Why is ##\omega_c \tau >>1## for several revolutions?

Click For Summary
SUMMARY

The discussion centers on the relationship between the cyclotron frequency (##\omega_c##) and the scattering time (##\tau##) in semiconductors subjected to a magnetic field. It is established that for multiple revolutions of charge carriers, the condition ##\omega_c \tau >> 1## is valid, indicating that the cyclotron motion is significantly influenced by scattering events. The participant Abbi questions why the condition is not expressed as ##\omega_c \tau >> 2 \pi##, which would imply a comparison for a single revolution. The clarification provided emphasizes the importance of "order of magnitude" comparisons in solid state physics.

PREREQUISITES
  • Understanding of cyclotron frequency (##\omega_c##)
  • Familiarity with scattering time (##\tau##)
  • Basic principles of charge carriers in magnetic fields
  • Knowledge of order of magnitude comparisons in physics
NEXT STEPS
  • Research the derivation of cyclotron frequency in semiconductor physics
  • Explore the implications of scattering time on charge carrier mobility
  • Study the concept of order of magnitude in physical equations
  • Investigate the behavior of charge carriers in varying magnetic field strengths
USEFUL FOR

Physics students, semiconductor researchers, and anyone interested in the dynamics of charge carriers in magnetic fields.

Abigale
Messages
53
Reaction score
0
Hey,
I read about charge carriers in semiconductors in a magnetic field.
They write that for several revolutions ##\omega_c \tau >>1## holds.
But I think for one revolution it is ##\omega_c \tau = 2 \pi##.
(##\tau## is the scattering time)
Why they do not write ##\omega_c \tau >> 2 \pi## in the solid state physics books?

Thank you
Abbi
 
Physics news on Phys.org
Think for a moment what ##a>>b## means as opposed to ##a>b##. This is an "order of magnitude" comparison. If 1,000 is much greater than 1 so is 6,318.53071 ...
 
Okay thank you,
makes sense.
But I would write larger than ##>>2 \pi## to denote to get more than one revolution.
 

Similar threads

Undergrad Hall effect in P-type semiconductors: electron-centric heuristic?
  • · Replies 0 ·
Replies
0
Views
3K
Graduate Hall resistance coefficient vs Seebeck coefficient signs for n-p type
  • · Replies 4 ·
Replies
4
Views
4K
Graduate Why the physical meaning of the quantum Hall effect is important
  • · Replies 5 ·
Replies
5
Views
2K
Graduate Why do we need to know "two-bands" Hall coefficient and magn
  • · Replies 2 ·
Replies
2
Views
3K
Undergrad Charge carrier density: Hall experiment vs Fermi-Dirac statistics
  • · Replies 11 ·
Replies
11
Views
4K
Graduate Why do conductivities and resistivities change with magnetic field strength?
  • · Replies 2 ·
Replies
2
Views
1K
Graduate Zeeman energy with an effective mass
  • · Replies 1 ·
Replies
1
Views
2K
Solid State Books: Weyl semimetals, Topological Insulators
  • · Replies 6 ·
Replies
6
Views
2K
Hall Effect Lab (Germanium SC) Without Hall Effect Sensor
  • · Replies 1 ·
Replies
1
Views
2K
Boltzmann Transport Equation : Hall Effect in the Relaxation Time Approximation
  • · Replies 1 ·
Replies
1
Views
5K