Gauss Law E

Chapter 22: The Electric Field

Gauss’s Law: The Equation ³ S E dA Q nc / H 0 & & •S is any closed surface. •Q enc is the net charge enclosed within S. •dA is an element of area on the surface of S. •dA is in the direction of the outward normal. 12 SI units 0 8.85 10 H u

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TIME VARYING MAGNETIC FIELDS AND MAXWELL’S …

D dS vdv Gauss's law . B = 0 S B dS 0 Nonexistence of magnetic monopole x E =-t B L s B dS t E dl Faraday’s Law x H = J + t D L s H dl J dS Ampere's circuit law MAXWELL’S EQUATIONS FOR TIME VARYING FIELDS These are basically four in number. Maxwell's equations in differential form are given by x H = t D + J x E = - t B

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Gauss’ Law

Gauss’ Law The result for a single charge can be extended to systems consisting of more than one charge Φ = ∑ i E q i 0 1 ε One repeats the calculation for each of the charges enclosed by the surface and then sum the individual fluxes Gauss’ Law relates the flux through a closed surface to charge within that surface

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6.007 Lecture 11: Magnetic circuits and transformers

Maxwell resolved this problem by adding a term to the Ampere’s Law. In equivalence to Faraday’s Law, the changing electric field can generate the magnetic field: l . d. C. H d· = COMPLETE AMPERE’S LAW . S J dA · + dt. S. E ·dA