Preface ......................................................... v
1 Introduction ................................................. 1
2 Taylor expansion and interaction diagram, electrostatic
Maxwell stresses and quadratic electrostriction .............. 2
2.1 Linear effects .......................................... 6
2.2 Quadratic effects ...................................... 12
2.3 Related phenomenon: quadratic electrostriction ......... 16
3 Derivation of the stress tensor from the force law .......... 18
3.1 Force law .............................................. 18
3.2 The concept of tensor divergence ....................... 19
3.3 Deriving the electrostatic Maxwell stress tensor ....... 20
4 Maxwell stress tensor ....................................... 24
4.1 Incorporating the dielectric tensor .................... 25
4.1.1 Tensor decompositions ........................... 30
4.1.2 Tensor symmetry ................................. 31
4.2 Transforming the Maxwell stress tensor ................. 35
4.2.1 Special case: Rotation in a plane ............... 36
4.2.2 General case .................................... 38
4.3 Transforming the dielectric tensor ..................... 40
4.3.1 Special case: Rotation in a plane ............... 40
4.3.2 General case .................................... 42
5 Maxwell stress tensors at the boundary of a dielectric
medium with another dielectric medium or with air ........... 46
5.1 Traction vector at the boundary with air ............... 46
5.2 Influence of the orientation of dielectric media on
the observed strain .................................... 50
5.2.1 Longitudinal effect ............................. 53
5.2.2 Transversal effect .............................. 56
6 Viscoelastic case: Application to polymers .................. 59
6.1 Derivation of the dynamic equation of state ............ 59
6.2 Discussion of the dynamic equation of state ............ 63
7 Applications ................................................ 65
7.1. Electromechanical breakdown ............................ 65
7.2 Scanning Maxwell-stress microscopes .................... 67
7.2.1 Measurement principle ........................... 67
7.2.2 Application examples ............................ 69
7.2.3 Related experimental techniques ................. 69
7.3 Correction of measurements of quadratic
electrostriction ....................................... 71
7.3.1 Stating the problem ............................. 71
7.3.2 Application to a cubic crystal .................. 73
7.4 Correction of low-frequency measurements of the
quadratic electrooptic effect .......................... 75
7.5 Maxwell stress actuators ............................... 79
7.6 Liquids ................................................ 84
7.6.1 Interface between two immiscible liquids ........ 84
7.6.2 Related effect: Electrowetting .................. 86
8 An analogous phenomenon: Magnetostatic Maxwell stresses ..... 90
8.1 Stating the problem .................................... 91
8.2 Mathematical analysis .................................. 91
8.3 Comparison of electromechanical and magnetomechanical
forces, relation to Maxwell's equations ................ 95
8.3.1 Electromechanical case .......................... 95
8.3.2 Magnetomechanical case .......................... 96
9 Outlook: Radiation forces ................................ 96
10 References ............................................... 97
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