Diamagnetism & Lengevin's Theory of Diamagnetism

 Diamagnetisum & Lengevin's Theory of Diamagnetism

[1] Diamagnetism :

- If External Magnetic Filed Applied On Material Then There Is

  Include Magnetic Moment In Opposite Direction As Per Leng's

  Law

- This Effect Is Known As Diamagnetism Effect,It Is Weak Effect.

- So Diamagnetism Property Of Material Comes Due To Indused

  Orbital Magnetic Moment Of Electron.

- Common Examples Of Diamagnetic Materials Include Bismuth,

  Copper, Silver, Water, And Most Organic Compounds.

- Diamagnetism Plays A Relatively Minor Role In Everyday Life,

  But It Is A Significant Aspect Of Magnetism And Has Essential

  Implications In The Study Of Materials And Condensed Matter

  Physics.

 

[2] Lengevin's Theory Of Diamagnetism :

 

- In The Absence Of External Filed Electron Move In Circular Orbit

  For Circular Motion Centripetal Force Provided By Coulumb

  Attracction Force

- So, Centerpetal Force Coulumb Force

- If External Magnetic Field B Is Applied Then

- (ω - ωo)(ω + ωo) = qvB/mr

   if ω = ωo = 2ωo

      ω - ωo = Δω

- (Δω)(2ωo) = qvB/mr    [v = ωor]

  (Δω)(2ωo) = q(ωor)B/mr

  (Δω)(2ωo) = qωoB/m.....(3)

- Now,Current In Circular Orbit

  I = q/T

  I = q/(2πr/v) [T = 2πr/v]

  I = 2ωo/2πr

- I = qωo/2π

- In The Present Of External Field

  ΔI = qΔω/2π

  ΔI = q/2π (qB/2m)

  ΔI = q^2 B/4πm .......(4)

- Now Induced Magnetic Moment

- Where,(-) Sign Represent That Induced Magnetic Moment Is In

  Opposite Direction Applied Field.

- Now,

- Where R Is Radius Of Circular Path So,

  r^2 = x^2 + y^2

- In 3 - Dimension

  ro^2 = x^2 + y^2 + z^2

  if,

  <x^2> = <y^2> = <z^2>

- then

  <r^2> = <x^2> + <y^2>

        = 2<x^2>

  <r^2> = 2<x^2>

- if, <x> = <y> = <z>

  ro^2 = <x^2> + <x^2> + <x^2>

       = 3<x^2>

  <ro^2> = 3<x^2>

- <r^2>/<ro^2> = 2/3

  <r^2> = 2/3 <ro^2>

- We Know That

  Magnetisation = Magnetic Moment / Volume

  For Unit Volume = Magnetisation = Magnetic Moment

- So, Accoroding To Lengevin's Theory

  Magnetic Succespatibility Of Diamagnetic Is Negative And

  Indepedant Of Temperature.

 

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