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
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhci1IHc0gsE0JORCVDtyosIeZQOicMXvuCIRgQyLRDGNsuwBind8-4hV_cnDXgjSCxzGscvgaClVfDWO5WYRAypdY69fSRehR0XFRj_d6NAH0UmNAvmeKDt5th6_xS-DrYCZvJzzFk7gGsnwRUqD0kH0mwiGYsJ2LBApMDcKPxQT-3WLZEB0f6E1Xixlc/w633-h256/di1.jpg)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhT-XhI_bs9jt2O6hp2rJzxCiBkqbijaV1QdObSbJv33fvSF8pn6_NswSivwbyuWm0sQS8-nquhPd340eM0TuKj6Qbj3_zhMdtoynHqYko05C6EkrG8Zj6heCZyDjMlreLsLgmT85iPLvVxOJ5FZhE4em2stQnJKnYnyzcKSHeWigqCdwMjxC42ZXVyxOM/w461-h267/di2.jpg)
- (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/(2Ï€r/v) [T =
2Ï€r/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
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi7zuIRSrw3dHQIgeqznHhwTXUVqQlcQ8XoTuHEkHNR5-M_SGoudUv_utFPDfMTIf6cnLLzGNpZXWw9Ahp4UPWem9EQ6K9K9DUxZ1zrX5IG4buQs6va7NnfIZUCtkSxi03_0LBvGz0ijCpDn1LMh9tzQxgoEbr8i7WInmngzBEz-HNv-8usNQSyj_hl_Q4/w485-h287/di3.jpg)
- Where,(-) Sign Represent That Induced Magnetic Moment Is In
Opposite Direction Applied Field.
- Now,
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiF3SaK__hfcav0nIgomY4pTo5rcEiZ7y5oZlwhGCRX2DIOiRWPFDKlHX2FsGLNuQ1XbBRj53meBAWHgoVE8nBIXRZf8FvDlaULHs-3lHbMkSiOVTcFiDH9tMAF_IiVDHJqqWW_gZYBt0ZR7gbOVJsGTX8tsRp1YtT7ogoIlYY6nxrI4b2IEellF1OClIw/w392-h90/di4.jpg)
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>
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiA46WHk9kycnRcNwgIGzTL5S43BAnr3StW0y1nFuIUA0Hsi-nuQq7Udn1-zF9U905fxBOrl-7jNcngrcW8u_aYcu93v2WwnFHyHQyKZtjBiTomDi1Ifhw28mW3Pw-RvOa1MyNK-TF-R2Vi7PfcBpHAhJuyYsD8DZf3CHjHGOl1FzKZ4nKWwaenS3tIUto/w250-h110/di5.jpg)
- We Know That
Magnetisation =
Magnetic Moment / Volume
For Unit Volume = Magnetisation = Magnetic Moment
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhJYo2MQs_v5aBDLUIC5aWcnUWzU1n7KoHgivjAcyOsjHF6VdN3ffwFtaE3kOGcx8fvqkFETZpgKRqUGl4FJ_H-njqXNYNyR2D7aCXTke8dyr379rsxBf5sGmYHgjkc9bUQwROLUr1u1vjJlhEFBANIyV2QriCRUVDwTBso7sK8Vh-2HGHcgpQSFcTEGRU/s320/di7.jpg)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgtjeLSgWLhqkPeB8R5aYkKzGoQfkxGiI9hhhKL0iTr26PPXzMHK72z58nWiwrZl7CUpQLGTimNMq3IIWJMnOu-UlNJV-Eabtdxq9diNIJItV-YqPPVKkP__FdQLszF5u3arhjZe_qeNjervgn9Lzd_HGUcJkfXpUW9tH3zepP315bT1040zHD_8aObtUQ/s320/di7.jpg)
- So, Accoroding To Lengevin's Theory
Magnetic Succespatibility Of Diamagnetic Is Negative And
Indepedant Of Temperature.
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