Class13

# Class13 - Maxwell’s Equations and = = = = J o o r ρ µ...

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Unformatted text preview: Maxwell’s Equations and = = = = J o o r ρ µ µ ε ε Maxwell’s Equations: in free space Integral form Differential form S d t B l d E C A r r r r ⋅ ∂ ∂ − = ⋅ ∫ ∫∫ t B E ∂ ∂ − = × ∇ r r (35b) (35a) t E B o o ∂ ∂ = × ∇ r r ε µ S d t E l d B C A o o r r r r ⋅ ∂ ∂ = ⋅ ∫ ∫∫ ε µ (36b) (36a) = ⋅ ∫∫ A S d E r r = ⋅ ∇ B r (37b) (37a) = ⋅ ∫∫ A S d B r r = ⋅ ∇ E r (38b) (38a) Wave Equations and Speed of Light Apply ∇ x on both sides of Eq. (35b): and space free in = = = = J o o r ρ µ µ ε ε ( ) (39) t B E ∂ ∂ × −∇ = × ∇ × ∇ r r = ⋅ ∇ ⇒ = E r ρ Make use of Eq. (34) and considering for free space, ( ) ( ) E E E E r r r r 2 2 −∇ = ∇ − ⋅ ∇ ⋅ ∇ = × ∇ × ∇ Same works for B: Combine the above two equations, we have wave equations: 2 2 2 2 2 2 t B B t E E o o o o ∂ ∂ = ∇ ∂ ∂ = ∇ r r r r µ ε µ ε (40) Speed of light and index of refraction In a scalar format, there are total six equations, one for each component:...
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Class13 - Maxwell’s Equations and = = = = J o o r ρ µ...

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