Statistical Physics number of particles with spin 1/2 in a B-field

In summary, the conversation is about a question regarding a sheet of N particles oriented along the magnetic field direction, where each particle can be oriented either "up" or "down". The conversation discusses how to calculate the total number of states for a given number of "up" particles, using combinatorics. The resulting formula is (1/2)(2n-N), and the conversation also addresses a specific example and the potential confusion with using the term N in the calculation.
  • #1
notnewton96
10
0

Homework Statement



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Homework Equations


The Attempt at a Solution



To be honest I'm clueless. I've missed a large amount of the course and just struggling to find any sources that explain this. I don't want the answer to the question, I want to figure that out for myself. What I really need is someone to point me in the right direction by either explaining the question in part or providing a good source of information such as a website or book.

I don't even know how to visualize the question. Would it be as a sheet of N particles orientated along the magnetic field direction? The particles can be orientated either positive to the direction of the magnetic field or opposed to it. When it is said that there are n up does this mean that the number of rows could be thought of as n? Or am I completely wrong?

Any and all information would be greatly appreciated. Thanks
 
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  • #2
Would it be as a sheet of N particles orientated along the magnetic field direction?
Something like that. You have N independent particles, each of them can be oriented along the magnetic field ("up", ms=+1/2) or in the opposite direction ("down", ms=-1/2). Spins are additive, so if you have n "up" and N-n "down", ...

(b) is combinatorics (which particles are "up" and which are "down"?). Once you have that, you can use it to calculate (c) and (d).
 
  • #3
Thank you so much for the reply. That's made it much clearer.

So part a is simply:

m_s = n(1/2) + (N-n)(-1/2)
m_s = n/2 - (1/2)(N-n)
m_s = (1/2)(2n-N)

I'm having a bit of trouble getting part b as a function of n. Because isn't the number of states simply (number of up + number of down)^N?

This gives N^N as the answer. I'm obviously missing something.
 
  • #4
Let's consider a simple example: N=3, n=1. You have the options (up, down, down), (down, up, down) and (down, down, up), for a total of 3 options.
 
  • #5
I'm sorry but the concept still isn't clear to me. Whichever way I try to define the number of possible states I have to use the term N. What am I missing?

Thanks again for the help :)
 
  • #6
Yes, N will show up in the result. Where is the problem?
 

Related to Statistical Physics number of particles with spin 1/2 in a B-field

1. What is statistical physics?

Statistical physics is a branch of physics that uses statistical methods and theories to study the properties and behavior of matter and energy at the macroscopic level. It aims to describe and predict the collective behavior of large groups of particles, such as atoms and molecules, using statistical laws and principles.

2. What is the significance of particles with spin 1/2 in a B-field?

Particles with spin 1/2 in a B-field are important because they exhibit a phenomenon called spin magnetism, where their spins align with an external magnetic field. This has implications in many areas of physics, such as quantum mechanics, solid state physics, and material science.

3. How does statistical physics explain the behavior of particles with spin 1/2 in a B-field?

Statistical physics explains the behavior of particles with spin 1/2 in a B-field through the use of statistical mechanics, which considers the statistical properties of a large number of particles to predict their behavior. This includes the distribution of spin states and the effects of external forces, such as a magnetic field.

4. What is the role of entropy in statistical physics?

Entropy is a fundamental concept in statistical physics that describes the measure of disorder or randomness in a system. It plays a crucial role in understanding the behavior of particles with spin 1/2 in a B-field, as it helps predict the probability of different spin states and their interactions in a given system.

5. What are some practical applications of statistical physics?

Statistical physics has many practical applications, including the study of phase transitions, the behavior of gases, and the properties of materials. It is also used in fields such as thermodynamics, astrophysics, and biophysics to analyze complex systems and predict their behavior. In addition, statistical physics has played a significant role in the development of technologies, such as semiconductors and computer memory devices.

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