![Analysis and Symmetry Assume: p // E ex ; n and p homogeneous Z Y X Coordinate axes: assume Z-axis // E ex E ex Result of polarization: Dipole distribution: n dipoles/m 3 ; each dipole moment p [Cm]](https://image.slidesharecdn.com/e-fieldpolarizedobject-100804085307-phpapp02/85/E-field-polarized-object-4-320.jpg)
E field polarized-object
- 1. Electric field of a Polarized Object © Frits F.M. de Mul
- 2. Electric field of a Polarized Object Question: Calculate E -field produced BY (not: IN) the polarized object. A dielectric object will become polarized. Available: An external E -field: E ex . E ex
- 3. Electric field of a Polarized Object Analysis and symmetry Approach to solution Calculations Conclusions
- 4. Analysis and Symmetry Assume: p // E ex ; n and p homogeneous Z Y X Coordinate axes: assume Z-axis // E ex E ex Result of polarization: Dipole distribution: n dipoles/m 3 ; each dipole moment p [Cm]
- 5. Approach to solution Approach: = calculate potential V ; = E from V by differentiation Distributed dipoles: dV - integration over volume elements dv filled with d p. E ex Z Y X v Question: calculate E -field in arbitrary point P outside v P
- 6. Calculations (1) E ex Z Y X P Z' r e r dp dz volume element dv with dp = np.dv = np.dS . . dz ; with dS Z-axis Dipole:
- 7. Calculations (2) E ex Z Y P Z' X r e r dp dz cross section through P and Z’-axis : P r dS r b r t z t : top z b : bottom
- 8. Calculations (3) dz -integration dr -integration : dr = -dz. cos dz = -dr / cos P r b r t r z t z b dS r dz dr P
- 9. Calculations (4) P r b r t r z t z b dS r dz dr P “Polarization” P = n p
- 10. Calculations (5) bound charges: d b = P.dS E ex Z Y P Z' X r e r dp dz P dS P.dS = P.dS
- 11. Conclusions the end bound charges: d b = P.dS P E ex Z Y X r bottom r top + - Conclusion: the field of a polarized volume is equivalent to that of bound surface charges (provided homogeneous polarization) + - + - - - + + + + + + + - - - -