Larmor Precession: Understand Charge Orbitting Fixed Charge

In summary, the equation that links inertial and rotational frames can be used to understand the precession of a charge orbiting around another fixed charge in a weak magnetic field. The term that describes this precession is the cross product, Qv(I) x B, which represents the Lorentz force.
  • #1
bman!!
29
0
i'm familiar with terminology used to denote rates of change in inertial and rotational frames, and the equation that links the two quantities, but working through a derivation/thought experiment to describe charge orbitting around another fixed charge in a weak magnetic field, it results in precession which is analagous to gyrscopic precession, but for the life of me, when working through the derivation, i can't explicitly see which term in the final equation describes this precession.

could someone point me in the right direction

cheers

p.s
the equation I am looking at (it may be the wrong one) is:

ma(I) = k r + Qv(I) x B

where
m=mass
a(I) = acceleration vector in inertial frame
k = coulomb attaraction betwwen the charges, -QQ/4piepislon etc
r = radius
Q=charge
V(I) = velocity in inertial
B = mag field
 
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  • #2
The term that is describing the precession is the cross product, Qv(I) x B. This term represents the Lorentz force, which is the force applied to the charge due to the interaction between the magnetic field and the charge. The Lorentz force causes the charge to precess around the fixed charge.
 

1. What is Larmor Precession?

Larmor Precession is a phenomenon in which the axis of rotation of a charged particle, such as an electron, changes due to its interaction with a fixed magnetic field. It is named after physicist Joseph Larmor who first described it in the late 19th century.

2. How does Larmor Precession occur?

Larmor Precession occurs when a charged particle, with a non-zero spin and magnetic moment, is placed in a fixed magnetic field. The particle experiences a torque that causes it to precess or rotate around the magnetic field lines at a frequency known as the Larmor frequency.

3. What is the importance of Larmor Precession?

Larmor Precession has many practical applications in various fields of science and technology. It is used in nuclear magnetic resonance (NMR) spectroscopy to study the structures and properties of molecules. It is also used in medical imaging techniques such as magnetic resonance imaging (MRI) to produce detailed images of the body's internal structures.

4. How can Larmor Precession be measured?

Larmor Precession can be measured using a variety of experimental techniques, such as optical spectroscopy, NMR, and MRI. These methods involve applying a magnetic field to the charged particle and observing its precession frequency, which can be used to determine the particle's properties.

5. What factors affect Larmor Precession?

The strength of the magnetic field, the charge and mass of the particle, and the particle's initial spin orientation all affect Larmor Precession. Additionally, the type of material the particle is moving through and any external forces acting on the particle can also influence its precession frequency.

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