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fields_lec7

fields_lec7 - Key Concepts for this section 1 Lorentz force...

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1: Lorentz force law, Field, Maxwell’s equation 2 : Ion Transport, Nernst-Planck equation 3: (Quasi)electrostatics, potential function, 4: Laplace’s equation, Uniqueness 5 : Debye layer, electroneutrality Goals of Part II: (1) Understand when and why electromagnetic (E and B) interaction is relevant (or not relevant) in biological systems. (2) Be able to analyze quasistatic electric fields in 2D and 3D. Key Concepts for this section

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Electroneutrality Protein A + + - + + + Protein B + - - - - - ~ Debye length ( κ -1 ) Buffer counterions
0 () x x e κ Φ= Φ 0 1/2 22 0 0 1e t a n h 2 2 4 l n , t a n h 4 x x zF zFc RT RT x zF zF RT RT ε ⎡⎤ Φ ⎛⎞ + ⎜⎟ ⎢⎥ ⎝⎠ = Φ ⎣⎦ When 0 zF RT Φ< < 0 0.5 1 1.5 2 2.5 3 0 2 4 6 8 10 12 0 0.5 1 1.5 2 2.5 3 0 0.5 1 1.5 2 zF x RT Φ zF x RT Φ x x 0 2 zF RT Φ = 0 10 zF RT Φ = D-H exact exact D-H Exact solution Debye-Huckel approximation

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0 0.5 1 1.5 2 2.5 3 0 2 4 6 8 0 0.5 1 1.5 2 2.5 3 0.9 0.95 1 1.05 1.1 1.15 0 () cx c x κ x 0 2 zF RT Φ = 0 0.1 zF RT Φ = 0 c c - (counterion) c + (co-ion) c + (co-ion) c - (counterion) When 00 zF RT ze kT Φ< < < thermal energy >> electrical potential energy (diffusion dominates.) When zF RT ze kT Φ> > > thermal energy << electrical potential energy (drift dominates. significant charge accumulation)
0.1M sucrose 0.01M sucrose Membrane permeable to sucrose 0.1M KCl 0.01M KCl Membrane permeable only to K + ?

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fields_lec7 - Key Concepts for this section 1 Lorentz force...

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