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

In summary, the conversation is about the expression ##\omega_c \tau >>1## in the context of charge carriers in semiconductors in a magnetic field. The speaker asks why the expression is not written as ##\omega_c \tau >> 2 \pi## in solid state physics books. The other person explains that the double arrow notation indicates an order of magnitude comparison, and it is not necessary to specify a specific number like 2π. The conversation ends with the understanding that the notation is used to represent a value that is significantly larger than the reference value.
  • #1
Abigale
56
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
 
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  • #2
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 ...
 
  • #3
Okay thank you,
makes sense.
But I would write larger than ##>>2 \pi## to denote to get more than one revolution.
 

1. Why is the product of ##\omega_c## and ##\tau## greater than 1 for several revolutions?

This is because ##\omega_c## represents the angular frequency of a spinning object, while ##\tau## represents the time it takes for the object to complete one revolution. When the product of these two values is greater than 1, it means that the object is rotating at a high speed and completing several revolutions in a short amount of time.

2. What is the significance of ##\omega_c \tau >>1## in scientific research?

This value is significant in many areas of scientific research, such as fluid dynamics, electromagnetics, and quantum mechanics. It helps us understand the behavior of spinning objects and their interactions with other forces, as well as the behavior of particles in a magnetic field.

3. How does a large value of ##\omega_c \tau## affect the stability of a spinning object?

A large value of ##\omega_c \tau## indicates that the object is spinning at a high speed, which can make it more difficult to control and stabilize. This is why many fast-spinning objects, such as gyroscopes, require precision engineering and design to maintain stability.

4. Can a spinning object have a ##\omega_c \tau## value less than 1?

Yes, it is possible for a spinning object to have a ##\omega_c \tau## value less than 1. This would indicate that the object is rotating at a slower speed and taking longer to complete one revolution. In some cases, a lower ##\omega_c \tau## value may be desired for stability or other purposes.

5. How does the value of ##\omega_c \tau## change with different types of spinning objects?

The value of ##\omega_c \tau## can vary greatly depending on the size, shape, and composition of the spinning object. For example, a small, lightweight object may have a higher ##\omega_c \tau## value than a larger, heavier object due to differences in their rotational speed and inertia. Additionally, the presence of external forces, such as friction or air resistance, can also affect the value of ##\omega_c \tau##.

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