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Maxwell’s Equations (integral form)

NameEquationDescriptionGauss Law for ElectricityCharge and electric fieldsGauss Law for MagnetismMagnetic fieldsFaraday s LawElectrical effects from changing B fieldAmpere s LawMagnetic effects from current0= AdBrr0 QAdE= rrdtdldEB = rrMaxwell s Equations (integral form) idlB0 = rThere is a serious to be modified. + ?cylindersquare00= = AdBQAdEenclosedrrrr Gauss Law s works for ANYCLOSED SURFACE bagelsphereRemarks on Gauss Law s with different closed surfacesSurfaces forintegration of E fluxFish bowldtAdBdldE = rrrrFaraday s Law works for any closed Loop and ANYattached surface areadiskLine integraldefines the Closed loopThis is proven in Vector Calculus with Stoke s TheoremcylinderRemarks on Faraday s Law with different attached surfacesSurface areaintegration for B fluxGeneralized Ampere s Law and displacement currentAmpere s original law, , is the parallel plate capacitor and suppose a current icisflowing charging up the plate.

Faraday’s Law Electrical effects from changing B field Ampere’s Law Magnetic effects from current ∫ ⋅ B dA =0 r r ε0 Q ∫ ⋅ E dA = r r dt d ∫ ⋅ E dlB r r Maxwell’s Equations (integral form) ∫ ⋅ = μ 0 B dl i r There is a serious asymmetry. Needs to be modified.

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