. By translating the values to a 45 degree triangle, and examining the various relationships with that of the 26.25400 degree triangle, it appears that the 45 degree triangle can be used as a reference for a number of purposes. This may be of interest to a number of scientific disciplines, physicists maybe?

The ratio between the cosecants of the two angles represents the differences in the "time base". Comments?

If you haven't already noticed, when the value of the wavelength multiplier is increased by 10^2 the calculated resultants are absolutely symmetrical, not just numerically symmetrical. That wavelength multiplier creates a mathematically perfect triangle, which is sort of novel.

The various characteristics associated with the precession of the magnetic moment of a proton are now being presented using the term "Larmor", ie: Larmor precession, Larmor frequency, etc. This term is being used to recognize the efforts of "Joseph Larmor" who provided significant insight into nuclear characteristics. Instead of the statement "precession frequency" it is becoming common to state it as "Larmor frequency". It is somewhat akin to the term "Hertz", abbreviated as Hz, which is a contraction of cps (cycles per second).

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• emtriangle2.pdf
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One of the issues that I have identified concerning this post is that many people are not familiar with transverse waveform notaton as it applies to electromagnetic (EM) waves. Physics texts usually introduce transverse waves in describing mechanical motions. I do not know where this subject is placed in current physics books, but it is many hundreds of pages deep in the older texts and there are separate chapters dealing with EM waves.

Electrical engineers get a thorough grounding in transverse wave notation beginning with AC circuits, but I know this is not a familiar subject with other science and mathematical disciplines. Entering "transverse waves" in your favorite search engine will bring up thousands of sites, and I haven't found a site that I can recommend at this time.

Using the quoted entry and the trailer ("transverse waves" radians) in the search algorithm points to web pages that are more pertinent to the issue of the primary post.

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## 1. What is the Larmor frequency?

The Larmor frequency is the frequency at which a charged particle or a spinning magnetic dipole precesses around an external magnetic field. It is named after physicist Joseph Larmor who first described this phenomenon in 1897.

## 2. How is the Larmor frequency related to the electromagnetic triangle?

The Larmor frequency is one of the three main components of the electromagnetic triangle, along with the electric field frequency and the magnetic field frequency. Together, these three frequencies form the fundamental relationship between electric and magnetic fields in electromagnetic waves.

## 3. What is the significance of exploring the Larmor frequency?

Exploring the Larmor frequency allows us to understand the behavior of charged particles in the presence of a magnetic field. It is also crucial in many applications such as nuclear magnetic resonance (NMR) and magnetic resonance imaging (MRI).

## 4. How is the Larmor frequency calculated?

The Larmor frequency is calculated using the formula f = γB/2π, where f is the Larmor frequency, γ is the gyromagnetic ratio (a constant specific to each particle), and B is the strength of the external magnetic field. This formula is derived from the classical theory of electromagnetism.

## 5. Can the Larmor frequency be manipulated?

Yes, the Larmor frequency can be manipulated by changing the strength of the external magnetic field. In NMR and MRI, this is how different types of tissues or molecules are distinguished from each other, as they have different Larmor frequencies. Additionally, in particle accelerators, the Larmor frequency can be manipulated to control the trajectory of charged particles.