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How do fields create dipoles?

How do fields create dipoles?. E. -. +. Charges are not free to move in a dielectric! But electrons can be driven by E a bit away from the Nucleus without completely leaving it, creating an excess Charge on one side and a deficit on the other, ....

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How do fields create dipoles?

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  1. How do fields create dipoles? E - + Charges are not free to move in a dielectric! But electrons can be driven by E a bit away from the Nucleus without completely leaving it, creating an excess Charge on one side and a deficit on the other, .... …. in other words, generating a dipole

  2. Polarization and Dielectrics - + - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + P - + - + - + - + - + - + Instead of creating new dipoles, E could align existing atomic dipoles (say on H20) creating a net polarization P  E

  3. Dipoles Screen field Displacement vector - + E=(D-P)/e0 D = e0E + P - + -P (opposing polarization Field) - + D (unscreened Field) - + - + - + - + Relative Permittivity er - + Susceptibility P = e0cE D = eE e = e0(1+c) Thus the unscreened external field D gets reduced to a screened E=D/e by the polarizing charges For every free charge creating the D field from a distance, a fraction (1-1/er) bound charges screen D to E=D/e

  4. The fields reduce only inside the dielectric - - + + - + - - + + + - - + + - + - - + + - + - For every free charge creating the D field from a distance, a fraction (1-1/er) bound charges screen D to E=D/e Think of two capacitors – the inner one is opposite and weaker, so you partly screen the original field. But since the inner capacitor cannot act outside (its fields are localized inside), the outside stays the same

  5. Free vs Bound Charges - + E=(D-P)/e0 - + -P (opposing polarization Field) - + D (unscreened Field) - + - + - + - + - + e0.E = rtotal =.D- .P = rfree+ rbound

  6. Interpreting P e0.P = -rbound From definition: divergence = flux/volume, We get ∫P.dS = -Qbound From pic then, –P.S = -rSS So that P = rS (polarization field = surface charge density, as we expect for a capacitor) Multiplying by dielectric thickness, we get P = dipole Mom/volume rs P

  7.  D.dS = q  E.dl = 0 Differential eqns (Gauss’ law) Fields diverge, but don’t curl Defines Scalar potential E = -U Integral eqns .D = rv  x E = 0 D = eE Constitutive Relation (Thus, E gets reduced by er) er = 1 (vac), 4 (SiO2), 12 (Si), 80 (H20) ~2 (paper), 3 (soil, amber), 6 (mica), Effect on Maxwell equations: Reduction of E

  8. Point charge in free space Point charge in a medium .E = rv/e0 .E = rv/e0er

  9. Electrostatic Boundary values Supplement with constitutive relation D=eE  D.dS=q .D = r  x E = 0  E.dl = 0 Maxwell equations for E D1n rs D2n Use Gauss’ law for a short cylinder Only caps matter (edges are short!) D1n-D2n = rs Perpendicular D discontinuous

  10. Electrostatic Boundary values Supplement with constitutive relation D=eE  D.dS=q .D = r  x E = 0  E.dl = 0 Maxwell equations for E E1t E2t No net circulation on small loop Only long edges matter (heights are short!) E1t-E2t = 0 Parallel E continuous

  11. Electrostatic Boundary values Perpendicular D discontinuous Parallel E continuous Can use this to figure out bending of E at an interface (like light bending in a prism)

  12. Example: Bending e1E1n=e2E2n Parallel E continuous Perpendicular D continuous if no free charge rs at interface e2 e1 q1 q2 E1t=E2t cosq1=cosq2 tanq1/tanq2 = e2/e1 D1n=D2n e1sinq1=e2sinq2 e2 > e1 means q2 < q1

  13. Images What about dielectrics? Fields not normal to surface any more ! Charge above Ground plane (fields perp. to surface)

  14. Images for a dielectric Good conductor Field lines perp to plate Poor conductor (vacuum) Acts as isolated charge http://www.falstad.com/vector3de/

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