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# 19_57 - VALUES FOR THE LANGEVIN FUNCTION £0 Compiled by...

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Unformatted text preview: VALUES FOR THE LANGEVIN FUNCTION £0.) Compiled by Allen L. King Because of random ﬂier-ma] rotations a dipole or dipole-like element ordinarily has an average dipole moment of zero. If it is placed in an orienting ﬁeld F however it tends to align itself with the ﬁeld so that the average component ofthe dipole moment parallel to the ﬁeld equals p. Classically, if the system is in thenna] equilibrium, .6 = Month at - UH) = poi-(u) Here pa is the permanent moment (electric or magnetic) of the dipole, and .1101) is the Langevin function of the argument it which equals Fpoi'ﬂ". The following table gives values off. (3). Note that foru « 1, £ (a) =5 I473; for u » 1. f (u) =6 {u - l)7u. (u) 0 1 2 3 4 5 6 7 8 9 10 Diff. 0.0 .0000 .0033 .0066 .0103 .0133 .0166 .0200 .0233 .0267 .0300 .0333 33 0. 1 .0333 .0366 .0400 .0433 .0466 .0499 .05 32 .0566 .0599 .0632 .0665 33 0.2 .0665 .0698 .0731 .0764 .0797 .0830 .0863 .0896 .0928 .0961 .0994 33 0.3 .0994 .1027 .1059 .1092 .1125 .1157 .1190 .1222 .1255 .1287 .1319 32.5 0.4 .1319 .1352 .1384 .1416 .1448 .1480 .1512 .1544 .1576 .1608 .1640 32 0.5 .1640 .1671 .1703 .1734 .1766 .1797 .1829 .1860 .1891 .1922 .1954 31 .1954 .1985 .2016 .2046 .2077 .2108 .2139 .2169 .2200 .2230 .2261 31 . .2261 .2291 .2321 .2351 .2381 .2411 .2441 .2471 .2500 .2530 .2559 30 0. .2559 .2589 .2618 .2647 .2677 .2706 .2735 .2763 .2792 .2821 .2850 29 .2850 .2878 .2906 .2935 .2963 .2991 .3019 .3047 .3075 .3103 .3130 .3130 .3158 .3185 .3213 .3240 .3267 .3294 .3321 .3348 .3375 .340] 27 .3401 .3428 .3454 .3481 .3507 .3533 .3559 .3585 .361! .3636 .3662 26 .3662 .3688 .3713 .3738 .3763 .3789 .3813 .3838 .3863 .3888 .3912 25 .3912 .3937 .3961 .3985 .4010 .4034 .4057 .4081 .4105 .4129 .4152 24 .4152 .4175 .4199 .4222 .4245 .4268 .4291 .4314 .4336 .4359 .4381 23 22 21 20 as: 5.1m 8:! .4381 .4404 .4426 .4448 .4470 .4492 .4514 .4535 .4557 .4578 .4600 .4600 .4621 .4642 .4663 .4684 .4705 .4726 .4747 .4767 .4788 .4808 .4808 .4828 .4849 .4869 .4889 .4908 .4928 .4948 .4967 .4987 .5006 .5006 .5026 .5045 .5064 .5083 .5102 .5120 .5139 .5158 .5176 .5194 19 .5194 .5213 .5231 .5249 .5267 .5285 .5303 .5321 .5338 .5356 .5373 18 . .5373 .5390 .5408 .5425 .5442 .5459 .5476 .5493 .5509 .5526 .5543 17 2. .5543 .5559 .5575 .5592 .5608 .5624 .5640 .5656 .5672 .5687 .5703 16 m._-._.._._.._.._-._._.._._o ocwuatuuhth—OND 2.2 .5703 .5719 .5734 .5750 .5765 .5780 .5795 .5810 .5825 .5840 .5855 15 2.3 .5855 .5870 .5885 .5899 .5914 .5928 .5943 .5957 .5971 .5985 .5999 14.5 2.4 .5999 .6013 .6027 .6041 .6055 .6068 .6082 .6096 .6109 .6122 .6136 14 2.5 .6136 .6149 .6162 .6175 .6188 .620] .6214 .6227 .6240 .6252 .6265 13 2.6 .6265 .6277 .6290 .6302 .6314 .6327 .6339 .6351 .6363 .6375 .6387 12 2.7 .6387 .6399 .6411 .6422 .6434 .6446 .6457 .6469 .6480 .6492 .6503 12 2.8 .6503 .6514 .6525 .6536 .6547 .6558 .6569 .6580 .6591 .6602 .6612 11 2.9 .6612 .6623 .6634 .6644 .6655 .6665 .6675 .6686 .6696 .6706 .6716 10.5 3.0 .6716 .6726 .6736 .6746 .6756 .6766 .6776 .6786 .6796 .6805 .6815 10 3.1 .6815 .6824 .6834 .6843 .6853 .6862 .6872 .6881 .6890 .6899 .6908 .6908 .6917 .6926 .6935 .6944 .6953 .6962 .6971 .6980 .6988 .6997 .6997 .7006 .7014 .7023 .7031 .7040 .7048 .7056 .7065 .7073 .7081 .7081 .7089 .7097 .7106 .7114 .7122 .7130 .7138 .7145 .7153 .7161 .7161 .7169 .7177 .7184 .7192 .7200 .7207 .7215 .7222 .7230 .7237 .7237 .7245 .7252 .7259 .7267 .7274 .7281 .7288 .7295 .7302 .7310 .7310 .7317 .7324 .7331 .7337 .7344 .7351 .7358 .7365 .7372 .7378 .7378 .7385 .7392 .7398 .7405 .7412 .7418 .7425 .7431 .7438 .7444 .7444 .7450 .7457 .7463 .7469 .7476 .7482 .7488 .7494 .7501 .7507 PP‘P’P‘P’P’P‘P OMHJOtUI-h-UJM auquwpuxoo ...
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