Explaining Larmor Frequency: How is w=q*B/2m Derived?

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SUMMARY

The Larmor frequency, also known as gyrofrequency, is defined by the equation w = qB/2m, where w represents the frequency, q is the charge of the particle, B is the magnetic field strength, and m is the mass of the particle. This equation is derived from the equations of motion, specifically the relation d\vec v/dt = (q/m) \vec v × \vec B. The term Larmor frequency also describes the precession rate of a magnetic moment in a magnetic field, such as that of an atomic nucleus.

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  • Familiarity with electromagnetic theory and magnetic fields
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  • Concept of magnetic moments and their behavior in magnetic fields
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meadow
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Can someone please explain Larmor frequency to me? (like how the equation w=q*B/2m is derived?) I would greatly appreciate it!
 
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The Larmor frequency aka the "gyrofrequency" is the frequency with which charge particles orbit in a magnetic field. It directly from the solution of the equations of motion:

\frac {d\vec v}{dt} = \frac {q}{m} \vec v \times \vec B

I don't think you meant to include the factor of 1/2.

The term is also used to denote the rate of precession of a magnetic moment in a magnetic field such as an atomic nucleus. I gathered you meant the "gyrofrequency" from the form you displayed.
 

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