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We present a new realization of weak electrostatic force based on Kelvin capacitor, which, compared with the conventional realization, simplifies the mechanical design without synchronously moving the central and guard-ring electrodes. However, a residual force due to the edge effect of the capacitor should be accurately known. In this paper, an analytic model of the electrostatic force generated from the edge effect is presented based on conformal transformations. The accuracy of the model is verified by the finite element calculation based on a micro-Newton weak force generation.
[1] Chan H B, Aksyuk V A, Kleiman R N, Bishop D J, Federico C 2001 Science 291 1941
[2] Craighead H G 2000 Science 290 1532
[3] Gross L, Mohn F, Moll N, Schuler B, Criado A, Guitián E, Pena D, Gourdon A, Meyer G 2012 Science 337 1326
[4] Solin S A, Hines D R, Rowe A C H, Tsai J S, Pashkin Y A, Chung S J, Goel N, Santos M B 2002 Appl. Phys. Lett. 80 4012
[5] Peng Y Z, Li Y, Ru B, Huo D X, Qian Z H 2014 Chin. Phys. B 23 097503
[6] Filippov A E, Klafter J, Urbakh M 2004 Phys. Rev. Lett. 92 135503
[7] Bustamante C, Bryant Z, Smith S B 2003 Nature 421 423
[8] Juan M L, Righini M, Quidant R 2011 Nature Photon. 5 349
[9] Huang X F, Li S J, Zhou D H, Zhao G J, Wang G Q, Xu J R 2014 Acta Phys. Sin. 63 178802 (in Chinese) [黄雪峰, 李盛姬, 周东辉, 赵冠军, 王关晴, 徐江荣 2014 63 178802]
[10] Rugar D, Budakian R, Mamin H J, Chui B W 2004 Nature 430 329
[11] Beer W, Fasel W, Moll E, Richard P, Schneiter U, Thalmann R, Egger J 2002 Metrologia 39 263
[12] Fang M H, Wei Z Y, Zhang Z X, Zhu L, Fu Y, Shi M, Li G W, Guo G 2013 Chin. Phys. B 22 116105
[13] Huan Q, Hu H, Pan L D, Xiao J, Du S X, Gao H J 2010 Chin. Phys. B 19 080517
[14] Liang P B, Lei J J, Liu Z H, Zhang Y, Yuan L B 2014 Chin. Phys. B 23 088702
[15] Ren H L, Ding P F, Li X Y 2012 Acta Phys. Sin. 61 210701 (in Chinese) [任洪亮, 丁攀峰, 李小燕 2012 61 210701]
[16] Berman G P, Doolen G D, Hammel P C, Tsifrinovich V I 2000 Phys. Rev. B 61 14694
[17] Girard G 1994 Metrologia 31 317
[18] Li S S, Zhang Z H, Zhao W, Li Z K, Huang S L 2014 Chin. Phys. B (accept for publication)
[19] Li S S, Han B, Li Z, Lan J 2012 Measurement 45 1
[20] Zimmerman N M 2010 Phys. Today 63 68
[21] Pratt J R, Kramar J A, Newell D B, Smith D T 2005 Meas. Sci. Technol. 16 2129
[22] Hamilton C A 2000 Rev. Sci. Instrum. 71 3611
[23] Trapon G, Thévenot O, Lacueille J C, Poirier W 2003 Metrologia 40 159
[24] Heerens W C, Vermeulen F C 1975 J. Appl. Phys. 46 2486
[25] Li W 2011 Chin. Phys. B 20 116201
[26] Bai Z W 2004 Acta Phys. Sin. 53 2472 (in Chinese) [白占武 2004 53 2472]
[27] He D W, Cheng X H, Wang Z J, Xu D W, Song Z R, Yu Y H 2011 Chin. Phys. B 20 010210
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[1] Chan H B, Aksyuk V A, Kleiman R N, Bishop D J, Federico C 2001 Science 291 1941
[2] Craighead H G 2000 Science 290 1532
[3] Gross L, Mohn F, Moll N, Schuler B, Criado A, Guitián E, Pena D, Gourdon A, Meyer G 2012 Science 337 1326
[4] Solin S A, Hines D R, Rowe A C H, Tsai J S, Pashkin Y A, Chung S J, Goel N, Santos M B 2002 Appl. Phys. Lett. 80 4012
[5] Peng Y Z, Li Y, Ru B, Huo D X, Qian Z H 2014 Chin. Phys. B 23 097503
[6] Filippov A E, Klafter J, Urbakh M 2004 Phys. Rev. Lett. 92 135503
[7] Bustamante C, Bryant Z, Smith S B 2003 Nature 421 423
[8] Juan M L, Righini M, Quidant R 2011 Nature Photon. 5 349
[9] Huang X F, Li S J, Zhou D H, Zhao G J, Wang G Q, Xu J R 2014 Acta Phys. Sin. 63 178802 (in Chinese) [黄雪峰, 李盛姬, 周东辉, 赵冠军, 王关晴, 徐江荣 2014 63 178802]
[10] Rugar D, Budakian R, Mamin H J, Chui B W 2004 Nature 430 329
[11] Beer W, Fasel W, Moll E, Richard P, Schneiter U, Thalmann R, Egger J 2002 Metrologia 39 263
[12] Fang M H, Wei Z Y, Zhang Z X, Zhu L, Fu Y, Shi M, Li G W, Guo G 2013 Chin. Phys. B 22 116105
[13] Huan Q, Hu H, Pan L D, Xiao J, Du S X, Gao H J 2010 Chin. Phys. B 19 080517
[14] Liang P B, Lei J J, Liu Z H, Zhang Y, Yuan L B 2014 Chin. Phys. B 23 088702
[15] Ren H L, Ding P F, Li X Y 2012 Acta Phys. Sin. 61 210701 (in Chinese) [任洪亮, 丁攀峰, 李小燕 2012 61 210701]
[16] Berman G P, Doolen G D, Hammel P C, Tsifrinovich V I 2000 Phys. Rev. B 61 14694
[17] Girard G 1994 Metrologia 31 317
[18] Li S S, Zhang Z H, Zhao W, Li Z K, Huang S L 2014 Chin. Phys. B (accept for publication)
[19] Li S S, Han B, Li Z, Lan J 2012 Measurement 45 1
[20] Zimmerman N M 2010 Phys. Today 63 68
[21] Pratt J R, Kramar J A, Newell D B, Smith D T 2005 Meas. Sci. Technol. 16 2129
[22] Hamilton C A 2000 Rev. Sci. Instrum. 71 3611
[23] Trapon G, Thévenot O, Lacueille J C, Poirier W 2003 Metrologia 40 159
[24] Heerens W C, Vermeulen F C 1975 J. Appl. Phys. 46 2486
[25] Li W 2011 Chin. Phys. B 20 116201
[26] Bai Z W 2004 Acta Phys. Sin. 53 2472 (in Chinese) [白占武 2004 53 2472]
[27] He D W, Cheng X H, Wang Z J, Xu D W, Song Z R, Yu Y H 2011 Chin. Phys. B 20 010210
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