fields_lec3_4

Fields_lec3_4 - Key Concepts for this section 1 Lorentz force law Field Maxwells equation 2 Ion Transport Nernst-Planck equation

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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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+V 0 -V 0 +V 0 +++ ----------------- + + + + + + + + + + - - - - - - - - - - - - E Cell Dielectrophoresis Electrophoresis v diffusion Chemical reaction hydrodynamic flow electroosmosis Debye layer Example : BioMEMS systems
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Differential form of Maxwell’s equations 0 e SV E ds dV ερ ⋅= ∫∫ JG G v 0 s d B S = CS d E dB d s dt G G A v 0 () e E ε ρ 0 B = 0 0 1 e E BJ t μ ∇× = + G G G t B E = × G G A ds A dV ⋅=∇ G G v A dl A ds =∇ × JG JJ GJ J G G v Gauss’ theorem Stokes’ theorem 1 eo S o d B ds J da E da dt ⋅+ G J J GG J v
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Maxwell’s equation in source-free space ~sin( ) cos( ) E tk r o r r
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This note was uploaded on 11/11/2011 for the course BIO 2.797j taught by Professor Matthewlang during the Fall '06 term at MIT.

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Fields_lec3_4 - Key Concepts for this section 1 Lorentz force law Field Maxwells equation 2 Ion Transport Nernst-Planck equation

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