The Mean Free Path and the Magnetic Field

[Anamitra]

A magnetic field curves the path of a charged particle for example the electron.So the application of a magnetic field should curve the path of the free electrons between successive collisions[More conspicuously for a large magnetic field].The"free path" of an electron then is no more a straight line.In such a situation the application of results that assume the mean free path of an electron to be straight line needs to be modified. Moreover the curving of particles caused by the magnetic field may also change the average number of collisions per second affecting the thermal state of the body.
Even a weak magnetic field like that of the Earth may bring about these effects in a small way.
Do we consider these factors seriously for metallic bodies (and other materials) at ordinary temperatures?

 

[Bob S]

There is no direct relationship between the magnetic field and the collisions per unit length in a magnetic field. The stopping power of charged particles is given by the Bethe-Bloch dE/dx equation. The most accurate early (1950's) measurements of the masses of stopping positive and negative muons, and stopping positive and negative pions, in photographic emulsions in roughly 1.5 Tesla magnetic fields. Look up Barkas Birnbaum and Smith in Physical Review:

http://prola.aps.org/abstract/PR/v101/i2/p778_1

Bob S

[added] The Bethe-Bloch dE/dx equation involves collisions between the incident charged particle and atomic electrons. There is a very small difference between the dE/dx of positive and negatively charged incident particles, but the collision distance is always less than atomic radii. The dE/dx equations also work well inside magnetized iron.

 

[AJ Bentley]

The shape of the path taken by a charged particle won't affect the distance it can travel between collisions.
The mean free path remains the same.

Running round in circles in a rainstorm won't keep you dry.

 

[Anamitra]

Running round in circles won't keep me dry.That is true but the manner in which I get drenched is indeed different(more conspicuously at the initial stages). Just try to compare rain coming down vertically and the same rain in a swirling wind. The matter should become clear now."The shape of the path taken by a charged particle won't affect the distance it can travel between collisions.
The mean free path remains the same."

The distance between a pair of points definitely depends on the path connecting the two points.

 

[Bob S]

If the dE/dx collision energy loss is 2 MeV per gram per cm² (minimum ionizing particle) and the energy loss per collision is ~ 30 eV, then there are ~66,000 collisions (with atomic electrons) per gram per cm². For normal solid materials, the distance between collisions is negligible when compared to the curvature of the track, so the track can be considered straight. In fact, the track deviation due to curvature between collisions is less than the rms scattering angle due to the individual electron collisions. But the track deviation due to the magnetic field is additive, while the multiple scattering angle (Moliere scattering) is reduced by statistical averaging.

Bob S

 

[Dickfore]

A magnetic field curves the path of a charged particle for example the electron.So the application of a magnetic field should curve the path of the free electrons between successive collisions[More conspicuously for a large magnetic field].The"free path" of an electron then is no more a straight line.In such a situation the application of results that assume the mean free path of an electron to be straight line needs to be modified. Moreover the curving of particles caused by the magnetic field may also change the average number of collisions per second affecting the thermal state of the body.
Even a weak magnetic field like that of the Earth may bring about these effects in a small way.
Do we consider these factors seriously for metallic bodies (and other materials) at ordinary temperatures?

You are right in thinking that a sufficiently large magnetic field alters the transport properties of valence electrons in a metal. The correct treatment of the effects you are discussing is by using the semi-classical approximation of the quantum mechanical equations for Bloch electrons in an external electromagnetic field.

 

[Bob S]

You are right in thinking that a sufficiently large magnetic field alters the transport properties of valence electrons in a metal. The correct treatment of the effects you are discussing is by using the semi-classical approximation of the quantum mechanical equations for Bloch electrons in an external electromagnetic field.

The correct treatment of charged particle energy loss in matter is given by the Bethe-Bloch dE/dx equation, given in Section 27.2 if the LBL Particle Data Group review:

http://pdg.lbl.gov/2009/reviews/rpp2009-rev-passage-particles-matter.pdf

Bob S

 

[Dickfore]

The correct treatment of charged particle energy loss in matter is given by the Bethe-Bloch dE/dx equation, given in Section 27.2 if the LBL Particle Data Group review:

http://pdg.lbl.gov/2009/reviews/rpp2009-rev-passage-particles-matter.pdf

Bob S

But, this is not what the op was asking.