Finite difference coefficient: Difference between revisions

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'''Polder tensor''' is a [[tensor]] used in description of magnetic [[Permeability (electromagnetism)|permeability]] of [[Ferrite (magnet)|ferrite]]s.<ref>[http://www.nature.com/nature/journal/v182/n4642/abs/1821080a0.html G. G. Robbrecht, J. L. Verhaeghe, ''Measurements of the Permeability Tensor for Ferroxcube'', Letters to Nature, ''Nature'' 182, 1080 (18 October 1958), ] {{doi|10.1038/1821080a0}}</ref> The tensor notation needs to be used because ferrimagnetic materials become [[anisotropy|anisotropic]] in the presence of magnetizing field.
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The tensor is described mathematically as:<ref>[http://books.google.co.uk/books?id=lqHsnZoa7wAC&pg=PA93&dq=polder+tensor&cd=5#v=onepage&q=polder%20tensor&f=false Ricardo Marqués, Ferran Martín, Mario Sorolla, ''Metamaterials with negative parameter: theory, design, and microwave applications, Willey, New Jersey, USA, 2009, ISBN 978047174582 {{Please check ISBN|reason=Invalid length.}}, page 93]</ref>
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::<math>B = \begin{bmatrix} \mu & j \kappa & 0 \\ -j \kappa & \mu & 0 \\ 0 & 0 & \mu_0 \end{bmatrix} H</math>
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:<math>\mu = \mu_0 \left( 1+ \frac{\omega_0 \omega_m}{\omega_0^2 - \omega^2} \right) </math>
:<math>\kappa = \mu_0 \frac{\omega \omega_m}{{\omega_0}^2 - \omega^2}</math>
:<math>\omega_0 = \gamma \mu_0 H_0 \ </math>
:<math>\omega_m = \gamma \mu_0 M \ </math>


and <math>\gamma = 17.6 \cdot g \ </math> [kHz/(A/m)] is a [[gyromagnetic ratio]] and ''g'' is a factor between 1.9-2.4 depending on ferrite material. Magnetizing frequency (''f'') is expressed as <math>\omega = 2 \pi f</math>,  ''H''<sub>0</sub> is a bias field, ''M'' is [[magnetization]] and <math>\mu_0</math> is magnetic [[permeability of free space]].
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==References==
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{{Reflist}}
{{Use dmy dates|date=September 2010}}
 
{{DEFAULTSORT:Polder Tensor}}
[[Category:Ferrites]]

Latest revision as of 09:40, 16 December 2014

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