charge conservation

Maxwell's equations

∇・D = ρ

∇・B = 0

∇×E = - ∂B/∂t

∇×H = i + ∂D/∂t


taking divergence of the last equation,

∇・(∇×H ) = 0 = ∇・( i + ∂D/∂t) = ∇・i + ∂(∇・D)/∂t) = ∇・i + ∂ρ/∂t

 

we get 

∇・i + ∂ρ/∂t = 0 (charge conservation)

 

by way of trial, taking divergence of the third equation,

 

∇・(∇×E) = - ∂∇・B/∂t

 

the left is zero using a formula of vector analysis,

the right also zero because ∇・B = 0, the second equation.

the results are trivial.

Write a comment

Comments: 0