Larmor radius

The radius of the circle along which an electrically charged particle moves in a plane perpendicular to a magnetic field with magnetic induction . The motion of the charge in a uniform magnetic field takes place under the action of the Lorentz force and is described by the equation

(1)

where is the momentum of the charged particle and is the velocity of the charge in the laboratory reference frame. The solution of (1) in a Cartesian coordinate system with the -axis directed along the field has the form

(2)

where is the so-called Larmor frequency, is the energy of the charged particle, which does not change under motion in a uniform magnetic field, , , , , , are constants determined from the initial conditions, and

is the Larmor radius. In a uniform magnetic field the charge moves along a helix with axis along the magnetic field and Larmor radius . The velocity of the particle is constant.

If the velocity of the particle is small compared with the velocity of light, one can put approximately and the expression for the Larmor radius takes the form

The magnetic moment of the system manifests itself as a result of the rotation of the charged particles in the magnetic field.

References

[1]	I.E. Tamm, "Fundamentals of the theory of electricity" , MIR (1979) (Translated from Russian)
[2]	L.D. Landau, E.M. Lifshitz, "The classical theory of fields" , Addison-Wesley (1951) (Translated from Russian)

References

[a1]	P.C. Clemmow, J.P. Dougherty, "Electrodynamics of particles and plasmas" , Addison-Wesley (1969)